Affixes Implications

三、 MORPHOLOGY 形态学请结合《词汇学中的构词法》进⾏学习。

语素：语⾔最⼩的意义单位 语素的类型 复合词的类型 复合词的特征 Morphology is a branch of grammar which studies the internal structure of words and the rules by which words are formed. It is divided into two sub-branches: inflectional morphology and lexical or derivational morphology. 形态学研究单词的内部结构以及构词规则，有屈折形态学和词汇形态学两⼤分⽀。

Morpheme:the smallest meaningful unit of language. 语素：语⾔最⼩的意义单位。

Free Morpheme: A free morpheme is one that can stand by itself. （independent） ⾃由语素可以作为单词独⽴使⽤。

Bound Morpheme: A bound morpheme is one that cannot stand by itself. 粘着语素必须和其他语素结合成单词 Bound Morpheme includes two types: （1） root （2）Affix（词缀） 1）Inflectional affixes （屈折词缀）（inflectional morphemes）: affixes attached to the end of words to indicate grammatical relationships are inflectional 2）Derivational affixes（派⽣词缀） A） prefix: A prefix comes before words. B）suffix An adjective suffix（形容词后缀） that is added to the stem, whatever classis belongs to , the result will be an adjective. free=free root（⾃由词根） Morpheme（词素） Bound root prefix bound derivational affix suffix inflectional Root and stem（词根和词⼲） 1） Root 2） Stem The differences between root and stem: A root is the basic form of a word which cannot be further analyzed without total loss of identity. A stem is the surplus part after the cutting of inflectional morpheme in a word with inflectional morphemes,can be further analyzed, it sometimes could be a root. Individualistic Undesirables Individualist （stem） undesirable （stem） Individual （stem） desirable （stem） dividual （stem） desire （root, stem） divide（root, stem） Affixation词缀法（Derivation派⽣法）：adding word-formation or derivational affixes to stem. Prefixation前缀@：It's the formation of new words by adding a prefixes to stems. 1）'表⽰否定'nagative prefixes: un-,non,in-,dis,a- etc. 2）''reversative or privative prefixes: un-,de-dis etc. 3）'表⽰贬义'pejorative prefixes: mis-, mal-, pseudo- etc. 4）'表⽰程度'degree or size prefixes: arch-, super-,out-,sub-,over-,under-,hyper-,ultra-,mini- etc. 5）'表⽰⽅向、态度'orientation & attitude prefixes:counter-,contra-,anti-,pro- etc. 6）locative prefixes:super-,sub-,inter-,trans- etc. 7）'表⽰时间、次序'time and order prefixes:fore-,pre-,post-,ex-,re- etc. 8）'表⽰数量'number prefixes:uni-/mono-,bi-/di-,tri-,multi-/poly- etc. 9）'混杂'miscellaneous prefixes：auto-, neo-, pan-, vice- Suffixation后缀@: It's the formation of a new word by adding suffixes to stems. 1）noun suffixes 2）adjective suffixes 3）Adverb suffixes 4）verb suffixes Compounding复合法（also called composition） Compounding: is the formation of new words by joining two or more stems Formation of compounds Noun + noun（名词＋名词） —— handbook, sunshine Adjective + noun（形容词＋名词）——highway, deadline Adjective + noun + -ed（形容词＋名词＋ed）——white-haired, red-eyed Verb + noun（动词＋名词）——driveway, breakwater（挡⽔板） Adverb + noun（副词＋名词）——downtown, overburden Noun + verb（名词＋动词）——toothpick, snowfall Verb + adverb（动词＋副词）——follow-up, kick-off Noun + adjective（名词＋形容词）——world-famous, lifelong -ing form + noun（ing+名词）——baking power, dining-room other forms（其他）——go-between, father-in-law Features of compounds复合词的特征 1.Orthographically书写特征 （Compounds are written in three ways: solid（airmail） hyphenated（air-conditioning） open（air force, air raid） 2.Syntactically句法特征（复合词的词性⼀般取决于复合词最后⼀个成分的词性） 3.Semantically语义特征（复合词的意义具有习语性质，许多复合词的意义都不是其构成成分意义和总和） 4.Phonetically语⾳特征（复合词的单词重⾳落在第⼀个构成成分上）。

一、Translation concerning negationAims: to understand the features of Chinese and English as regards negation, the application of negation in the process of translationKey points: the application of negation in the process of translationDifficulties: affirmative in Chinese but negative in English, negative in Chinese but affirmative in EnglishTeaching procedures:Negation being an important conception in one’s expression of thoughts, expressions of negations is to be found in any tongue. This is naturally true of Chinese and English. However, the ways of indicating negation are quite different in the two languages. This frequently causes a lot of trouble to translators, who if not careful enough, would often make mistakes.1. Features of the two languages as regards negation1. Both languages have negatives or expressions formed with negatives. In modern Chinese, the much-used negative words are: 不,没,别. These words express three different meanings: 不signifies denial of a statement;没denial of a being or occurrence(,非and 否can be put under this category);别dissuasion or prohibition(甭,勿,and 莫can be put under this category)The often-used negatives in English are “not”, and “no”, in addition to “nothing”, ”nobody” “none”, “without”, “ neither…nor”, “never”, etc.Chinese negatives are generally capable of producing derivatives, particularly the word 不, 无and 非. Their derivatives are equivalent to English words formed by adding affixes, e.g. 不法unlawful, 不便inconvenient, 无边boundless,非正规irregularsIn English, apart from using negatives to express negation, words with a negative sense can be formed by adding affixes to root words. The affixes thus used are mainly “less” suffix “un” “in”, and “non”However, English words formed with affixes with a negative, while adjective and nouns formed with “un”such as “unavoidable” and “unbelief” are negative, for instance, verbs formed with affixes such as “unclasp” and “uncork” affirmative.⊙In Chinese, words formed with negatives are generally negative in sense but in some cases they assume new meaning like 非常, which practically means 很.In English, the same word formed with a different affix differs in meaning (comparediscord with uncord). Sometimes, words formed with different affixes with a negative sense would produce words with different implications---derogatory and the other non-derogatory. For instance, immoral means 不道德,and is therefore derogatory while unmoral means 非道德,无道德观念的,and is therefore non derogatory.2.英语为肯定式,汉语译作否定式(affirmative in English but negative in Chinese) You are quite a stranger here.Wet paintKeep off the lawnI failed to understand your meaning.A person who does a regrettable action is often regretful afterwards.一个人做了不该做的事,日后往往会懊悔.Another person runs to avoid doing anything else, to dodge a decision about how to lead his life or a realization that his life is leading nowhere.另一个人跑步则是为了避而不做别的事,不对如何生活作出决定,不去感受自己生活碌碌无为.3. 英语为否定式,汉语译为肯定式(affirmative in Chinese but negative in English) Where is the wretched girl? Why do you not come when I call you?Pierre: hey, what the …! You old fool.Lena: don’t talk to me that way! I am not your wife.Even so, I still insist that for the individual himself nothing is more important than his personal, interior sense of right and wrong and his determination to follow that rather than to be guided by what everybody does or merely the criterion of “social usefulness.”即便如此,我仍然坚持认为,对个人而言,最重要的莫过于这种根植于个人心灵深处的是非感，以及坚决按这种是非感行事的决心，而不是随波逐流，或仅仅以是否“对社会有益”为准则。

题型I．简答题5×1’=5’例：类似于自由词素、词根、词干、连着词素、曲折词素等待解释II．判断正误T/F 20×1’=20’例：动词是逆构词法中产生最多的词。

III．单项选择题20’例：奥斯丁、姆斯金、德莱斯提出的理论？IV．写音标10×1’=10’P35～36V．划分词素10×3×0.5’=15’VI．翻译10×1’=10’分英翻汉和汉翻英例：合作原则、聚合关系、组合关系、曲折后缀、词缀、前缀、后缀VII．选择答题2×5’=10’VIII．树形图给词，分析意思，是否有歧义？用树形图解释出来。

样卷AI．1. displacement2. pragnatics3. stem4. syntax5. hyponymyII. T/F9. Lang is arbitrary to the sense that there is no intrinsic connection between words and what these words actually refer to. F10. The meaning-distinctive function of the tone is especially important in English because English, unlike Chinese, is a typical tone language. F11. The syntactic rules of any language are finite in umber, and yet there is no limit to the umber of sentences native speakers of that language are able to produce and comprehend. F12. Agreement is the requirement that the forms of two or more words in a syntactic relationship should agree with each in terms of categories. T13. Speech Act Theory is the first major theory in the study of language in use; it originated with John Langs Shaw Austin. T14.15.Vibretion of the vocal cords results in a quality of speech sounds called voucing. F?16. The word “flower” is the super ordinate of the typonyms “rose” “tulip” and “rose”. T17．Chomsky defines competence as the ideal user’s knowledge of the rules of his language in linguistic communication. T18.The English sound [m]is a bilabial nasal voice. T19. A study of the features of the Chinese used in the Tang Dynasty in diachronic study. T?20.While English has borrowed most heavily form French, other languages have also made their contributions. F21. Inflectional affixs are those whose major function is to attach themselves to the morphemes to form a new word. F22. A syllable without a coda is a closed syllable. F23. Only words of the same parts of speech can be combined to form compounds. F24. The phrase “green house” with the first element stressed means “a house which is green in colour” F25. Sentences are not formed by randomly combining lexical items, but following a set of syntactic rules that arrange linguistic elements in a particular order. F26. The compound word “book store” is the place where books are sold. This indicates that the meaning of a compound is the sum total of the meaning of its compounments. F27. Only when a maxim under cooperative principle is blatantly violated can the hearer know that it’s being violated and conversational implications arise. T28. The word “photo graphically” is made up of 4 morphemes. TIII.29. The famous quotation from Romeo and Juliet arose by any other name world smell as sweet well illustrates: the conventional nature of language.30. If a linguistic study describes and analyses the language people actually use, it’s a said to be: descriptive.31. Which of the following is not a design feature of human language? Phonology32. Phonetially, the stress of a compound always falls on the first element.33. The description of a language as it changes through time is a diachronic… …36. The word “trasist~” is formed through: lending37. Number is a grammatical category used for the analysis of classed displaying such contrasts as singular, dual, plural, etc. In English, number is mainly observed in nouns.38. Concord is a type of control over the form of some words by other words in certain syntactic constructions.39. Chomsky uses the term performance to refer to the actual realization of a language user’s knowledge of the rules of his langua ge in linguistic com.40. In terms of the place of articulation, the following sounds [t][s][d][z][n] share the feature of P3541. Translate formational Generative Crammer was introduced by N. Chomsky in 1957.42. The relationship between “married/ single” is complementary.43. Of the 3 speech acts, linguists are most interested in the illocutionary act because of this kind of speech act is identical with the speaker’s intention.44. The pair of words “lend” and “borrow” are synomy~s.45. The function of the sentence “A nice day, isn’t it?” is 寒暄46.47. We can do things with words “this” is main idea of the speech act theory.48. The utterance “we are already working 25 hours a day, 8 days a week” obviously violates the maxim of quantity.IV.49. voiceless dentalfricative50. high front tense unroundedvowel51. voiced alveolarstop52. high back tense roundedvowel53. voiceless bilabialstop54. voiced labiodentalfricativeV.55. What are the 4 maxims of the cooperative Principle?56. What are the distinctions between inflectional affix and derivational affix?VIII.Leave the book on the shelf.1 leave the book on the shelfPut the book on the shelf.2 leave book on the shelfKeep away from the book on the shelf1. Language is a system of arbitrary vocal symbols used for human communication.2. Design Features of LanguageArbitrariness (Saussure)This feature means that the forms of linguistic signs bear no natural relationship to their meanings.DualityThe elements of the spoken language are sounds that do not convey meaning in themselves.CreativityBy creativity we mean language is resourceful because of its duality and its recursiveness.DisplacementThis means that human languages enable their users to symbolize objects, events and concepts which are not present (in time and space) at the moment of communication.3. Functions of Language(1) Informative FunctionLanguage serves an informative function when it is used to tell what the speaker thinks, to give information about facts.(2) Interpersonal functionThis is by far the most important socio-logical use of language. People establish and maintain their status in a society.(3) Performative FunctionThis function is primarily to change the social status of persons. The kind of language employed in performative verbal acts is usually quite formal and even ritualized.(4) Emotive functionThe emotive function of language is one of the most powerful usesof language because it is so crucial in changing the emotional status of an audience for or against someone or something.(5) Phatic communionIt refers to the social interaction of language which is used for establishing an atmosphere or maintaining social contact rather than forexchanging information or ideas.Greetings, farewells and comments on the weather serve this function.(6) Recreational functionThis function refers to the use of language for the sheer joy of using it.(7) Metalingual functionOur language can be used to talk about language itself.4. What is linguistics?Linguistics is scientific discipline with the goal of describing language and speech in all relevant theoretical and practical aspects and their relation to adjoining disciplines.5. Main Branches of Linguistics*PhoneticsIt studies speech sounds, including the production of speech, that is how speech sounds are actually made, transmitted and received, the sounds of speech, the description and classification of speech sounds, words and connected speech.* MorphologyIt is concerned with the internal organization of words. It studies the minimal units of meaning---morphemes and word-formation processes.*PhonologyIt studies the rules governing the structure, distribution, and sequencing of speech sounds and the shape of syllables. It deals with sound system of a language by treating phoneme as the point of departure.*SyntaxIt is about principles of forming and understanding correct English sentences. The form or structure of a sentence is governed by the rules of syntax. These rules specify word order, sentence organization, andthe relationships between words, word classes and other sentence elements.*SemanticsIt examines how meaning is encoded in a language. It is not only concerned with meanings of words as lexical items, but also with levels of language below the word and above it.*PragmaticsIt is the study of meaning in context. It deals with particular utterances in particular situations and is especially concerned with the various ways in which the many social contexts of language performance can influence interpretation.6. Important Distinctions in Linguistics*Descriptive vs. prescriptiveA linguistic study is DESCRIPTIVE if it describes and analysesfacts observed; it is PRESCRIPTIVE it tries to lay down rules for “correct” behavior.* Synchronic vs. diachronicSynchronic description refers to a language description at some point in time;Diachronic description is about a language description as it changes through time.* Langue & paroleLANGUE refers to the abstract linguistic system shared by all the members of a speech community;PAROLE refers to the actualized language, or realization of langue.*Competence & performanceCompetence is the ideal language user’s knowledge of the rules of his language;Performance is the actual realization of this knowledge in utterance.7. CONSONANTS and VOWELSConsonants are produced by constricting or obstructing the vocal tract at some place to divert, impede, or completely shut off the flow of air in the oral cavity;A vowel is produced without such obstruction so no turbulence or atotal stopping of the air can be perceived.8. Manners of Articulation*Stop (or plosive)(爆破音): complete closure of the articulators involved so that the air-stream cannot escape through the mouth.There are two kinds of stops: oral stops and nasal stops* Fricative(摩擦音): close approximation of two articulators sothat the air-stream is partially obstructed and turbulent airflow is produced.* Approximant(无摩擦延续音):This is an articulation in which one articulator is close to another, but without the vocal tract being narrowed to such an extentthat a turbulent air-stream is produced.* Lateral(舌边音): obstruction of the air-stream at a point along the center of the oral tract, with incomplete closure between one orboth sides of the tongue and the roof of the mouth.* Affricates (破擦音)：When the obstruction, complete at first, is released slowly withthe friction resulting from partial obstruction (as in fricatives), the sounds thus produced are affricates. In English there are two affricates.* Nasals (鼻音):When the nasal passage is opened by lowering the soft palate at the back of the mouth and air is allowed to pass through it, the sounds thus produced are called nasals. There are three nasals in English.* Glides (滑音):They are sometimes called “semivowels”. They are produced with a narrower passage between the lips and the tongue and the hard palate to cause some slight noise from the local obstruction. In English, they are [w,j]9. The place of Articulation* Bilabial(双唇音):In the production of these sounds, the upper and the lower lips are brought together to create obstruction. In English, bilabial sounds include [p,b,m]* Labiodental(唇齿音):In the obstruction of these sounds, the lower lip is brought into contact with the upper teeth, thus creating the obstruction. The labiodental sounds in English are [f,v* dental(齿音):The obstruction is created between the tip of the tongue and the upper teeth. There are two dental sounds in English.* alveolar(齿龈音):The tip of the tongue is brought into contact with the upper teeth-ridge to create the obstruction. The alveolar sounds are [t,d,s,z,n,l,r]* palatal(颚音):The obstruction is between the back of the tongue and the hard palate.* velar(软腭音):The back of the tongue is brought into contact with the velum(软腭), or the soft palate.* glottal(喉音):The vocal cords are brought momentarily together to create the obstruction. There is only one glottal sound in English: [h].10. Classification of English vowels* Vowel sounds are differentiated by a number of factors: the position of the tongue in the mouth, the openness of the mouth, the shape of the lips, and the length of the vowels.11.12. The Phoneme theoryThe phoneme simply refers to a “unit of explicit sound contrast”13. Allophones(音位变体)Peak and speak are not actually pronounced as they are transcribed in dictionaries.We know that in English there is a rule that this sound is unaspirated after /s/ but aspirated in other places. In what we have talked about, different variants of a phoneme are called allophones of the same phoneme. In this case the allophones are said to be in complementary distribution(互补分布) because they never occur in the same context.14. Assimilation(同化)*This is a process by which one sound takes on some or all the characteristics of a neighboring sound.*There are two possibilities of assimilation:If a following sound is influencing a preceding sound, we call it regressive assimilation(逆同化);The converse process, in which a preceding sound is influencing a following sound, is known as progressive assimilation(顺同化).* Assimilation can occur across syllable or word boundaries, as shown in the following:pancakesunglassesYou can keep them.He can go now.Define the following termsconsonant phoneme allophoneWhat isassimilation?15. SuprasegmentalsThe syllable structureStressIntonationTone16. Identification of words*StabilityWords are the most stable of all linguistic units, in respect of their internal structure, i.e. the constituent parts of a complex word have little potential for rearrangement.* Relative uninterruptibility:This means that new elements are not to be inserted into a word even when there are several parts in a word. Nothing can be used to insert in the three parts of the word disappointment: dis+appoint+ment.* A minimum free form:This was first suggested by Leonard Bloomfield. He advocated treating sentence as “the maximum free form” and word “the minimum free form”, the latter being the smallest unit that can constitute a complete utterance.17. Classification of wordsVariable & invariable words*Variable words refer to those that we can find ordered and regular series of grammatically different word forms, for the word write, there are several grammatically different forms: wrote, written, writing* Grammatical words & lexical words:Those which express grammatical meanings, such as conjunctions, prepositions, articles, and pronouns, are grammatical words, also known as function words. Those which have lexical meanings,i.e. those which refer to substance, action and quality, such as nouns, verbs, adjectives, and adverbs, are lexical words, also known as content words.* Closed-class words and open-class words:A word that belongs to the closed-class is one whose membership is fixed or limited. New members are not regularly added such as pronouns, prepositions, conjunctions, articles, etc., are all closed items. The open-class is one whose membership is in principle infinite or unlimited.With the emergence of new ideas, inventions, etc.New expressions are continually and constantly being added to the lexicon. Nouns, verbs, adjectives and many adverbs are all open-class items.* Word class:Traditionally, we had such word classes as “n. adj. v. adv. prep. etc.” But here are some of the categories newly introduced:a. ParticlesThey include the infinitive marker “to”, the negative marker “not” and the subordinate units in phrasal verbs, such as “get by”, “do up”, “look back”.Chapter Three: Morphologyb. AuxiliariesAuxiliaries used to be regarded as verbs, but linguists today tend to define them as a separate word class:Negation: I can’t come.*I wantn’t come.Inversion: Is he coming? *Keeps he coming?Code: I’ll come and so will Bill.*I intend to come and so intend Bill.Emphasis: He has come. *He seems to come.c. Pro-formIn order to refer collectively to the items in a sentence which substitute for other items or constructions, it is advisable to regard pro-form as a separate word class.Pro-adjective: Your pen is red. So is mine.Pro-verb: He knows English better than he did.Pro-adverb: He hopes he’ll win and I hope so too.Pro-locative: Jane’s hiding there, behind the door.d. Determiners:This is a new word class which refer to words that are used before the noun acting as head of a noun phrase, and determine the kind of reference: the, a, some, all, etc.Quirk, et al proposes that there are three subclasses of determiners:Predeterminers: all, both, half, one-third,etc.Central determiners: the, a, this, that, these, those, etc.Postdeterminers.next, last, past, other, (a) few, much, etc.18. The formation of word* Morpheme & morphologyMorpheme is the smallest unit of language in terms of relationship between expression and content, a unit that cannot be divided into further smaller units without destroying or drastically altering the meaning, whether it is lexical or grammatical, e.g.boys---boy+-schecking---check+-ingdisappointment---dis-+appoint+-mentMorphology studies the internal structure of words, and the rules by which words are formed. For example, the verb purify consistsof two parts: pur(e) and –ify, from which we can work out a rule: a new form of verb can be created by adding –ify to an adjective. This is a morphological rule that may explain the formation, of a set of verbs ended with –ify, such as simplify, beautify, amplify,etc.。

Translation concerning negationAims: to understand the features of Chinese and English as regards negation, the application of negation in the process of translationKey points: the application of negation in the process of translationDifficulties: affirmative 肯定in Chinese but negative in English, negative in Chinese but affirmative in EnglishTeaching procedures:Negation being an important conception in one’s expression of thoughts, expressions of negations is to be found in any tongue. This is naturally true of Chinese and English. However, the ways of indicating negation are quite different in the two languages. This frequently causes a lot of trouble to translators, who if not careful enough, would often make mistakes.1. Features of the two languages as regards negation●1. Both languages have negatives or expressions formed with negatives. In modern Chinese, the much-used negative words are: 不,没,别. These words express three different meanings: 不signifies表示denial of a statement;没denial of a being or occurrence(,非and 否can be put under this category);别dissuasion or prohibition(甭,勿,and 莫can be put under this category)●The oft-used negatives in English are “not”, and “no”, in addition to “nothing”, ”nobody” “none”, “without”, “ neither…nor”, “never”, etc.●Chinese negatives are generally capable of producing derivatives, particularly the word 不, 无and 非. Their derivatives are equivalent to English words formed by adding affixes, e.g. 不法unlawful, 不便inconvenient, 无边boundless,非正规军irregulars●In English, apart from using negatives to express negation, words with a negative sense can be formed by adding affixes to roo t words. The affixes thus used are mainly “less”suffix “un” “in”, and “non”●However, English words formed with affixes with a negative, while adjective and nouns formed with “un” such as “unavoidable” and “unbelief” are negative, for instance, verbs forme d with affixes such as “unclasp” and “uncork” affirmative.●In Chinese, words formed with negatives are generally negative in sense but in some cases they assume new meaning like 非常, which practically means 很.●In English, the same word formed with a different affix differs in meaning (compare discord with uncord). Sometimes, words formed with different affixes 词缀with a negative sense would produce words with different implications含义---derogatory贬义and the other non-derogatory褒义. For instance, immoral means 不道德,and is therefore derogatory while unmoral means 非道德,无道德观念的,and is therefore non derogatory. 1．W arm-up exercises2．I don't’ think Tom is correct.3．I don’t think Xiaoming is coming tomorrow.4．A re you not going tomorrow?---- No, I am not going .5．A frica is not kicking out W estern imperialism in order to invite other new masters.6．T he world today is far from peaceful.7．O ur PLA is worthy of being called a great army of the people.8．H e tried his best to overcome the lack of technical data.9．T he window refused to open.10．Y esterday he failed to get to school on time.11．They excluded children from getting in.12．The building is in a state of neglect.13．He is often absent- minded.14．To do this is beyond me.15．Lei Feng’s noble deeds are above all praise.16．I, rather than you , should do the work.17．The truth is quite other than what you think.18．She refrained from laughing.19．She was refused admitance by them.20．An opportunity is not likely to repeat itself.21．Live up to the expectations of our own people and the people throughout the world.22．Slips are scarely avoidable when you are new to your work.23．The meetings were marked by such an absence of lively discussions that at times they were almost on the piont of breaking up.24．Avoid operating the keys roughly.25．The scientists made a solemn plege at the conference, saying, “W e’ll forever live up to what our Party expecs of us.”26．The evidence is conclusive, excluding all possibilities of doubt.27．That fellow is far from being honest.28．Luan Ping stood still, trying vainly (in vain) to answer the battery of questions Y ang Zirong raised.29．That served to strenghen instead of weaken our determination.30．But for their help. W e should not succeeded in this experiment.31．All that glitters is not gold.32．All is not lost.33．All criminals are murderers.34．But aal men are born to reign.35．All that flatter you too much are not faithful friends.36．Both children are not clever.37．W e never thought of nothing wrong.我们从来没有想到有什么错误。

阅读训练材料Word StudyContext CluesAlthough there is no formula that you can memorize to improve your ability to guess the meaning of unfamiliar words, you should keep the following points in mind: e the meanings of the other words in the sentence (or paragraph) and the meaningof the sentence as a whole to reduce the number of possible meanings.e grammar and punctuation clues that point to the relationships among the variousparts of the sentence.3.Be content with a general idea about the unfamiliar word; the exact definition orsynonym is not always necessary.4.Learn to recognize situations in which it is not necessary to know the meaning of thewordExample1.I removed the ____from the shelf and began to read.2.Harvey is a thief; he would ____the gold from h is grandmother's teeth and notfeel guilty.3.Our uncle was a ____, an incurable wanderer who never could stay in one place.4.Unlike his brother, who is truly a handsome person, Hogartty is quite ____.5.The Asian ____, like other apes, is specially adapted for life in trees.6.But surely everyone knows that if you step on an egg, it will ____.7.Tom got a new ____for his birthday. It is a sports model, red, with white interiorand bucket seats.Stems and AffixesPrefixescom-, con-, col-, cor-, co- together, with cooperate, connectin-, ira-, il-, ir- in, into, on invade, insertin-, im-, il-, ir- not impolite, illegalmicro- small microscope, microcomputerpre- before prepare, prehistoricre-, retro- back; again return, retrorocket Stems-audi-,-audit- hear auditorium, auditor-chron- time chronology, chronological-dic-, -dict- say, speak dictator, dictation-graph-, -gram- write, writing telegraph, telegram-log-,-ology- speech, word, study biology-phon- sound telephone-scrib-, -script- write describe, script-spect- look at inspect, spectator-vid-, -vis- see video, vision Suffixes-er, -or one who worker, ,spectator-ist one who typist, biologist-tion, -ation condition, the act of action, celebration Exercise 11. In each item, select the best definition of the italicized word.a. He lost his spectacles.____ 1. glasses ____ 3. pants____ 2. gloves ____ 4. shoesb. He drew concentric circles.____ l. OO ____ 3.____2. ____ 4.c. He inspected their work.____ 1. spoke highly of ____ 3. examined closely____ 2. did not examine ____ 4. did not like2. Circle the words where in- means not. Watch out; there are false negatives in this list.inject inside insane inspectinvaluable inflammable inactive invisibleExercise 2Word analysis can help you to guess the meaning of unfamiliar words. Using context clues and what you know about word parts, write a synonym, description, or definition of the italicized words.1. __________________ The doctor asked Martin to inhale deeply and hold his breathfor 10 seconds.2. __________________ Many countries import most of the oil they use.3. __________________ Three newspaper reporters collaborated in writing this seriesof articles.4. __________________ Calling my professor by her first name seems too informal tome.5. __________________ It is Joe's prediction that by the year 2000 there will befemale president of the United States.6 .__________________ Historians use the inscriptions on the walls of ancient templesto guide them in their studies.7. __________________ You cannot sign up for a class the first day it meets in September;you must preregister in August.8. __________________ After his long illness, he didn't recognize his own reflection inthe mirror.9. _________________ I dictated the letter to my secretary over the phone.10. _________________ I'm sending a sample of my handwriting to a graphologist whosays he can use it to analyze my personality.Difficult SentenceRead the following sentences carefully. The questions that follow are designed to you‟re your comprehension of complex grammatical structures. Select the best answer.ExampleThe student revolt is not only a thorn in the side of the president's newly established government, but it has international implications as well.Whom or what does this revolt affect?____ a. the students____ b. the side of the president's body____ c. only the national government____ d. national and international affairsExplanation____ a. According to the sentence, the students are the cause of certain events, not those affected.____ b. Although you may not have been familiar with the idiom a thorn in someone‟s side, context clues should have told you that this phrase means a problem anddoes not actually refer to the side of the president's body.____ c. National government is an incomplete answer. The construction not only.., but...as well should tell you that more than one element is involved. Thepresident's newly established government (the national government) is not theonly area affected by the revolt.____ d. The revolt affects both national and international affairs.1.I disagreed then as now with many of John Smith‟s judgments, but always respectedhim, and this book is a welcome reminder of his big, honest, friendly, stubborn personality.How does the author of this sentence feel about John Smith?____ a. He dislikes him but agrees with his ideas.____ b. He considers him to be a disagreeable person.____ c. He disagrees with his ideas but respects him.____ d. He disagreed with him then but agrees with him now.2.Concepts like passivity, dependence, and aggression may need further research ifthey are to continue to be useful ways of thinking about human personalities.What might require more research?____ a. human thought processes____ b. certain concepts____ c. human personalities____ d. useful ways of thinking3.In order for you to follow the schedule set by the publisher, your paper must be lookedover over the weekend, revised, and handed in in its final form on Monday.What must you do on Saturday and Sunday?____ a. meet the publisher ____ c. hand in a paper____ b. examine your paper ____ d. look over the weekend4.The real reason why prices were, and still are, too high is complicated, and no shortdiscussion can satisfactorily explain this problem.What word or phrase best describes prices?____ a. complicated ____ c. too high in the past, but low now____ b. adequately explained ____ d. too high in the past and in the present5.This is not just a sad-but-true story; the boy's experience is horrible and damaging, yeta sense of love shines through every word.How does the author of this sentence feel about the story?____ a. It transmits a sense of love.____ b. It is just sad.____ c. It is not true.____ d. It is horrible and damaging.6.In the past five years the movement has grown from unorganized groups of poorlyarmed individuals to a comparatively well-armed, well-trained army of anywhere from 10,000 to 16,000 members.What is the present condition of this movement?____ a. The members are poorly armed.____ b. There are only a few poor individuals.____ c. There are over 16,000 members.____ d. The members are organized and well armed.7.The financial situation isn't bad yet, but we believe that we have some vitalinformation and, if it is correct, unemployment will soon become a serious problem.What do we know about the financial situation?____ a. It won't change.____ b. It will become a serious problem.____ c. It is not bad now.____ d. It will improve.8.The general then added, “The only reasonable solution to the sort of problems causedby the current unstable political situation is one of diplomacy and economic measures and not the use of military force.”What type of solution does the general support?____ a. economic and diplomatic action____ b. diplomatic and economic, action if military force fails____ c. only diplomatic action____ d. military actions in response to political problems9.Because the supply of natural gas was plentiful in comparison to other choices likecoal and fuel oil, and because it burns cleaner, many people changed their heating systems to natural gas, thereby creating shortages.Why did people prefer gas?____ a. It was natural.____ b. There were no other choices.____ c. The other fuels were dirtier and less plentiful.____ d. There is, even today, a plentiful supply of it.10. My discovery of Tillie Olsen was a gift from a friend; years ago she gave me her copyof Tell Me a Riddle because she liked the stories and wanted to share the experience.What do we know about Tillie Olsen?____ a. She is a friend.____ b. She likes stories.____ c. She gives gifts.____ d. She is an author.Main IdeaExampleBy the time the first European travelers on the American continent began to record some of their observations about Indians, the Cherokee people had developed an advanced culture that probably was exceeded only by the civilized tribes of the S outhwest: Mayan and Aztec groups. The social structures of the Cherokee people consisted of a form of clan kinship in which there were seven recognized clans. All members of a clan were considered blood brothers and sisters and were bound by honor to defend any member of that clan from wrong. Each clan, the Bird, Paint, Deer, Wolf, Blue, Long Hair, and Wild Potato, was represented in the civil council by a councilor or councillors. The chief of the tribe was selected from one of these clans and did not inherit his office from his kinsmen. Actually, there were two chiefs, a Peace chief and War chief. The Peace chief served when the tribe was at peace, but the minute war was declared, the War chief was in command.Select the statement that best expresses the m ain idea of the paragraph.____a. The Cherokee chief was different in war time than in peace time.____b. Before the arrival of the Europeans the Cherokees had developed a well-organized society.____c. The Mayans and the Aztecs were part of the Cherokee t ribe.____d. Several Indian cultures had developed advanced civilizations before Europeans arriveExplanation____a. This is not the main idea. Rather, it is one of several examples the author uses to support his statement that the Cherokee people had deve loped anadvanced culture.____b. This statement expresses the main idea of the paragraph. All other sentences in the paragraph are examples supporting the idea that the Cherokees haddeveloped an advanced culture by the time Europeans arrived on thecontinent.____c. This statement is false, so it cannot be the main idea.____d. This statement is too general. The paragraph describes the social structure of the Cherokee people only. Although the author names other advanced Indian cultures, he does this only to strengthen his argument that the Cherokees had developed an advanced culture.Paragraph 1The first invention of human beings was the wheel. Although no wheel forms are found in nature, undoubtedly the earliest “wheels” were smooth logs which were used for moving weights over the earth's surface. No one recorded who he or she was or when it happened, but when the “first inventor” placed a wheel on an axle, people began to roll from one place to another. Records of this type of wheel have been found among Egyptian relics dating back to 2,000 B.C. and earlier Chinese civilizations arecredited with independent invention of the same mechanism. The wheel so fascinated the human mind that people have spent centuries building machines around it; yet in over 4,000 years its basic design has remained unchanged. All about us we see the spinning shafts, gears, flywheels, pulleys, and rotors which are the descendents of the first wheel. The roaring propeller of an aircraft engine, the whirling wheel of a giant ste am turbine, and the hairspring of a tiny watch are examples of the rotary motion which characterizes our mechanical world. It is hard to conceive of continuous motion without the wheel. Select the statement that best expresses the main idea of the paragrap h.____a. The wheel is used today in industry and transportation.____b. One of human beings' first inventions, the wheel, has remained important for years.____c. The basic design of the wheel has been changed to meet the needs of industrial society.____d. Although we don't know exactly who invented the wheel, it is evident that Egyptians and Chinese used it about 4,000 years ago.Paragraph 2At the University of Kansas art museum, investigators tested the effects of different colored walls on two groups of visitors to an exhibit of paintings. For the first group the room was painted white; for the second, dark brown. Movement of each group was followed by an electrical system under the carpet. The experiment revealed that those who entered the dark brown room walked more quickly, covered more area, and spent less time in the room than the people in the white environment. Dark brown stimulated more activity, but the activity ended sooner. Not only the choice of colors but also the genera appearance of a room communicates and influences those inside. Another experiment presented subjects with photographs of faces that were to be rated in terms of energy and well-being. Three groups of subjects were used; each was shown the same photos, but each group was in a different kind of room. One group was in an “ugly” room that resembled a messy storeroom. Another group was in an average room--a nice office. The third group was in a tastefully designed living room with carpeting and drapes. Results showed that the subjects in the beautiful room tended to give higher ratings to the faces than did those in the ugly room. Other studies suggest that students do better tests taken in comfortable, attractive rooms than in ordinary-looking ugly rooms.Select the statement that best expresses the main idea of the paragraph____a. People in beautiful rooms tend to give higher ratings to photographs of faces than people in ugly rooms.____b. The color and general appearance of a room influence the behavior and attitudes of the people in it____c. The University of Kansas has studied the effects of the color of a room on people's behavior.____d. Beautifully decorated, light-colored rooms make people more comfortable than ugly, dark rooms.Paragraph 3 Teaching is supposed to be a professional activity requiring long and complicated training as well as official certification. The act of teaching is looked uponas a flow of knowledge from a higher source to an empty container. The student's role is one of receiving information; the teacher's role is one of sending it. There is a clear distinction assumed between one who is supposed to know (and therefore not capable of being wrong) and another, usually younger person who is supposed not to know. However, teaching need not be the province of a special group of people nor need it be looked upon as a technical skill. Teaching can be more like guiding and assisting than forcing information into a supposedly empty head. If you have a certain skill you should be able to share it with someone. You do not have to get certified to convey what you know to someone else or to help them in their attempt to teach themselves. All of us, from the very youngest children to the oldest members of our cultures should come to realize our own potential as teachers. We can share what we know, however little it might be, with someone who has need of that knowledge skill.Select the statement that best expresses the main idea of the paragraph.____a. The author believes that it is not difficult to be a good teacher.____b. The author believes that every person has the potential to be a teacher.____c. The author believes that teaching is a professional activity requiring special training.____d. The author believes that teaching is the flow of knowledge from a higher source to an empty container.Paragraph 4Albert Einstein once attributed the creativity of a famous scientist to the fact that he "never went to school, and therefore preserved the rare gift of thinking freely." There is undoubtedly truth in Einstein's observation; many artists and geniuses seem to view their schooling a disadvantage. But such a truth is not a criticism of schools. It is function of schools to civilize, not to train explorers. The explorer is always a lonely individual whether his or her pioneering be in a music, science, or technology. The creative explorer of unmapped lands shares with the genius what William James described as the "faculty of perceiving in an unhabitual way." Insofar as schools teach perceptual patterns they tend to destroy creativity and genius. But if schools could somehow exist solely to cultivate genius, then society would break down. For the social order demands unity and widespread agreement, both traits that are destructive to creativity. There will always be conflict between the demands of society and the impulses of creativity and genius.Select the statement that best expresses the main idea of the paragraph.____ a. Albert Einstein and other geniuses and artists have said that schools limit creativity a nd genius.____ b. Schools should be designed to encourage creativity.____ c. Explorers can be compared to geniuses because both groups look at the world differently from the way most people do.____ d. Schools can never satisfy the needs of both geniuses and society as a whole.Paragraph 5Perhaps the most startling theory to come out of kinesics, the study of body movement, was suggested by Professor Ray Birdwhistel He believes that physical appearance is often culturally programmed. In other words, we learn our looks--we are not born with them. A baby has generally unformed facial features. A baby, according to Birdwhistell,learns where to set the eyebrows by looking at those around --family and friends. This helps explain why the people of some regions of the United States lo0k so much alike. New Englanders or Southerners have certain common facial characteristics that cannot be explained by genetics. The exact shape of the mouth is not set at birth, it is learned after. In fact, the final mouth shape is not formed until well after permanent teeth are set. For many, this can be well into adolescence. A husband and wife together for a long time often come to look somewhat alike. We learn our looks from those around us. This is perhaps why in a single country there are areas where people smile more than those in other areas. In the United States, for example, the South is the part of the country where the people smile most frequently. In New England they smile less, and in the western pan of New York st ate still less. Many Southerners find cities such as New York cold and unfriendly, partly because people on Madison Avenue smile less than people on Peachtree Street in Atlanta, Georgia. People in densely populated urban areas also tend to smile and greet each other in public less than do people in rural areas and small towns.Select the statement that best expresses the main idea of the paragraph.____a. Ray Birdwhistell can tell what region of the United States a person is from by how much he or she smiles.____ b. Ray Birdwhistell is a leader in the field of kinesics.____ c. Ray Birdwhistell says that our physical appearance is influenced by the appearance of people around us.____ d. People who live in the country are more friendly than people who live in densely populated areasParagraph 6In any archaeological study that includes a dig, the procedures are basically the same: 1) selecting a site 2) hiring local workers 3) surveying the site and dividing it into sections 4) digging trenches to locate levels and places to excavate 5) mapping architectural features 6) developing a coding system that shows the exact spot where an object is found 7) and recording, tagging, cleaning and storing excavated materials. Neilson C. Debevoise, writing on an expedition to Iraq in the early 1930's, described the typical “route” of excavated pottery. Workers reported an object to staff members before removing it from the ground. The date, level; location and other important information were written on a piece of paper and placed with the object. At noon the objects were brought in from the field to the registry room where they were given a preliminary cleaning. Registry numbers were written with waterproof India ink on a portion of the object previously painted with shellac. The shellac prevented the ink from soaking into the object, furnished a good writing surface, and made it possible to remove the number in a moment. From the registry room objects were sent to the drafting department. If a clay pot, for example, was of a new type, a scale drawing was made on graph paper Measurements of the top, greatest diameter, base, height, color of the glaze, if any, the quality and texture of the body and the quality of the workmanship were recorded on paper with the drawing. When the drafting department had completed its work the materials were placed on the storage shelves, grouped according to type for division with the Iraq government and eventually shipped to museums. Today, the steps of a dig remain basically the same, although specific techniques vary.Select the statement that best expresses the main idea of the paragraph.____ a. For a number of years, archaeologists have used basically the same procedure when conducting a dig.____b. Neilson C.Debevoise developed the commonly accepted procedure for organizing a dig._____c. Archaeologists take great care to assure that all excavated objects are properly identified.____d. A great deal of important historical and archaeological information can be provided by a dig.Restatement and InferenceSentence StudyEach sentence below is followed by five statements. The statements are of four types:1. Some of the statements are restatements of the original sentence. They give the sameinformation in a different way.2. Some of the statements are inferences (conclusions) that can be drawn from the informationgiven in the original sentence.3. Some of the statements are false based on the information given.4. Some of the statements cannot be judged true or false based on the information given in theoriginal sentence.Put a check (/) next to all restatements and inferences (types 1 and 2). Note: do not check a statement that is true of itself but cannot be inferred from the sentence given.Example Heavy smokers and drinkers run a fifteen-times greater risk ofdeveloping cancer of the. mouth and throat than nonsmokers andnondrinkers._____ a. Cancer of the mouth and throat is more likely to occur in heavy smokers and drinker than in nonsmokers and nondrinkers._____ b. People who never drink and smoke will not get mouth or throat cancer._____ c. Heavy drinkers who run have a greater risk of developing cancer than nondrinkers._____ d. People who don't smoke and drink have less chance of getting cancer of the mouth and throat than those who smoke ,and drink heavily._____ e. People would probably be healthier if they did not drink and smoke too much. Explanation_____ a. This is a restatement of the original sentence. If heavy smokers and drinkers run a greater risk of developing cancer than those who do not drink or smoke, then cancer is morelikely to occur in heavy smokers and drinkers._____ b. It is not true that people who never smoke and drink will never get mouth or throat cancer. We only know that they are less likely to get this kind of cancer._____ c. The word run in the original sentence is part of the phrase to run a risk which means to be in danger. The sentence does not tell us anything about heavy drinkers who enjoy thesport of running._____ d. This is a restatement of the original sentence. If people who drink and smoke heavily have a greater chance of getting mouth and throat cancer than those who don't, then itmust be true that those who don't smoke and drink heavily have less chance ofdeveloping this kind of cancer._____ e. This is an inference that can be drawn from the information given. If people who smoke and drink heavily run a high risk of developing cancer, then we can infer that peopleprobably would be healthier ff they didn't smoke and drink too much (heavily).1.Nine out of ten doctors responding to a survey said they recommend our product to theirpatients if they recommend anything._____ a. Nine out of ten doctors recommend the product._____ b. Of the doctors who responded to a survey, nine out of ten doctors recommend the product._____ c. If they recommend anything, nine out of ten doctors responding to a survey recommend the product._____ d. Most doctors recommend the product._____ e. We don't know how many doctors recommend the product.2. This organization may succeed marvelously at what it wants to do, but what it wants to domay not be all that important._____ a. The organization is marvelous._____ b. The organization may succeed._____ c. Although the organization may reach its goals, the goals might not be important._____ d. What the organization wants is marvelous._____ e. The author questions the goals of the organization.3. This book contains a totally new outlook that combines the wisdom of the past with scientificknowledge to solve the problems of the present._____ a. Problems of the past and present are solved in this book._____ b. In this book, current knowledge and past wisdom are combined to solve current problems._____ c. Only by using knowledge of the past and present can we solve problems._____ d. None of today's problems can be solved without scientific knowledge._____ e. This book is different because it combines the wisdom of the past with scientific knowledge.4. Like other timeless symbols, flags have accompanied mankind for thousands of years, gainingever wider meaning, yet losing none of their inherent and original force._____ a. In spite of losing some of their original force, flags are a timeless symbol that has accompanied mankind for thousands of years._____ b. Flags have existed for thousands of years._____ c. Timeless symbols typically gain wider meaning while not losing their inherent force._____ d. Thousands of years ago flags accompanied mankind but through time they have lost their force._____ e. Because flags are considered a timeless symbol, they have gained continually wider meaning without losing their inherent original force.5. When there is an absence of reliable information about drugs, the risks involved in using them are greatly increased.____ a. There is no reliable information about drugs.____ b. Using drugs is more dangerous when we don't know what effects and dangers are involved.____ c. The risks involved in using drugs have increased.____ d. People should try to find out about drugs before using them.____ e. There are no risks involved in using drugs if we have reliable information about them.6. The project of which this book is the result was first suggested in the summer of 1992, in the course of some leisurely conversations at the foot of and occasionally) on top of the Alps of western Austria.____ a. This book was written in 1992.____ b. This book was written in Austria.____ c. This book is a collection of conversations held in 1992.____ d. This book is the end result of a project.____ e. This book is about western Austria.7. Los Angeles' safety record with school buses is generally a good one, but of course this record is only as good as the school bus drivers themselves.____ a. In spite of a generally good safety record for their school buses, Los Angeles school bus drivers are not very good.____ b. If school bus drivers are not very good, the town‟s school bus safety record will not be very good either.____ c. If cities wish to maintain good safety records with school buses, they should hire good school bus drivers.____ d. With better school buses, drivers will be able to maintain better safety records.____ e. Los Angeles' safety record with school buses has improved because better bus drivers have been hired.8. Taxes being so high, the descendents of the wealthy class of the nineteenth century are being forced to rent out their estates to paying guests.____ a. In the nineteenth century, the wealthy class rented out its estates.____ b. Because of high taxes, families that were rich one hundred years ago now rent out their estates.____ c. Guests pay high taxes when they rent old estates.____ d. Some families that were once wealthy are having trouble paying their taxes.____ e. High taxes have changed the lives of some of the old wealthy families.9. According to the definition of Chinese traditional medicine, acupuncture is the treatment of disease--not just the alleviation of pain--by inserting very fine needles into the body at specific points called loci.____ a. The author believes some people do not know that acupuncture can be used to treat illness.____ b. Finely pointed needles Called loci are used in acupuncture.____ c. In Chinese traditional medicine, acupuncture is known to treat disease and alleviate pain.____ d. Those using acupuncture treat disease by placing needles into the body at specific points.____ e. Only those who practice traditional Chinese medicine use acupuncture.10. It would be difficult to overpraise this book._____ a. This is a difficult book._____ b. This book deserves much praise._____ c. It is difficult not to overpraise this book._____ d. It is difficult to praise this book._____ e. The author of this sentence thinks this is an excellent book.。

On interval fuzzy S-implicationsB.C.Bedregal a,*,G.P.Dimuro b ,R.H.N.Santiago a ,R.H.S.Reiser ca Universidade Federal do Rio Grande do Norte,Departamento de Informática e Matemática Aplicada,Campus Universitário,59072-970Natal,BrazilbUniversidade Federal do Rio Grande,Programa de Pós-Graduação em Modelagem Computacional,Campus Carreiros,96201-090Rio Grande,Brazilc Universidade Católica de Pelotas,Programa de Pós-Graduação em Informática,Rua Felix da Cunha 412,96010-000Pelotas,Brazil a r t i c l e i n f o Article history:Received 6March 2008Received in revised form 21August 2009Accepted 21November 2009Keywords:Fuzzy logic Interval mathematicsInterval representationInterval fuzzy implicationInterval S-implicationInterval automorphisma b s t r a c tThis paper presents an analysis of interval-valued S-implications and interval-valued auto-morphisms,showing a way to obtain an interval-valued S-implication from two S-implica-tions,such that the resulting interval-valued S-implication is said to be obtainable .Someconsequences of that are:(1)the resulting interval-valued S-implication satisfies the cor-rectness property,and (2)some important properties of usual S-implications are preservedby such interval representations.A relation between S-implications and interval-valued S-implications is outlined,showing that the action of an interval-valued automorphism on aninterval-valued S-implication produces another interval-valued S-implication.Ó2009Elsevier Inc.All rights reserved.1.IntroductionFuzzy set theory was introduced by Zadeh [76],allowing the development of soft computing techniques centered on the idea that computation,reasoning and decision making should exploit,whenever possible,the tolerance for imprecision and uncertainty [78].Like classical set theory,the corresponding fuzzy logic has been developed as formal deductive systems,but with a com-parative notion of truth that formalizes deduction under vagueness.It provides tools for approximate reasoning and decision making together with a framework to deal with imprecision,uncertainty,incompleteness of information,conflicting infor-mation,partiality of truth and partiality of possibility [79],improving the design of flexible information processing systems[51].It has been applied in several areas,such as control systems [18],decision making [17],expert systems [67],pattern recognition [19,50],etc.On the other hand,fuzzy logic may be viewed as an attempt to formalize/mechanize the human capability to perform a wide variety of physical and mental tasks without any measurements or computations [79].Fuzzy sets were originally defined by membership functions of the form l A :X !½0;1 ,where any membership degree l A ðx Þwas a precise number.However,in some situations,we do not have precise knowledge about the membership function (or the membership degree)that should be taken into account.This consideration has led to some extensions of fuzzy sets,giving rise to type-n fuzzy sets [77],which incorporated uncertainty about membership functions and membership degrees into fuzzy set theory,where the ‘‘precise number”representing a membership degree was generalized to a value carrying its uncertainty.0020-0255/$-see front matter Ó2009Elsevier Inc.All rights reserved.doi:10.1016/j.ins.2009.11.035*Corresponding author.Tel.:+558432153814;fax:+558432153813.E-mail addresses:bedregal@dimap.ufrn.br (B.C.Bedregal),gracaliz@ (G.P.Dimuro),regivan@dimap.ufrn.br (R.H.N.Santiago),reiser@ucpel.tche.br (R.H.S.Reiser).Information Sciences 180(2010)1373–1389Contents lists available at ScienceDirectInformation Sciencesj o u r n a l ho m e p a g e :w w w.e l s e vier.c om/loc ate/ins1374 B.C.Bedregal et al./Information Sciences180(2010)1373–1389Type-2fuzzy sets have been largely applied since the works of Jerry Mendel[48]in the90s,with the increase of the the-oretical research on their properties[49,71].Interval-valued fuzzy sets are a particular case of type-2fuzzy sets with a rich structure provided by Interval Mathematics[52].Interval Mathematics is a mathematical theory that aims at the representation of uncertain input data and parameters, originally interested in the automatic and rigorous control of the errors that arise in numerical computations[37].It has been applied to deal with the uncertainties in the results of numerical algorithms in Engineering and Scientific Computing,with contributions1/interval-comp/.in several areas[40,41],such as electrical power systems[8],mechan-ical engineering[54],chemical engineering[68],artificial intelligence[38],multiagent systems[26]and geophysics[2].Interval mathematics is another form of information theory which is related to,but independent from,fuzzy logic.In one hand,intervals can be considered to be a particular type of fuzzy set.On the other hand,interval membership degrees can be used to represent the uncertainty and the difficulty of an expert to precisely determine the fairest membership degree of an element with respect to a linguistic term,as considered in interval-valued fuzzy sets.In this case,the radius of an interval is used as an error measure[57],providing an estimation of the uncertainty during membership assignment.Interval degrees can also be viewed as summarizing the opinions of several experts about the exact membership degree for an element with respect to a linguistic term.In this case,the left and right interval endpoints are,respectively,the least and the greatest de-grees provided by a group of experts[29,57,70].In both cases,the richness of interval structures provides tools to deal with such notions of uncertainty.Interval-valued fuzzy sets were introduced independently by Zadeh[77]and other authors in the70s(e.g.,[36,39,63]), allowing to deal not only with vagueness(lack of sharp class boundaries),but also with uncertainty(lack of information) [29,45].Since then,the integration of fuzzy theory with interval mathematics has been studied from different viewpoints, as properly pointed out by Lodwick[45],generating several different approaches(as in[21,27–29,33,44,45,53,56,57,71,75]).In this paper,we follow the approachfirst introduced in Bedregal and Takahashi’s works[12,13],which has already been applied in our previous papers,where we provided interval extensions for some fuzzy connectives(see[9,15,25,59])by con-sidering both correctness(accuracy)and optimality aspects of interval methods[37,64].In particular,we are interested in the investigations of interval extensions of the various types of fuzzy implications and their related properties.Fuzzy implications[4–7,11,31,46,47,58,61,62,66,65,74]play an important role in fuzzy logic.In a broad sense,fuzzy implications are important not only because they are used to formalize‘‘If...then”rules in fuzzy systems,but also because they have different meanings(e.g.,S-implications,R-implications,QL-implications,D-implications etc.)to be used in per-forming inferences in approximate reasoning and fuzzy control[46].The role of fuzzy implications on the development of applications also motivates the research in the narrow sense through the investigation of related logical aspects[47].The aim of this work is to introduce an interval generalization for a particular meaning of fuzzy implications,namely,S-implications[5,6,16,47,61,30,31].This generalization,which we call interval S-implication,satisfies the correctness property mentioned above.We present an analysis of interval S-implications and interval automorphisms,showing a way to obtain an interval S-implication from two S-implications,so that the resulting interval S-implication is said to be obtainable.We prove that interval S-implications are closed under the action of the interval-valued automorphisms introduced in[33,34].We also prove that several analogous important properties of S-implications are also valid for interval S-implications,showing their applicability on interval-based fuzzy systems.Thus,this work is an important step towards the fundamentals for the devel-opment of such interval-based fuzzy systems.The paper is organized as follows:Section2discusses the notions of interval representations of real functions providing the related definitions and results.The main results related to the interval extensions of fuzzy t-conorms introduced in pre-vious works[12–14]are presented in Section3.In Section4,we discuss the interval extensions of fuzzy negations.A brief review about fuzzy implications,and,in particular,S-implications,is presented in Section5,where the main properties of S-implications are presented.Section6introduces interval fuzzy implications and the definition of interval S-implications, showing that several analogous properties of S-implications also hold for interval S-implications.The action of an interval automorphism on an interval S-implication is analyzed in Section7.Section8concludes this paper,summarizing its main results,presenting somefinal remarks and pointing out future works.2.Interval representationsConsider the real unit interval U¼½0;1 #R and the set U¼f½a;b j06a6b61g of subintervals of U.The left and right projections of an interval½a;b 2U are given by the functions l;r:U!U,defined,respectively,bylð½a;b Þ¼a and rð½a;b Þ¼b:ð1ÞFor a given interval X2U;lðXÞand rðXÞare also denoted,respectively,by X and X.The following partial orders play important roles in this paper:(i)The product order(also called component-wise order or Kulisch-Miranker order),defined,for all X;Y2U,by:X6Y()X6Y^X6Y;ð2Þ1For a survey on applications of Interval Mathematics,see,e.g.,/interval-comp/.(ii)The inclusion order,defined,for all X ;Y 2U ,by:X #Y ()X P Y ^X 6Y :ð3ÞThese partial orders can be naturally extended to U n .For example,considering the product order defined in Eq.(2),forany ~X ¼ðX 1;...;X n Þ;~Y ¼ðY 1;...;Y n Þ2U n ,one has that ~X 6~Y ()X 16Y 1^ÁÁÁ^X n 6Y n :ð4ÞAn interval function F :U n !U is said to be strictly increasing if,for each ~X ;~Y 2U n ,whenever ~X <~Y (that is,~X 6~Y and ~X –~Y )it holds that F ð~X Þ<F ð~Y Þ.The notion of interval correctness plays a very important role in numerical computations [64].A correct interval method can always guarantee that if x 2X then f ðx Þ2F ðX Þ,where F is the interval method that evaluates a real function f .In [64],the notion of correctness is formalized by the so-called Interval Representation ,considering that interval methods are represen-tations of punctual methods.In what follows,we reproduce such definition,but,instead of considering the set of real num-bers R ,we consider the set U ¼½0;1 #R .Definition 1[64].An interval X 2U is said to be a representation for a real number a if a 2X .Considering two interval representations X and Y for a real number a ;X is said to be a better interval representation of a than Y ,denoted by Y v X ,if X #Y .The notion of better interval representation can also be easily extended for n -tuples of intervals.Definition 2[64].A function F :U n !U is said to be an interval representation of a real function f :U n !U if,for each ~X 2U n and ~x 2~X ;f ð~x Þ2F ð~X Þ.F is also said to be correct with respect to f .An interval function F :U n !U is said to be a better interval representation of a real function f :U n !U than an intervalfunction G :U n !U ,denoted by G v F ,if F ð~X Þ#G ð~X Þ,for each ~X 2U n [64].In [64],the notion of optimality of interval methods was formalized by the so-called canonical interval representations of real functions,also known by the best interval representations [12]of real functions:Definition 3[64].The best interval representation of a real function f :U n !U is the interval function b f :U n !U ,defined byb f ð~X Þ¼½inf f f ð~x Þj ~x 2~X g ;sup f f ð~x Þj ~x 2~X g :ð5ÞNotice that the interval function b f is well defined and it is clearly an interval representation of f .Moreover,for any other interval representation F of f ,F v b f .This means that b f always returns a narrower interval than the intervals produced by any other interval representation of f .Thus,b f has the optimality property of interval algorithms mentioned by Hickey et al.[37],when it is seen as an algorithm to compute a real function f .Observe that if the real function f is continuous in the usual sense then,for each ~X 2U n ,one has thatb f ð~X Þ¼f f ð~x Þj ~x 2~X g ¼f ð~X Þ;ð6Þthat is,the best interval representation b f of a real function f coincides with its range [64].Definition 4.An interval function F :U n !U is obtainable if there exist projections P 1;...;P 2n :U !U ,where P i 2f l ;r g ,for i ¼1;...;2n ,and functions f 1;f 2:U n !U such that,for each X 1;...;X n 2U ,it holds thatF ðX 1;...;X n Þ¼½f 1ðP 1ðX 1Þ;...;P n ðX n ÞÞ;f 2ðP n þ1ðX 1Þ;...;P 2n ðX n ÞÞ :ð7ÞThe concept of obtainable function generalizes the notion of representable function,as proposed by Deschrijver et al.[22–24,32]in the context of interval t-norms.On the other hand,observe that every obtainable interval function F is an interval representation of some real function f (at least f 1and f 2).However,the converse is not true.For example,the interval functionF :U n !U ,defined by F ðX Þ¼½max ð0;X ÀX Þ;min ð1;X þX 10Þ ,is an interval representation of the identity on U ,id U ðx Þ¼x ,but F is not obtainable.An interval function F :U n !U preserves degenerate intervals ,if it maps degenerate intervals into degenerate intervals,that is,if,for each x 1;...;x n 2U ,there exists y 2U such that F ð½x 1;x 1 ;...;½x n ;x n Þ¼½y ;y .Notice that the best interval representation of any real function is #-monotonic (inclusion-monotonic),obtainable and preserves degenerate intervals.In this paper,we adopt the following notions of continuity defined on the set U of subintervals of ½0;1 :(i)Moore continuity [52]:is defined as an extension of the continuity on the set of the real numbers by considering themetric given by the distance between two intervals X ;Y 2U ,which is defined by:d ðX ;Y Þ¼max fj X ÀY j ;j X ÀY jg .(ii)Scott continuity:is defined as an extension of the continuity on the set of the real numbers,considering the quasi-met-ric q ðX ;Y Þ¼max f Y ÀX ;X ÀY ;0g defined over U ,introduced in [1,64].An alternative way to define the Scott continu-ity on U is to consider the set U with the reverse inclusion order as a continuous domain [35],and a function B.C.Bedregal et al./Information Sciences 180(2010)1373–138913751376 B.C.Bedregal et al./Information Sciences180(2010)1373–1389f:ðU; Þ!ðU; Þis said to be Scott-continuous if it is monotonic and preserves the least upper bound of directed sets[35].2The main result in[64]can be adapted to our context,considering the set U instead of R,as shown in the following: Theorem5.Let f:U n!U be a real function.The following statements are equivalent:(i)f is continuous;(ii)b f is Scott-continuous;(iii)b f is Moore-continuous.3.Interval t-conormsA triangular conorm(t-conorm for short)is a function S:U2!U that is commutative,associative,monotonic and has an identity‘‘0”,generalizing the classical disjunction.Among several t-conorms,in this paper,we consider the maximum t-con-orm S M:U!U,defined asS Mðx;yÞ¼max f x;y g:ð8ÞAn interval generalization of t-conorms was introduced in[13],applying the principles discussed in Section2.The so-called interval t-conorm is defined as an interval representation of a t-conorm.This generalizationfits the idea of interval member-ship degrees as approximations of exact degrees.Definition6[13].A function S:U2!U is an interval t-conorm,whenever it is commutative,associative,monotonic with respect to the product and inclusion orders,and½0;0 is the identity element.In the following,the main results related to interval t-conorms are presented.Proposition7[13,Theorems5.1and5.2].If S is a t-conorm,then its best interval representation b S:U2!U is an interval t-conorm.For example,the supremum interval t-conorm S M:U2!U,defined byS MðX;YÞ¼sup f X;Y g;ð9Þis the best interval representation of the maximum t-conorm S Mðx;yÞ,given in Eq.(8),that is,S M¼c S M.3Proposition8[14,Corollary 5.3].The function S:U2!U is an interval t-conorm if,and only if,the real functions S;S:U2!U,defined bySðx;yÞ¼lðSð½x;x ;½y;y ÞÞand Sðx;yÞ¼rðSð½x;x ;½y;y ÞÞ;ð10Þare t-conorms andSðX;YÞ¼½SðX;YÞ;ð;;ð11Þwhere l and r are,respectively,the left and right projections defined in Eq.(1).Therefore,one has that interval t-conorms are obtainable.The following result is immediate:Corollary9.Let S:U2!U be an interval t-conorm and S:U2!U be a t-conorm.If S represents S then S6S6S. Given a t-conorm S,the interval t-conorm b S can be expressed by:b SðX;YÞ¼½SðX;YÞ;SðX;YÞ :ð12Þ4.Interval fuzzy negationsLike t-conorms,fuzzy negations generalize the classical negations.A function N:U!U is a fuzzy negation ifN1:Nð0Þ¼1and Nð1Þ¼0;N2:If x P y then NðxÞ6NðyÞ;8x;y2U.Fuzzy negations satisfying the involutive property N3are called strong fuzzy nega-tions[16,43]:N3:NðNðxÞÞ¼x;8x2U.In addition,a continuous fuzzy negation is strict whenN4:If x>y then NðxÞ<NðyÞ;8x;y2U.2A directed set ofðU; Þis a non-empty subset S#U such that every pair of intervals in S has an upper bound in S.3sup denotes the supremum related to the Kulisch-Miranker or product order.B.C.Bedregal et al./Information Sciences180(2010)1373–13891377As is well known,all strong fuzzy negations are strict.An element e2U is said to be an equilibrium point of a fuzzy negation N whenever NðeÞ¼e.If N is a strict fuzzy negation, then there exists a unique equilibrium point e N2U and it holds that NðxÞP e N,for all x6e N.Conversely,one has that NðxÞ6e N,for all x P e N.Definition10.An interval function N:U!U is an interval fuzzy negation if,for all X;Y in U,the following properties hold: N1:Nð½0;0 Þ¼½1;1 and Nð½1;1 Þ¼½0;0 ;N2a If X P Y then NðXÞ6NðYÞ;N2b If X#Y then NðXÞ#NðYÞ.If N also satisfies the involutive property N3,then it is said to be a strong interval fuzzy negation:N3:NðNðXÞÞ¼X;8X2U.A Moore and Scott-continuous interval fuzzy negation N is strict if it also satisfies the following properties:N4a If X<Y then NðYÞ<NðXÞ;N4b If X&Y then NðXÞ&NðYÞ.The concepts of interval representation and obtainability show their strength on the context of fuzzy negations in the fol-lowing results.We show that those concepts guarantee that punctual properties are preserved by the interval generalization of fuzzy negations.Let N:U!U be a fuzzy negation.The interval function b N can be expressed as:b NðXÞ¼½NðXÞ;NðXÞ :ð13ÞThe proofs of the next propositions in this section can be found in[10].Proposition11.A function N:U!U is a(strict)interval fuzzy negation if,and only if,the functions N;N:U!U,defined, respectively,byNðxÞ¼lðNð½x;x ÞÞand NðxÞ¼rðNð½x;x ÞÞ;ð14Þare(strict)fuzzy negations andNðXÞ¼½NðXÞ;NðXÞ ;ð15Þwhere l and r are,respectively,the left and right projections defined in Eq.(1).Remark12.If N¼N,then NðXÞ¼b NðXÞ¼b NðXÞ.Therefore,one has that(strict)interval fuzzy negations are obtainable.Proposition13.A function N:U!U is a strong interval fuzzy negation if,and only if,there exists a strong fuzzy negation N such that N¼b N.From Eq.(13)and Remark12,if the conditions of Proposition13hold,then it follows that N¼N¼N.From Propositions11and13,it is immediate that:Corollary14.Let N:U!U be a fuzzy negation.Then b N is an interval fuzzy negation.In addition,if N is a strong(strict)fuzzy negation then b N is a strong(strict)interval fuzzy negation.An interval E2U is an equilibrium point of an interval fuzzy negation N if NðEÞ¼E.Trivially,½0;1 is an equilibrium point of any interval fuzzy negation.Thus,if an equilibrium interval E is such that E–½0;1 then E is said to be a non-trivial equi-librium point.Proposition15.If N is a strong interval fuzzy negation,then N has a degenerate equilibrium.Moreover,it is the unique non-trivial equilibrium point.5.Fuzzy implications and S-implicationsSeveral definitions for fuzzy implications together with related properties have been given(see, e.g.,[4–7,16,30,31,46,47,58,61,60,62,66,65,72–74]).However,there is just one consensus on what a fuzzy implication should be, namely:‘‘a fuzzy implication should present the behavior of the classical implication when the crisp case is considered”[47].In other words,a function I:U2!U is a fuzzy implication whenever it satisfies the minimal boundary conditions:Ið1;1Þ¼Ið0;1Þ¼Ið0;0Þ¼1and Ið1;0Þ¼0:ð16ÞSeveral reasonable properties may be required for fuzzy implications,among them we consider the following: I1:If x6z then Iðx;yÞP Iðz;yÞ(first place antitonicity);I2:If y6z then Iðx;yÞ6Iðx;zÞ(second place isotonicity);I3:Ið1;xÞ¼x(left neutrality principle);I4:Iðx;Iðy;zÞÞ¼Iðy;Iðx;zÞÞ(exchange principle);I5:Iðx;yÞ¼Iðx;Iðx;yÞÞ(iterative boolean-like law);I6:Iðx;NðxÞÞ¼NðxÞ,where N is a strong fuzzy negation;I7:NðxÞ¼Iðx;0Þis a strong fuzzy negation;I8:Iðx;1Þ¼1(dominance of truth of consequent);I9:Iðx;yÞP y;I10:Iðx;yÞ¼IðNðyÞ;NðxÞÞ,where N is a strong fuzzy negation(contra-positive);I11:Ið0;xÞ¼1(dominance falsity).Some relations between classical implications and negations can be recovered for the fuzzy case.For example,if I:U2!U is a fuzzy implication satisfying the Property I1,then there is a fuzzy negation N I:U!U that can be defined by[6,Lemma2.1]:N IðxÞ¼Iðx;0Þ:ð17ÞAnother relation between negation and implication follows the opposite direction,showing that it is possible to define a fuz-zy implication from a fuzzy negation.Let S be a t-conorm and N be a fuzzy negation.An S-implication[5,6,16,30,31,47,61]is a fuzzy implication I S;N:U2!U defined byI S;Nðx;yÞ¼SðNðxÞ;yÞ:ð18ÞIn some texts(e.g.,[16,30,31]),the definition of an S-implication requires a strong fuzzy negation.Such S-implications are called here strong S-implications.Similar definitions can be introduced for continuous S-implications and strict S-implications.Trillas and Valverde[69,Theorem3.2](see also[30,Theorem1.13]and[6,Theorem1.6])provided the following char-acterization for strong S-implications:a function I:U2!U is a strong S-implication if,and only if,it satisfies the Properties I1–I4,and tely,Baczynsky and Jayaram[6,Theorem2.6])introduced a new characterization of strong S-implications, considering properties I1,I4and I7.Strong S-implications also satisfy the properties I8–I11and the following two extra properties below:I12:Iðx;yÞP N IðxÞ;I13:Iðx;yÞ¼0if,and only if,x¼1and y¼0.Notice that any S-implication I S;N satisfies the properties I1–I3,I8,I9,and I11.If a fuzzy implication I is an S-implication then N I,as given in Eq.(17),is the underlying negation of I,that is: N IS;NðxÞ¼I S;Nðx;0Þ¼SðNðxÞ;0Þ¼NðxÞ:ð19ÞTherefore,N I is a strict fuzzy negation if,and only if,I is a strict S-implication.Baczynsky and Jayaram[6,Theorem5.2]provided a characterization for strict S-implications,where an S-implication I S;N is strict if and only if N IS;Nis strict and the properties I1and I10also hold.If a fuzzy implication I:U2!U is a strong S-implication,then I satisfies I6if,and only if,the underlying t-conorm of I isthe maximum t-conorm S M,given in Eq.(8),and,therefore,one has I¼I SM;N ,where N is a strong fuzzy negation.The strong S-implication I SM ;Nalso satisfies the properties I1–I11.Moreover,it is the only S-implication satisfying I6.Given an equilibriumpoint e N,if x2U and x P e N then one has that I SM;Nðx;xÞ¼x.6.Interval fuzzy implicationsSince real numbers may be identified with degenerate intervals in the context of interval mathematics,the boundary con-ditions that must be satisfied by the classical fuzzy implications can be naturally extended to interval fuzzy degrees,when-ever degenerate intervals are considered.Then,a function I:U2!U is said to be an interval fuzzy implication if the following interval-based boundary conditions hold:(i)Ið½1;1 ;½1;1 Þ¼Ið½0;0 ;½0;0 Þ¼Ið½0;0 ;½1;1 Þ¼½1;1 ;(ii)Ið½1;1 ;½0;0 Þ¼½0;0 .The properties presented in Section5can then also be naturally extended to an interval-based approach:I1:If X6Z then IðX;YÞP IðZ;YÞ(first place antitonicity);I2:If Y6Z then IðX;YÞ6IðX;ZÞ(second place isotonicity);1378 B.C.Bedregal et al./Information Sciences180(2010)1373–1389I 3:I ð½1;1 ;X Þ¼X (left neutrality principle);I 4:I ðX ;I ðY ;Z ÞÞ¼I ðY ;I ðX ;Z ÞÞ(exchange principle);I 5:I ðX ;Y Þ¼I ðX ;I ðX ;Y ÞÞ(iterative boolean-like law);I 6:N ðX Þ¼I ðX ;N ðX ÞÞ,where N is a strong interval fuzzy negation;I 7:N ðX Þ¼I ðX ;½0;0 Þis a strong interval fuzzy negation;I 8:I ðX ;½1;1 Þ¼½1;1 (dominance of truth of consequent);I 9:I ðX ;Y ÞP Y ;I 10:I ðX ;Y Þ¼I ðN ðY Þ;N ðX ÞÞ,where N is a strong interval fuzzy negation (contra-positive);I 11:I ð½0;0 ;X Þ¼½1;1 (dominance falsity).It is always possible to canonically obtain an interval fuzzy implication from any fuzzy implication.The interval fuzzy implication satisfies the optimality property and preserves the properties satisfied by the corresponding fuzzy implication.Proposition 16.If I is a fuzzy implication then b I is an interval fuzzy implication.Proof.It is straightforward.hIn the next results,we adopt a canonical way to construct,under some conditions,interval fuzzy implication from fuzzy implication and vice-versa.The properties of fuzzy implications presented in Section 5are related with the respective prop-erties of interval fuzzy implications enrolled above.Theorem 17.Let I 1and I 2be fuzzy implications satisfying the Properties I1and I2and such that I 16I 2.If I 1and I 2satisfy a Property Ik ,for k ¼1;...;6;8;...;11,then I :U 2!U ,defined byI ðX ;Y Þ¼½I 1ðX ;Y Þ;I 2ðX ;Y Þ ;ð20Þsatisfies the Property I k .Proof.Since I 16I 2and by the Properties I1and I2,one has that I 1ð;Y Þ6I 1ðX ;Y Þ6I 2ðX ;Y Þ6I 2ðX ;,and,therefore,I is well defined.It follows that:I 1:Let X ;Y ;Z 2U such that X 6Z .Since X 6Z ;X 6Z ,and I 1and I 2satisfy Property I1,then it holds that I 1ðZ ;Y Þ6I 1ðX ;Y Þand I 2ðZ ;6I 2ðX ;Þ.So,by Eq.(20),it follows that I ðZ ;Y Þ6I ðX ;Y Þ.I 2:Let X ;Y ;Z 2U such that Y 6Z .Since Y 6Z ;Y 6Z ,and I 1and I 2satisfy Property I2,then it holds that I 1ðX ;Y Þ6I 1ðX ;Z Þand I 2ðX ;Y Þ6I 2ðX ;Z Þ.Then,by Eq.(20),it follows that I ðX ;Y Þ6I ðX ;Z Þ.I 3:It holds that I ð½1;1 ;X Þ¼½I 1ð1;X Þ;I 2ð1;¼½X ; ¼X .I 4:By Property I4,it follows that:I ðX ;I ðY ;Z ÞÞ¼I ðX ;½I 1ð;Z Þ;I 2ðY ;Þ Þ¼½I 1ðI 1ðZ ÞÞ;I 2ðX ;I 2ðY ;¼½I 1ð;I 1ð;Z ÞÞ;I 2ðY ;I 2ðX ;ÞÞ ¼I ðY ;I ðX ;Z ÞÞ:I 5:By Property I5,it follows that:I ðX ;Y Þ¼½I 1ðX ;Y Þ;I 2ðX ;Y Þ ¼½I 1ðX ;I 1ðX ;Y ÞÞ;I 2ðX ;I 2ðX ;Y ÞÞ ¼I ðX ;½I 1ðX ;Y Þ;I 2ðX ;Y Þ Þ¼I ðX ;I ðX ;Y ÞÞ:I 6:Let N be a strong interval fuzzy negation.By Proposition 13,there exists a strong fuzzy negation N such thatN ðX Þ¼½N ðX Þ;N ðX Þ .It follows that:I ðX ;N ðX ÞÞ¼I ðX ;½N ð;N ðX Þ Þ¼½I 1ðN ðÞÞ;I 2ðX ;N ðX ÞÞ ¼½N ð;N ðX Þ ðby Property I6Þ¼N ðX Þ:I 8:One has that I ðX ;½1;1 Þ¼½I 1ðX ;1Þ;I 2ðX ;1Þ ¼½1;1 .I 9:By Property I9,it holds that I 1ðX ;Y ÞP Y and I 2ðX ;Y ÞP Y .Then,it follows that I ðX ;Y Þ¼½I 1ðX ;Y Þ;I 2ðX ;Y Þ P Y .I 10:Let N be a strong interval fuzzy negation.By Proposition 13,there exists a strong fuzzy negation N such thatN ðX Þ¼½N ðX Þ;N ðX Þ .So,by Property I10,it follows that:I ðX ;Y Þ¼½I 1ðY Þ;I 2ðX ;Þ ¼½I 1ðN ðY Þ;N ðÞÞ;I 2ðN ð;N ðX ÞÞ ¼I ð½N ð;N ðY Þ ;½N ðÞ;N ðX Þ Þ¼I ðN ðY Þ;N ðX ÞÞ:I 11:One has that I ð½0;0 ;X Þ¼½I 1ð0;X Þ;I 2ð0;Þ ¼½1;1 .hRemark 18.According to the conditions stated by Theorem 17,the Property I 7does not hold even if both I 1and I 2satisfy the Property I7.For example,considering I 1ðx ;y Þ¼min f 1Àx þy ;1g and I 2ðx ;y Þ¼min f ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1Àx 2þy p ;1g ,it is immediate that I 1and I 2are fuzzy implications,as they satisfy Eq.(16),and it holds that I 16I 2.Moreover,considering N I 1ðx Þ¼I 1ðx ;0Þ¼1Àx and N I 2ðx Þ¼I 2ðx ;0Þ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffi1Àx 2p ,it is immediate that N I 1is a strong fuzzy negation,and,sinceB.C.Bedregal et al./Information Sciences 180(2010)1373–13891379。

colony词根词缀Colony: Exploring the Root and AffixesIntroductionLanguage is a fascinating tool that constantly evolves and grows. One aspect of language that showcases this evolution is the use of prefixes, suffixes, and roots in constructing words. These linguistic elements enable us to understand the meaning of words and make connections between seemingly unrelated terms. In this article, we will explore the colony root and its accompanying prefixes and suffixes, delving into the rich world of vocabulary that it has given rise to.The Root: ColonyThe root word "colony" originates from the Latin word "colonia," meaning "a settled area" or "a group of individuals living in close proximity." The concept of a colony, whether in a biological or societal context, refers to a group of organisms or individuals living together and sharing resources. This central meaning forms the foundation for the various derivatives and related words that we will explore next.Prefixes: Co- and Colo-The prefix "co-" is derived from the Latin word "com," meaning "together" or "with." When attached to the root "colony," it emphasizes the collective aspect of a group living together. For example:1. Coexist: This word signifies the peaceful coexistence of different groups or individuals within a shared space.2. Cooperation: Referring to the act of working together or collaborating, this word highlights the collective effort involved in achieving a common goal.3. Coauthor: By combining "co-" with "author," this term acknowledges the collaborative nature of writing, as multiple individuals contribute to the creation of a piece.On the other hand, the prefix "colo-" is an alternative form of the prefix "co-," often seen in particular words derived from Latin. It carries the same meaning of "together" or "with." For instance:1. Colonel: Originally referring to the leader of a column of soldiers, this title highlights the individual who leads a group, emphasizing the collective identity.2. Colocation: In the context of technology, this term describes the practice of housing multiple servers or equipment in a shared physical location.Suffixes: -ial, -ialism, and -ialistThe suffix "-ial" is derived from the Latin suffix "-ialis" and is commonly added to root words to form adjectives. In relation to the root "colony," it indicates a characteristic or quality associated with a colony. Examples include:1. Colonial: Describing something related to or originating from a colony, this adjective highlights the connection to a specific group or territory.2. Celestial: Derived from "coelum," the Latin word for "heaven" or "sky," this term denotes something related to the sky or stars. It roots back to the belief that colonies settled by individuals originated from heavenly powers.The suffix "-ialism" is derived from the French "-isme" and denotes a belief, doctrine, or system. When attached to the root "colony," we find:1. Colonialism: This term refers to the policy or practice of acquiring and maintaining colonies, often for economic exploitation or political control. It underscores the positioning of one group as dominant over another.2. Neocolonialism: With a focus on modern forms of colonial practices or influence, this word describes a system where economic or cultural control persists despite formal political independence.Building on the suffixed form, the suffix "-ialist" denotes a practitioner or advocate of a particular belief or system. Examples encompass:1. Colonialist: Referring to an individual who supports or engages in colonial activities, this term carries a negative connotation due to historical contexts of exploitation.2. Environmentalist: Although not directly tied to the root "colony," the suffix "-ialist" is frequently used in words like "environmentalist," indicating a person dedicated to protecting and preserving the environment.ConclusionExploring the colony root and its associated prefixes and suffixes reveals a wealth of vocabulary that adds depth and nuance to our language. From discussing collaborative efforts through the prefix "co-" to examining the historic legacy of colonialism through the suffix "-ialism," these linguistic elements shape our understanding of the world. By delving into the etymology and meaning of words, we can uncover the fascinating connections and broader implications that the colony root and its affixes offer, expanding our linguistic abilities and enriching our communication.。

主题：implications的语料内容：1. 什么是implications？Implications是一个英文单词，它的意思是“暗示”、“含义”或者“意义”。

在不同的语境中，这个词可能会有不同的解释和使用方式。

在语言学上，implications可以指一个词语或者语句所包含的意义和暗示，也可以指由某个事实或者观点所引起的可能的结果或者影响。

2. 如何使用implications？使用implications时，可以通过一些固定的词语搭配，比如“have implications for”（对...有影响）、“carry implications”（具有含义）、“draw implications from”（从...中得出暗示）等。

在句子结构上，通常可以使用宾语从句或者介词短语来表达implications所涉及的内容和影响范围。

3. impications的语料来源implications这个词的语料来源非常广泛，可以来自于各种语言文本、学术文章、新闻报道、讨论论坛等。

一些大型语料库中也会包含大量的implications相关的语料，可以作为语言学研究和自然语言处理的素材来源。

4. impications的语料分析对于implications的语料分析，可以从不同的角度进行研究和探讨。

首先可以从语义角度对语料进行分析，探究implications所指代的具体意义和蕴含的信息；其次可以从语用角度对语料进行分析，探究implications在不同语境下的使用方式和含义转化；还可以从语篇角度对语料进行分析，探究implications的出现对整个语篇所带来的影响和意义。

5. impications的语料应用implications的语料在语言学研究、自然语言处理、文本分析、语言教学等领域都具有重要的应用价值。

通过对implications相关的语料进行大规模的收集、整理和分析，可以帮助人们更好地理解自然语言的使用规律和文本的含义，也可以为一些自然语言处理系统的构建和优化提供重要的参考资料。

sqcrififice词根词缀Sacrifice: Understanding the Root and AffixesIntroductionThe study of language and etymology plays a crucial role in comprehending the origins and meanings of words. In this article, we will delve into the root and affixes of the word "sacrifice." By examining its components, we can gain a deeper understanding of its nuances and implications. Let us embark on this linguistic journey to unravel the intricacies of "sacrifice."Part 1: Unveiling the Root - "Sacr-"The root of the word "sacrifice" originates from the Latin term "sacrificium." The Latin root "sacr-" carries the primary meaning of "sacred" or "holy." This root serves as the foundation for various words related to religious or solemn acts. It conveys the notion of offering or giving up something valuable in reverence to a higher power.Part 2: Exploring the Affixes - "-Fice" and "-I"-The affixes in the word "sacrifice" further contribute to its overall meaning. The suffix "-fice" derives from the Latin suffix "-ficere," which connotes "to make" or "to do." Adding this suffix to the root creates a verb, implying the act of making something sacred or holy through an offering.Additionally, the affix "-i" in "sacrifice" functions as a connective element between the root and suffix. It aids in the smooth transition from theroot to the suffix, ensuring the formation of a coherent and recognizable word.Part 3: Broadening the Context - Sacrifice in Different Fields3.1 Sacrifice in ReligionSacrifice holds significant importance in various religious practices worldwide. It serves as a spiritual act of devotion and surrender to a deity or belief system. People offer sacrifices as a symbol of their faith and commitment, seeking spiritual blessings or redemption.Throughout history, sacrificial rituals have been intrinsic to many religions, such as ancient Greek and Roman traditions, Aztec ceremonies, and the sacrificial practices of indigenous cultures. The act of sacrifice demonstrates the willingness to give up personal desires or material possessions in service of one's religious convictions.3.2 Sacrifice in Personal RelationshipsBeyond its religious connotations, sacrifice manifests in interpersonal relationships. It encompasses the willingness to prioritize the needs and well-being of others above one's own. Sacrifices made within relationships often entail compromising personal goals or desires for the betterment of the partnership.Acts of sacrifice in relationships can be seen in various forms, ranging from making career adjustments to support a partner's ambitions to investing time and energy into maintaining a healthy work-life balance. Sacrifices made within personal relationships exemplify the commitment and devotion individuals are willing to make for the sake of their loved ones.3.3 Sacrifice in Wartime and HeroismIn times of conflict or war, sacrifice takes on a different meaning, portraying acts of courage, valor, and selflessness. Soldiers willingly risk their lives to protect their country and fellow citizens. Their sacrifices, often the ultimate sacrifice of giving up their lives, embody the highest form of devotion to a cause or ideal.Sacrifices made by heroes extend beyond the battlefield. Firefighters, police officers, and emergency responders willingly put themselves in harm's way to protect others from danger. Their willingness to sacrifice personal safety for the well-being of their communities showcases the epitome of bravery and altruism.Part 4: The Power of SacrificeSacrifice, as embodied through its root and affixes, holds immense power in shaping individuals and societies. It promotes a sense of devotion, commitment, and selflessness. The act of sacrifice calls upon believers, partners, and heroes to set aside personal interests and desires for a greater cause or purpose.ConclusionIn conclusion, by dissecting the word "sacrifice" and exploring its root and affixes, we have gained insight into its meaning, context, and significance. Whether it be within religion, personal relationships, or acts of heroism, sacrifice remains a powerful concept that speaks to humanity's capacity for devotion and selflessness. Let us continue to appreciate andhonor the sacrifices made by others, recognizing the transformative impact they have on our lives and society as a whole.。

Sichuan International Studies UniversityThe Treatment of Affixoids in English Learner’s Dictionaries:A Corpus-based StudybyCheng JianyunA thesissubmitted to the Graduate Schoolin partial fulfillment of the requirements for the degree ofMaster of ArtsinEnglish Language and Literatureunderthe supervision ofProfessor Wang RenqiangChongqing, P. R. ChinaJune 2013摘 要现代英语中大量存在的类词缀是一种介于实词素与词缀之间的特殊构词成分。

虽然很多学者在其著作中或多或少的提及了英语类词缀这一语言现象，但由于类词缀自身的特殊性和复杂性，大部分学者将类词缀置于其上位概念“组合形式”之下进行了讨论，缺乏深入的调查和系统的研究。

本文在回顾英语组合形式研究和类词缀研究的基础上，以基于使用的语言理论作为理论基础，并借助当代美语语料库对类词缀在英语学习词典（《牛津高阶英语词典》（第七版）、《柯林斯高阶英语学习词典》（第五版）和《朗文当代英语词典》（第四版））中的处理情况进行了深入调查。

调查发现，三部词典对类词缀的标注不够准确，类词缀被等同于组合形式进行标注或将其列为某个词条的义项之一，极大地忽略了类词缀的地位和构词能力。

文章建议，英语学习词典处理类词缀时，应基于大型平衡语料库中词语使用模式调查为基础，研究其形态地位及构词能力，而不能片面地将类词缀置于“组合形式”之下或列为义项进行标注。

本项研究不仅对英语学习词典类词缀的处理有一定应用价值，对英语形态学研究也有一定的学术价值。

HOAE-Root / prefixes / suffixes词根词根解释例词1.ache=ache 痛earache 耳痛2.ag=do, act 做，动agent 代理人3.agri, agro=agriculture 田地，农田agriculture 农业，农艺4.ann, enn=year 年annual 每年的，年度的5.astro, aster=star 星astronomy 天文学6.audi, audit=hear 听audible 听得见的7.bell=war 战争rebellion 反叛，反抗8.bio, bi=life 生命，生物biology 生物学9.brev=short 短abbreviate 缩短，节略10.ced, ceed=go 行走precedent 先行的，在前11.cept=take 拿，取exception 例外，除外12.circ=ring 环，,圆circle 圆，圈，环状物13.cid, cis=cut, kill 切，杀suicide 自杀14.claim, clam=cry, shout 喊叫exclaim 呼喊，惊叫15.clar=clear 清楚的，明白的clarify 澄清；使清楚16.clud, clus=close, shut 关闭exclude 排除，排斥，拒绝接纳17.cogn=know 知道cognition 认知18.cord=heart 心cordial 衷心的，诚心的19.corpor, cor=body 体corporation 团体，社团20.cred=believe, trust 相信，信任credibility 可信，可靠，21.cruc=cross 十字crucify把……钉在十字桇上；折磨22.cur=care 关心，挂念，注意security 安全23.cru, curs, cour, cours=run 跑cruise巡航舰24.di=day 日diary 日记25.dit=give 给edit 编辑26.dict,dic=say 言，说dictator 独裁者，口授者27.duc, duct=lead 引导conduct 引导，指导，经营28.ed=eat 吃edible 可以吃的，食用的29.ev=age 年龄，时代longevity 长寿，长命30.fact, fac=do, make 做，作factory 工厂31.fer=bring, carry 带，拿different 不同的，相异的32.flor, olour=flower 花florid 如花的，华丽的33.flu=flow 流fluency 流利，流畅34.fus=pour 灌，流，倾泻refuse 拒绝，拒受35.geo=earth 地geography 地理学36.gon=angle角trigon 三角形37.grad=step, go, grade 步，走，级gradual 逐步的38.gram=write 写telegram 电报39.graph=write, writing 写，画photograph 照相，拍照40.gress=go, walk 行走progress 进步41.hap=chance,luck,accident 机会，偶发happen 发生，巧遇42.hibit=hold 拿，持exhibit 展出，展览43.hospit, hosp=guest 客人hospitable 好客的44.idio=particular, own, private, proper 特殊的，个人的，专有的idiom 惯用语，方言45.insul=island 岛insular 岛的，偏狭的46.it=go 行走exit 出口，退出47.ject=throw 投掷projection 投掷，发射48.lect, leg, lig=choose, gather 选，收elect 选举49.lev=raise 举、升elevate 抬起，使升高50.liber=liberty 自由liberation 解放51.lingu=language 语言linguist 语言专家52.liter=letter 文字，字母literate 识字的，有文化的53.loc=place 地方local 当地的54.log=speak 言，说dialogue 对话55.loqu=speak 言说eloquent 有口才的，雄辩的56.lun=moon 月亮lunar 月亮的，似月的57.manu, man=hand 手manuscript 手稿58.mar=sea 海marine 海上的，航海的59.medi=middle 中间mediate 居中调解，调停60.memor=memory,mindful 记忆，记住的memory 记忆，记忆力it=soldier 兵military 军事的，军队的62.mini=small,less 小minimum 最小数63.mir=wonder 惊奇，惊异admire 赞赏，钦佩64.mort=death 死mortal 终有一死的65.mot=move 移动motion 运动，动66.nomin=name 名nominal 名义上的，有名无实的67.nov=new 新novel 新的，新奇的68.numer=number 数numeral 数字，[语]数词69.oper=work 工作operation 手术，工作，操作70.ori=rise 升起orient 东方，东方的71.paci=peace 和平pacify 使和平，抚慰72.past=feed 喂，食pasture 放牧、牧场，吃草73.pel=push, drive 推，逐，驱propel 推动74.pend, pens=hang 悬挂pendent 悬空的，悬而未决的75.pet=seek 追求compete 竞争，比赛（pet：走impetus 推动，促进）76.phon=sound 声音phone 电话77.plen=full 满，全plenty 大量，丰富78.pone=put 放置postpone 推后，推迟79.popul=people 人民population 人口，全体居民80.port=carry 拿，带，运import 输入，进口81.pos=put 放置expose 揭露，揭发82.preci=price 价值precious 宝贵的，珍贵的83.pur=pure 清，纯purify 使纯净84.rect=right, straight 正，直correct 改正，纠正85.rupt=break 破rupture 破裂，使裂开86.sal=salt 盐salary 薪水87.sci=know 知science 科学88.sec, sequ=follow 跟随sequence 继续，连续89.sect=cut 切割section 切开，一部分90.sent, sens=feel 感觉sentiment 感情，思想感情91.son=sound 声音sonic 声音的，音速的92.spect=look 看spectate 出席，观看93.spir=breathe 呼吸inspire 鼓舞，吸入94.tail=cut 切，割tailor 裁缝，成衣商95.tain, ten=hold 握，持，守contain 容纳，包含，内装96.tect=cover 掩盖detect 侦查，发觉97.tempor=time 时temporary 暂时的，临时的98.tend, tens=draw 拉tension 拉紧，引力99.tent, tract=draw 拉，抽，引tractor 拖拉机100.urb=city 城市suburb 郊区，近郊101.ut=use 用utility 效用, 有用102.vac, vacu=empty 空vacancy 空白，空虚103.vad, vas=walk, go 行走invasion 入侵，侵略104.vari=change 变化variable 可变的，反复的105.ven=come 来convene 召集（会议），集会106.vert, vers=turn 转subvert 推翻，颠覆107.vi, via=way 路via 取道，经由108.vis, vid=see 看visible 可见的，看得见的109.vit=life 生命vital 充满活力的110.viv=live 活vivid 活泼的，有生气的前缀有如下几类：第一类：表示正负（或增减）的，如：un-in-im-il-ir-non-mis-mal-dis-anti-de-under-re-over-等；第二类表示尺寸的，如：semi-equi-mini-micro-macro-mega-等；第三类表示位置关系，如：inter-super-trans-ex-extra-sub-infra-peri-等；第四类表示时间和次序，如：ante-pre-prime-post-retro-等；第五类表示数字，如：semi-mono-bi-tri-quad-penta-hex-sept(em)-oct-dec-multi-等；其它类别，如：pro-auto-co-con-等表示否定的前缀1．dis－加在名词、形容词，动词之前。