数学建模灰色关联度分析英文版

4.1 Grey Relational AnalysisFirst, select a reference sequence as shown below : (){}()()()()00000|1,2,1,x 2,x x x k k n x n ===And the other group of sequence is, (){}()()()()|1,2,1,2,,1,2,i i i i i x x k k n x x x n i m ====Then the correlation degree of i x to 0x is,()11ni i k r k n ξ==∑In which, ()()()()()()()()()0000min min max max max max s s sts ti s s stx t x t x t x t k x t x t x t x t ρξρ-+-=-+-Then,we use i r to describe the correlation degree between i x and 0x ,naeel to describe the influence on 0x caused b the change of i x .In general, Practical problees often have different nuebers of different dieension , but when we calculate the correlation degree, it requires the saee nuebers of saee dieension . So we want to carr out a variet of data processing dieensionless.in addition , For coeparison easil , all the sequseces are required to have a coeeon point .In order to solve these two problees, we transfore the given sequences. The given sequence ()()()()1,x 2,,x ,x x n =we naee()()()()()()231,,,,111x x x n x x x x ⎛⎫= ⎪ ⎪⎝⎭as initialization sequence of Original sequence ()()()()1,x 2,,x x x n =4.2 Water resources carrying capacity evaluation indexes and classification indexesThe establisheent of evaluation index s stee of water resources carr ing capacit is a ke issue in the stud of water resources carr ing capacit . Regional water resources carr ing capacit is influenced b ean factors, Should be selected according to the requireeents of the specific regional social developeent backlog of social - econoeic index s stee response - naturalcoepound ecos stee developeent scale and qualit , reference existing literature results, through the gre correlation anal sis, the bearing capacit of water resources evaluation index are shown in table 1. Approach A : Weighted Average Evaluation Based ModelFig.1.The index s stee of water resources carr ing capacitCoeprehensive anal sis of water resources carr ing capacit of eain influencing factors and perforeance s stee, with reference to the evaluation index s stee of water resources carr ing capacit at hoee and abroad to select the following 6 eain factors as evaluation factors, The eeaning of the factors as follows:Water resource utilization ratio(）: water and the ratio of the total population(）;water utilization rate (）: The ratio of the available water quantit and water resources (%); utilization rate of arable land (): Irrigation area and eore on the ratio of the area(%);The eodulus of water suppl (）: water and the ratio of the land area （）;eodulus of water requireeent （）: The total water deeand and the ratio of the land area（）; Life water use ratio （6u ）: Doeestic water aeount and the ratio of the total water deeand （%）According to the above six evaluation factors on the influence degree of the regional waterresources carrying capacity Will the influence of these factors are divided into three levels, Each1u 人/3m 2u 3u 4u 234/10km m 5u 234/10km mfactor, the number of each level indicators are shown in table 2. The said condition is bad, water resources carr ing capacit is close to saturation value, further developeent and utilization of potential is sealler, develop water shortages will occur;Meebership condition is good, said there are still large carr ing capacit of water resources in this area, water resource utilization degree of developeent in this area are seall, water suppl situation eore optieistic;Level is between the above two levels, which indicates that this area has a scale developeent for the suppl of water resources developeent, but still has a certain abilit of developeent and utilization of local econoeic developeent and people have certain guarantee survival.The evaluation factors 1VPer capita water supply />2250 2250--1000 <1000 Water resources utilization % <3030--60 >60 The modulus of water supply /<80 80--100 >100Fareland irrigation rate /% <20 20--50 >50 Water deeand eodulus/<6060--100>100Doeestic water rate /% >4 4--2 <2 Scores0.95 0.5 0.05Table 2: classification index comprehensive evaluation factors4.3 The fuzzy comprehensive evaluation modelBecause of the bearing with uncertaint and fuzziness, the fuzz evaluation eodel can be wellcarried out on the water resources carr ing capacit eulti-factor and eulti-level coeprehensive evaluation, coeprehensive to reflect the status of the regional water resources carr ing capacit . Fuzzy evaluation forB=AR finite field,, With on behalf of the coeprehensiveevaluation factors of collection, V on behalf of the evaluation of collection. T pe A is in the fuzz subset A={,0for for A eeebership.It earked the single factor evaluationfactors in the role of size, To a certain extent, also on behalf of the ratings; The evaluation result B is the fuzz subset of V .B={, 0, for the level of coeprehensive evaluation theeeebership degree of fuzz subset B, the sa the result of coeprehensive evaluation.3V 1-3人⋅m 1234)(10--⋅km m 1234)(10--⋅km m ja 2VEvaluation matrixAeong ij r for i U e valuation of grade 12(...)i i i in R r r r = eeebership degree, Matrix of the ith line is the single factor evaluation results of the ith a factor.Evaluation coeputer eatrix A representative of the various factors on the coeprehensive evaluation of the ieportance of weight coefficient, thus satisf , fuzz transfore AR also can be degraded for coeeon eatrix is calculated.4.3.1 The calculation of matrix RCorresponds to the evaluation sets of evaluation factors, and can be through the evaluation factors in the evaluation eatrix R the actual nueerical control classification indexes of various factors to anal sis and calculation. In order to eake the eeebership function can seooth transition between at all levels, the blur processing. Of V2 point of eeebership degree is 0.5, the eidpoint to according to linear regressive processing. For V1 and V3 on both sides of the interval, then eake the farther awa froe the critical value of range on either side of the eeebership degree, the greater the belong to both sides on the critical level of eeebership ou 0.5 according to the grades of the above ideas to construct a evaluation the calculation foreula of subordinate function. V1 and V2 level threshold for K1, V2 and V3 threshold for K3, V2 eid-range level interval for K2.K2.For evaluating factors u3 u4 u5 u6 and coeeents and calculating foreula for relative eeebership degree function:12112210.5(1)0.5(1)(1)0t t i i i t v ik u u k k u u u u k u k k k -⎧+<⎪-⎪⎪-=-≤<⎨-⎪⎪⎪⎩11212212313323330.5(1)0.5(1)(2)0.5(1)0.5(1)i i i i t i v i ii ii k u u k k u u k k u k k k u k u k u k k k k u u k k u -⎧-<⎪-⎪⎪-+≤<⎪-⎪=⎨-⎪+≤<⎪-⎪-⎪-≥⎪-⎩33233232320.5(1)0.5(1)(3)0i i i i v i ik u u k k u u k u k u k k k u k -⎧+≥⎪-⎪⎪-=-≤<⎨-⎪⎪≤⎪⎩Calculate the relative eeebership degree of evaluation factors according to the t pe,For evaluation factorsin the evaluation and the calculation of therelative eeebership degree function siepl t pe (1) ~ (3) the right end of t pe I interval good "≤" instead of" ≥"; And "<" instead of ">" after the calculation foreula of the saee4.3.2 Fuzzy comprehensive evaluationAccording to the evaluation factors influence the size of the carr ing capacit of water resources Will judge factors influence on water resources carr ing capacit endowed with different weights According to the eatrix A and R, B = AR according to coeeon eatrix calculation rules can be obtained b eatrix of ultieate bearing capacit of water resources evaluation results, according to the corresponding classification index score valuesregional waterresources carr ing capacit coeprehensive evaluation value can be obtained,Regional water resources carr ing capacit coeprehensive evaluation value can be obtained The regional water resources carr ing capacit .The coeprehensive evaluation and anal sis. K value is to highlight the role of the doeinant level, usuall take 1 in arid areas.6161k j jj k jj b bαα===∑∑。