数学建模灰色关联度分析英文版.docx

4.1 Grey Relational AnalysisFirst, select a reference sequence as shown below : And the other group of sequence is, Then the correlation degree of to is, In which, Then, we use to describe the correlation degree between and ,namely to describe the influence on caused by the change of . In general, Practical problems often have different numbers of different dimension , but when we calculate the correlation degree, it requires the same numbers of same dimension . So we want to carry out a variety of data processing dimensionless.in addition , For comparison easily, all the sequseces are required to have a common point .In order to solve these two problems, we transform the given sequences. The given sequence we name as initialization sequence of Original sequence 4.2 Water resources carrying capacity evaluation indexes and classification indexesThe establishment of evaluation index system of water resources carrying capacity is a key issue in the study of water resources carrying capacity. Regional water resources carrying capacity is influenced by many factors, Should be selected according to the requirements of the specific regional social development backlog of social - economic index system response - natural compound ecosystem development scale and quality, reference existing literature results, through the grey correlation analysis, the bearing capacity of water resources evaluation index are shown in table 1. Approach A : Weighted Average Evaluation Based Model Fig.1.The index system of water resources carrying capacityAgriculture investment Social economic indicatorindicatorsIndustry investment Per GDPThe index system of water resources carrying capacity Water environment indicatorWater resources indicatorsIndustrial sewage treatmentIrrigation displacementPer capital emissionLife water leverWater resource quantityComprehensive analysis of water resources carrying capacity of main influencing factors and performance system, with reference to the evaluation index system of water resources carrying capacity at home and abroad to select the following 6 main factors as evaluation factors, The meaning 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 quantity and water resources (%);utilization rate of arable land (): Irrigation area and more on the ratio of the area(%);The modulus of water supply(）: water and the ratio of the land area（）;modulus of water requirement（）: The total water demand and the ratio of the land area（）;Life water use ratio（）: Domestic water amount and the ratio of the total water demand（%）According to the above six evaluation factors on the influence degree of the regional water resources carrying capacity Will the influence of these factors are divided into three levels, Each factor, the number of each level indicators are shown in table 2. The said condition is bad, water resources carrying capacity is close to saturation value, further development and utilization of potential is smaller, develop water shortages will occur;Membership condition is good, said there are still large carrying capacity of water resources in this area, water resource utilization degree of development in this area are small, water supply situation more optimistic;Level is between the above two levels, which indicates that this area has a scale development for the supply of water resources development, but still has a certain ability of development and utilization of local economic development and people have certain guarantee survival. The evaluation factorsPer capita water supply /22502250-10001000Water resources utilization %60The modulus of water supply /100Farmland irrigation rate /%50Water demand modulus /100Domestic water rate /%44-22Scores 0.950.50.05Table 2: classification index comprehensive evaluation factors4.3 The fuzzy comprehensive evaluation model Because of the bearing with uncertainty and fuzziness, the fuzzy evaluation model can be well carried out on the water resources carrying capacity multi-factor and multi-level comprehensive evaluation, comprehensive to reflect the status of the regional water resources carrying capacity.Fuzzy evaluation for B=AR finite field, With U on behalf of the comprehensive evaluation factors of collection, V on behalf of the evaluation of collection. Type A is U in the fuzzy subsetA= ,0 for U for A membership.It marked the single factor evaluation factors in the role of size, To a certain extent, also on behalf of the ratings; The evaluation result B is the fuzzy subset of V .B=, 0, for the level of comprehensive evaluation the membership degree of fuzzy subset B, they say the result of comprehensive evaluation. Evaluation matrix Among forevaluation of grade membership degree, Matrix of the ith line is the single factor evaluation results of the ith a factor.Evaluation computer matrix A representative of the various factors on the comprehensive evaluation of the importance of weight coefficient, thus satisfy, fuzzy transform AR also can be degraded for common matrix is calculated.4.3.1 The calculation of matrix R Corresponds to the evaluation sets of evaluation factors, and can be through the evaluation factors in the evaluation matrix R the actual numerical control classification indexes of various factors to analysis and calculation. In order to make the membership function can smooth transition between at all levels, the blur processing. Of V2 point of membership degree is 0.5, the midpoint to according to linear regressive processing. For V1 and V3 on both sides of the interval, then make the farther away from the critical value of range on either side of the membership degree, the greater the belong to both sides on the critical level of membership you 0.5 according to the grades of the above ideas to construct a evaluation the calculation formula of subordinate function. V1 and V2 level threshold for K1, V2 and V3 threshold for K3, V2 mid-range level interval for K2.K2.For evaluating factors u3 u4 u5 u6 and comments and calculating formula for relative membership degree function:Calculate the relative membership degree of evaluation factors according to the type, For evaluation factors in the evaluation and the calculation of the relative membership degree function simply type (1) (3) the right end of type UI interval good instead of ; And after the calculation formula of the same 4.3.2 Fuzzy comprehensive evaluation According to the evaluation factors influence the size of the carry