Dissertation
Dissertation > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Fuzzy Mathematics

Two Classes of Intuitionistic Multi-attribute Decision Making and Optimal Grey GM(1,1)Model

Author JiaJingLi
Tutor MaoJunJun
School Anhui University
Course Probability Theory and Mathematical Statistics
Keywords interval grey number intuitionistic fuzzy sets intuitionistic fuzzysets grey relational analysis TOPSIS principle score function entropy grey system GM (1,1) model
CLC O159
Type Master's thesis
Year 2013
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Related to fuzzy set, a new parameter—on-membership degree is proposed by intuitionistic fuzzy set, so it can descript fuzziness of the world more exactly, which makes it be a wide range of application. Intuitionistic fuzzy set’s membership degree and non-membership degree can hardly be described by exact way because of the objective world’s complexity and fuzziness. Atanassov proposed Interval-valued intuitionistic fuzzy set in1989, which expanded the intuitionistic fuzzy sets in the application of multi-attribute decision making. Grey relational analysis have the advantages of integrity compared with distance space which is pair comparison. Score function can apply to multi-attribute decision making, the higher the score the more better programs. Entropy indicates the degree of uncertainty of things, thus we define the concept of entropy which can avoid subjective assignment defects.Right decisions need scientific predictions for support. Grey system theory is based on the evolution of the things that have little sample, incomplete information. Improved optimization form of GM(1,1) make an extensive application in the fields of industry, agriculture, health care, population projections, economic, society and so on. To improve GM(1,1) model prediction more accurately and to expand its scope of application, more and more scholars committed to optimized GM(1,1) model to make it better for the production and humans’ lives. The improvement is mainly based on the background value the initial conditions.This thesis mainly studies the content of three parts:multi-attribute decision making based on interval grey number intuitionistic fuzzy sets and on interval-valued intuitionistic fuzzy set, finally this thesis gives a new GM(1,1) model whose background values and initial conditions has been improved.1, it is mainly studying interval grey number intuitionistic fuzzy set’s multi-attribute decision making. Computing grey relational grade between every alternative and positive and negative ideal solution by TOPSIS principle, next give relative relational grade associated every alternative with positive ideal solution. Finally, multi-attribute decision making based on grey relational analysis is given based on the interval grey number intuitionistic fuzzy sets.2, interval-valued intuitionistic fuzzy set of unknown weight is presented. A score function for interval-valued intuitionistic fuzzy set has been proposed based on hesitancy degree. Next it gives an expression of a new entropy. Finally, multi-attribute decision making approach for interval-valued intuitionistic fuzzy information has been put forward and practical example shows that the improved model is feasible.3, a new GM(1,1) model of integrated optimizing its back ground value and original conditions is presented. Especially, the optimization for initial conditions introduces a parameter a which solved by the conditional extreme of Lagrange Method of Multiplier. When tested with the average relative error and Deng’s relational grade both obtain superior forecasting results over literature [62].

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