A Study On The Method Of Fuzzy Multiple Attribute Decision Making Based On Mahalanobis-Taguchi System

In the last decade’s years, Fuzzy Multiple Attribute Decision Making (FMADM) theory and method have achieved fruitful results. However, the actual decision problems become more and more complicated, the theory and method of FMADM need to be further improved and the research perspectives need to be further expanded. Mahalanobis-Taguchi System (MTS) is a pattern recognition technology; it is widely used in the field of quality engineering. MTS has a unique theory of classification and dimension reduction. In this paper, MTS is introduced into the field of FMADM for solving the problems of fuzzy integral multiple attribute decision making and interval number multiple attribute decision making. The main work is as follows:(1) Fuzzy Integral Multiple Attribute Decision Making. The key to solving this kind of problems is to identify the fuzzy measures. This paper uses the dimension reduction theory of MTS to present several identification methods of fuzzy measures.1) The identification method of fuzzy measures by Classic MTS and φs transformation function. In the method, the importance of the attributes set is measured by MTS and the global importance of a single attribute is solved using optimization model. Then the relative importance and global importance is fused into Shapley value of a single attribute. Finally, Shapley values of attributes are transformed into fuzzy measure throughφs, transformation function.2) The identification method of fuzzy measures by MTGS (Mahalanobis-Taguchi Gram-Schmidt) and φs transformation function. In the method, a new identification method of the weights of attributes is presented. Then the weights are transformed into fuzzy measure by φs transformation function.3) The identification method of fuzzy measures by Weighted MTS.Firstly, a new subjective and objective identification method of the density of a single attribute is proposed. In the method, the dimension reduction principle based on orthogonal experimental design of MTS is used. Then, λ-fuzzy measures are calculated by the density of a single attribute.4) The identification method of fuzzy measures by Interval MTS. In the method, firstly the traditional MTS is improved to process the interval data, and then the identification method of fuzzy measures for interval attribute is proposed based on the improved MTS.In addition, the fuzzy integral operator as the important tool to solve the fuzzy integral multiple attribute decision making problem. The research contents of the fuzzy integral operator are as follows:1) Grey fuzzy integral correlation degree is proposed. The traditional gray correlation degree is composed of simple arithmetic average aggregation operators. The premise of application of the simple arithmetic average aggregation operators is assumed that all the attributes are mutually independent. Therefore the traditional gray correlation degree cannot effectively deal with the interaction between attributes. This paper proposed grey fuzzy integral correlation degree on the basis of the traditional grey correlation degree and Choquet fuzzy integral operator to solve the interaction between attributes.2) A calculation method of 2-order additive Choquet integral aggregation operator is proposed. The operator is derived from 2-order additive fuzzy measure and fuzzy Choquet integral operator. Because the operator is only composed of Shapley value and interaction index between attributes, it not only can greatly reduce the computational complexity, but also can improve the accuracy of decision making. This paper gives the method of Shapley value and interaction index.(2) Interval Number Multiple Attribute Decision Making. For interval number multiple attribute decision making problems, the existing research results have been quite rich and mature. This paper uses the three key tools of MTS to deal with the interval numbers decision information from three-dimensional perspective and presents the theory and method of multiple attribute decision making with interval number based on generalized MTS and expands the research ideas of multiple attribute decision making with interval number. At the same time, this paper combines orthogonal experimental design ideas with relative entropy, gray relative correlation and Euclidean distance function to propose three expansion methods.