Theory And Application Research Of Multiple Attribute Decision Making Based On Intuitionistic Fuzzy Information

With the increasing complexity and uncertainty of the social economic environment, there often exist different hesitancy degree or show a certain degree of lack of knowledge in the decision making process. Intuitionistic fuzzy (IF) sets can well describe the decision makers to the hesitation and uncertainty of judgment through the addition of a non-membership parameters. Compared with fuzzy set, IF sets are more flexible and practical in dealing with ambiguity and uncertainty. Thus IF sets have been applied widely in the field of decision.Although research of intuitionistic fuzzy MADM has made some achievements, the researchs on theory and application are still not deep enough, and there exist many issues which need to be improved and further studied. This article firstly improved existing information measures and ranking functiosn, then developed intuitionistic fuzzy MADM method, and further considered the decision makers’ behavior factors to the new MADM method. Concretely, the main research work of this thesis is as follows:(1) Intuitionistic fuzzy entropy measurement problem and its application in MADM are studied in this thesis. The existing shortcomings of the existing entropy measures are firstly pointed out, then this thesis puts forward new improved intuitionistic fuzzy entropy measures with respect to IF set and interval-valued IF set respectively. The new entropy measures not only consider the absolute value of the deviation between membership and non-membership degrees, but also consider the effect of hesitancy degree of intuitionistic fuzzy sets. For the two cases with attribute weights information unknown and partially known, new weighting methods are put forward by using the extended entropy method and by establishing the minimum entropy optimization model to solve the optimal weights. Further a compromise ratio method of intuitionistic fuzzy MADM problems is put forward, and application examples proved the effectiveness and feasibility of the proposed methods.(2) Research on similarity measures and applications for MADM problems under IF environment. Though analyze the shortcomings of the existing IF similarity measures, new improved similarity measures of IF sets and interval-valued IF set are proposed respectively. New similarity measures consider the impacts of membership, non membership and median point of IF sets or interval-valued IF sets. For the two cases with attribute weights information completely unknown and partly known in MADM problems, two weighting methods:maximizing deviations method and through the establishment of an optimization model for solving the optimal weight maximum similarity, are proposed. Further, new decision making methods are put forward on the basis of proposed similarity measures, and application examples proved the effectiveness and feasibility of the proposed methods.(3) Research on intuitionistic fuzzy number ranking function problems and propose new intuitionistic fuzzy MADM methods based on proposed ranking functions. Through the analysis on the deficiency of the existing ranking functions, three ranking functions with respect to intuitionistic fuzzy numbers, interval intuitionistic fuzzy numbers and intuitionistic trapezoidal fuzzy number are put forward respectively. The ranking functions of intuitionistic fuzzy numbers and interval intuitionistic fuzzy numbers consider the two aspects of information amount and reliability at the same time with the idea of TOPSIS, can give better ranking of fuzzy numbers; for the study of ranking function corresponding to intuitionistic trapezoidal fuzzy number, psychology behavior of the decision maker is described by introducing a attitude factor, the new ranking function can better reflect the actual situation of decision-making process; Further based on the new proposed ranking functions, new weighting methods and MADM methods are poropsed, and application examples proved the effectiveness and feasibility of the proposed methods.(4) Fuzzy MADM methods considering the decision maker’s behavior factors are studied in this thesis. The prospect theory with interactive multiple criteria decision making (TODIM) method are respectly introduced to the intuitionistic trapezoidal fuzzy number MADM problem. For the parameter type trapezoidal intuitionistic fuzzy number, a distance formula and a new ranking function of fuzzy number are firstly put forward, and then for the MADM problem with trapezoidal intuitionistic fuzzy number, the extended TODIM method is proposed, which leads the decision process consider the mentality behavior of decision maker. The advantage of this approach is that the decision maker can mentality and the decision to consider the perceived value of the gains and losses in the decision making process, make the decision making process more accord with the objective reality, and application examples are examined to show that the proposed methods are effective and practical; Aiming at generalized trapezoidal intuitionistic fuzzy number, and a MADM method is put forward combining with prospect theory. According to the given distance formula of trapezoidal intuitionistic fuzzy numbers, firstly the prospect value functions of trapezoidal intuitionistic fuzzy number are calculated through the positive and negative ideal solution as a reference scheme of a different approach to the "profits" and "loss", then the decision maker can obtain more accurate decision weights. In this thesis, the proposed method combining with prospect theory has many advantages, such as clear in concept, simple calculation process and easy realization of software features, thus it has a high practical value.