Research On Methods Of Intuitionistic Fuzzy Reasoning And Decision-making

The concept of Intuitionistic fuzzy sets is an extension of Zadeh's fuzzy sets. Because of the nonmembership function, the Intuitionistic fuzzy sets can express uncertainty better than the ordinary ones. The Fuzzy reasoning problem and Multiple attribute decision making problem are studied in this paper. TripleⅠmethod and MultipleⅠmethod based on pointwise sustaining degree on Intuitionistic fuzzy sets are established. A new kind of TOPSIS method for multiple attribute decision making problems with intuitionistic fuzzy valued elements of the decision matrix and real number weights, as well as those with intuitionistic fuzzy valued elements of the decision matrix and weights is proposed. This paper contains three chapters as follows:Chapter 1 introduces the concepts of Intuitionistic fuzzy sets,L-(L*-) fuzzy sets and interval-valued fuzzy sets and the links between the different models. Situations of studies of TripleⅠmethod and TOPSIS method on Intuitionistic fuzzy sets are reviewed.In Chapter 2, TripleⅠmethod and MultipleⅠmethod based on pointwise sustaining degree on Intuitionistic fuzzy sets are considered. The concepts of residual pair (Def. 2.14) and pointwise sustaining degree (Def. 2.19) on Intuitionistic fuzzy sets are defined. Based on these concepts, the Intuitionistic Fuzzy Modus Ponens (IFMP) and the Intuitionistic Fuzzy Modus Tollens (IFMT) problems are discussed.α(u,v)-tripleⅠIFMP principle andα(u,v)-tripleⅠIFMT principle are given,α(u,v)-tripleⅠIFMP method (Th. 2.7) andα(u,v)-tripleⅠIFMT method (Th. 2.11) are established and the reversibility (Th. 2.8) and continuity (Th.2.9) of triple I IFMP method are proved. Then, by extending the conclusions of IFMP problem to the generalized Intuitionistic fuzzy reasoning problem, theα(u1,u2,v)-multipleⅠprinciple is given and theα(u1,u2,v)-multipleⅠmethod (Th. 2.14) is proved which is generalized to a(u1,…,un,v)-multipleⅠmethod (Th. 2.15) later. Compared with the previous methods, the new methods do not ask the implications to be the residual implications generalized by Intuitionistic fuzzy triangular norms which satisfy the residual principle. It extends the applied range of the new methods greatly that they only require the implications fulfil the theorems'conditions.In Chapter 3, the multiple attribute decision making problem on Intuitionistic fuzzy sets is studied. A new kind of TOPSIS method for multiple attribute decision making problems with intuitionistic fuzzy values of elements of the decision matrix and real number weights, as well as those with intuitionistic fuzzy valued elements of the decision matrix and weights is proposed. New methods to construct the Intuitionistic fuzzy weighted decision matrix are established. By distinguishing the Intuitionistic index, which expresses the uncertainty, with membership tendency from those with nonmembership tendency in different kinds attibutes (benefit attributes or cost attributes), four positive and negative ideal solutions computing methods are given. Two numerical examples are computed in this chapter.The innovations in this paper can be summarized as follows:1. The concept of Intuitionistic fuzzy pointwise sustaining degree is defined;2. TripleⅠIFMP/IFMT methods and MultipleⅠmethod based on pointwise sustaining degree are established;3. New methods to construct the Intuitionistic fuzzy weighted decision matrix are established and new kinds of ideal sulusions computing methods for Intuitionistic fuzzy TOPSIS are given.