Fuzzy Integrals And Its Application Of Linguistic Qantifiers And Decision-making Sciences

In recent years, with the constant development of the theory of fuzzy integrals, the application problems of the related various fields can be realized, especially in clustering analysis, system evaluations, decision sciences, linguistic quantifiers, etc. Based on the semantic of Sugeno integral, M. S. Ying proposed a novel approach to model linguistic quantifiers, in this model, each quantifier is represented by a family of fuzzy mrasures indexed by nonempty sets, and the truth value of a quantified proposition is evaluated by using Sugeno integral. Due to the uncertainty and fuzziness of decision processes, the fuzzy integrals also widely used in multi-attribute decision-making with linguistic quantifiers.The paper mainly discusses the extension of the integral semantic of linguistic quantifiers and application of fuzzy integral in decision-making, the achievements of this paper mainly include:(1) this paper generalizes M.S. Ying's model of linguistic quantifiers based on Sugeno integrals to generalized Sugeno integrals (generalized Sugeno integrals refers to the Sugeno integral form of"min"substituting for"t-norm"), in this model, linguistic quantifiers is represented by a family fuzzy measures, the truth value of a quantified proposition is evaluated by using generalized Sugeno integral, and obtain the logical properties of the first order language with linguistic quantifiers(including the theorem of a weak prenex normal and decomposition, etc.).(2) this paper further expands the integral semantic theory of linguistic quantifiers, and interval-valued intuitionistic fuzzy integral is used in dealing with linguistic quantifiers, and establishs the model of interval-valued intuitionistic Sugeno integral semantic of linguistic quantifiers. In this model, and interval-valued intuitionistic linguistic quantifiers is represented by a family fuzzy interval-valued intuitionistic measures, and the truth value of a quantified proposition (the interval of the degree of satisfaction and non- satisfaction) is evaluated by using interval-valued intuitionistic Sugeno integral, and discusses the logical properties of the first order language with interval-valued intuitionistic linguistic quantifiers, and obtain the corresponding theorem of a prenex normal.(3) Based on the above two models of linguistic quantifiers, this paper applies the fuzzy integrals in multi-attribute decision-making with linguistic quantifiers, and respectively provides the new mehuod of multi-attribute decision-making in the fuzzy information environment and the interval-valued intuitionistic fuzzy information environment, and gives some corresponding application examples.