The Characterization Of Transitive Rationality And Quasitransitive Rationality Of Fuzzy Choice Functions

Both transitive rationality and quasitransitive rationality are two extremely important rationality properties no matter whether the involved choice function is crisp or not. In the thesis, we enrich and complete the current investigations into transitive rationality and quasitransitive rationality of crisp choice functions by suggesting some new rationality conditions. For the research of fuzzy choice functions, we put forth some conditions that can characterize transitive rationality of fuzzy choice functions. Finally, some existing rationality conditions are fuzzified so that necessary or sufficient conditions are proposed to characterize transitive or quasitransitive rationality. The main research work isdescribed in detail in the following:Firstly, we complete Suzumura's investigations into relationships between two kinds of normality and two kinds of rationality properties for crisp choice functions and prove the equivalency of these four definitions. Afterwards, the concepts of fuzzy greatest set and fuzzy maximal set are introduced and three kinds of normality and three kinds...