A Further Study On Reationality Indicators Of Fuzzy Choice Functions

In this thesis, under the assumptions that every involved choice set is normal , and ? is a continuous t-norm, we systematically investigate the connections between some rationality indicators of fuzzy choice functions. Our main work and results are summarized as follows.Firstly, based on the similarity of fuzzy choice functions formulated by Georgescu, we further discuss the links between the similarity of fuzzy choice functions and that of the fuzzy preference relations. Then, we investigate properties of the similarity degrees of various fuzzy revealed preferences and obtain several new results.Secondly, we give a degree description of some rationality conditions of fuzzy choice functions which were introduced by Georgescu, and discuss connections between the rationality indicators of fuzzy choice functions in detail in the sense of both revealed preference and contraction-extension. Note that there exist some crisp results which cannot be extended to the fuzzy case although most conclusions concerning classic rationality conditions of fuzzy choice functions have fuzzy counterparts in the sense of rationality indicators. In view of this, we impose some restrictions on the involved t ?norm, and derive some ideal results related to links between rationality indicators under the Minimum t-norm. Main results include: the WAFRP indicator is equal to WFCA indicator, and both of them are less than the M-normality indicator under the Minimum t-norm.Finally, we introduce two transitive rationality indicators, the transitive G-rationality indicator and the transitive M-rationality indicator. Under the Minimum t-norm, we investigate the relationships between the transitive G-rationality indicator and the Fα2? consistency indicator, the Fβ2?consistency indicator, the FA indicator.In summary, we present a detailed investigation into the relationships between rationality indicators of fuzzy choice functions, and obtain some satisfactory conclusions under our assumptions. Our study is essential to the characterization of the rationalization of fuzzy choice functions.