A Further Study On Rationality Conditions Of Fuzzy Choice Functions

In this thesis, under the assumption that every involved choice set is normal, we systematically investigate the connections between some rationality conditions of fuzzy choice functions. Our main work and results are summarized as follows.Firstly, we systematically review the existing research related to rationality conditions of crisp choice functions and discuss the relationships between these rationality conditions. And then, we carry out research on some rationality conditions and obtain several new results. As a consequence, the rationality research of crisp choice functions is completed.Secondly, we put forward some rationality conditions for fuzzy choice functions by means of fuzzy logic connectives. Based on the conclusions for crisp choice functions, we discuss links between the corresponding rationality conditions of fuzzy choice functions in detail by both revealed preference and contract-expansion approach. As a consequence, some work done by Sen, Suzumura et al. is generalized. The major result is that a fuzzy choice function satisfies WFCA is equivalent to that the choice function satisfies Fα, Fβcondition.We notice that almost all conclusions concerning crisp choice functions can be extended to fuzzy case under our assumption. However, there indeed exist some results that are true in crisp case, but not valid any longer when choice functions are fuzzified. In view of this, we impose some restrictions on fuzzy choice functions, and derive some ideal results. With this consideration. we investigate the relationships between rationality conditions under some special t-norms. We draw the conclusion that a fuzzy choice function satisfies WAFRP is equivalent to that the choice function satisfies WFCA condition under the De Morgan triple and that Fa is equivalent to FC condition under the Godel t-norm.In summary, we present a detailed investigation into the relationships between rationality conditions of fuzzy choice functions, and obtain some satisfactory conclusions under our assumptions. The study is essential to the characterization of fuzzy choice functions' rationalization.