A Study On The Fuzzification Of Schwartz's Theory

In the study of individual or collective choice, one often requires the choice function to fulfill certain so-called "rationality" conditions formulated in terms of binary relations. As a result, the rationality of choice function has been one of the most commonly addressed issues in the choice theory. It can be seen from the existing literature that there are a lot of research on the rationality of crisp choice function, the conclusions are relatively complete; while the study on fuzzy cases is merely limited to a class of special rationality (transitivity rationality), thus the research is still in its infancy. In view of this, based on the Schwartz's rationality conditons we discuss the rationality of fuzzy choice functions in detail in this thesis. The main research is summarized as follows.First, we systematically review the research related to rationality of crisp choice functions and expose the relationships between these conclusions,...