An Investigation On Semiorder Rationality Of Georgescu Fuzzy Choice Functions

This paper systematically investigates the relationships between the rationality condi-tions and the semiorder rationality under Georgescu fuzzy choice functions.The conclusions are based on the corresponding conclusions of crisp choice functions and Banerjee fuzzy choice functions.Firstly,the relationships between the rationality conditions of crisp choice functions and the semiorder rationality are introduced in detail.Then,the relationships between the rationality conditions of Banerjee fuzzy choice functions and the semiorder rationality are summarized.All these studies provides the basis for the research on the semiorder rationality of Georgescu fuzzy choice functions.Secondly,the conditions FA1-FA9 in the meanig of Georgescu fuzzy choice functions are redefined.Meanwhile,the relationships between these conditions and the semiorder rationality are systematically discussed.We find that the condition Al,the conditions A8 and A9,the transitivity of revealed preference are equivalent in the crisp choice functions.However,the conclusions can not be extended to Georgescu fuzzy choice functions.For the crisp choice functions,the conditions A4 together with A6 is necessary and sufficient condition for semiorder rationality.But for the semiorder rationality of the Banerjee fuzzy choice functions,the conditions FA4 and FA6 is only sufficient but not necessary condition.And for the semiorder rationality of the Georgescu fuzzy choice functions,the conditions FA4 and FA6 is neither sufficient nor necessary condition.For the further investigation of the semiorder rationality of Georgescu fuzzy choice functions,we obtain the three sufficient conditions which are the rationality of the choice functions and the condition FAl,the rationality of the choice functions and the condition FA8 together with FA9,and the rationality of the choice functions and the condition FA6.Finally,we give some examples to illustrate the conclusions,which are true under the crisp and Banerjee fuzzy choice functions and not hold under the Georgescu fuzzy choice functions.