A Study On Pseudo-Transitive Rationality Of Fuzzy Choice Functions

In this thesis,we carry out a detailed study on the pseudo-transitive rationality of Georgescu fuzzy choice functions.Some sufficient conditions for pseudo-transitive rationality are proposed and the relationships of these conditions are investigated.Firstly,we systematically introduce rationality conditions of crisp choice functions,and review conclusions related to the necessary and sufficient conditions of pseudo-transitive ra-tionality,which provide the theoretical basis for the corresponding study in fuzzy case.Secondly,we fuzzify rationality conditions of crisp choice functions,and with the assump-tion of the normal choice sets,discuss the relationships between some rationality conditions and the pseudo-transitive rationality of Georgescu fuzzy choice functions.The specific inves-tigation and main results are summarized as follows:(1)In crisp case,the normality and the Condition A3 of choice functions are equivalent to pseudo-transitive rationality.We directly fuzzify A3 as FA3,and show that the normality and FA3 are still sufficient conditions of pseudo-transitive rationality in fuzzy case,but the Condition FA3 is not a necessary condition any more.(2)In crisp case,the Condition W2 is equivalent to pseudo-transitive rationality,which can not be extended to fuzzy case while fuzzifying W2 as FW2.We strengthen the conditions by adding normality condition,and show that the normality and FW2 imply pseudo-transitive rationality of fuzzy choice functions,but the Condition FW2 is not necessary condition any more.(3)In crisp case,the Condition A4 and A5 are equivalent to pseudo-transitive rationality,which can not be extended to fuzzy case while fuzzifying A4 and A5 as FA4 and FA5.In this case,the normality,FA4 and FA5 aren't still sufficient conditions of pseudo-transitive rationality although we strengthen the conditions by adding normality.(4)For the completeness of the study,we supply some examples to show that these conditions are independent in fuzzy case(although they are equivalent in crisp case).