An Investigation On Quasi-Transitive Rationality Of Fuzzy Choice Functions

In this thesis,we put forward some rational conditions of Georgescu fuzzy choice function.At the same time,we investigate the relations between these rational condi-tions and quasi-transitive rationality.The main work and results are summarized as follows:Firstly,we introduce the relations between rational conditions and quasi-transitive rationality of crisp choice function in detail.As a result,the study provides the basis for the quasi-transitive rationality of fuzzy choice function.Secondly,we summarize the research related to Banerjee fuzzy choice function quasi-transitive rationality systematically.Meanwhile,under the intuitive negation,Banerjee fuzzy choice function quasi-transitive rationality is discussed furthermore.Based on the normal choice function,we also obtain some new conclusions.For exam-ple,T-quasi-transitive rationality is equivalent to the condition F?.Quasi-transitive rationality and condition FA1 are equivalent.If a choice function satisfies one of the conditions FA3,FA4,FA6 and FA7,then the choice function is T-quasi-transitive rational.Lastly,we present some Georgescu fuzzy choice function rationality conditions by means of the fuzzy logic connections.Next,based on the results of crisp choice function and Banerjee fuzzy choice function,we deal with the relations between these rational conditions and quasi-transitive rationality.Based on the different conditions,we ob-tain some necessary and sufficient conditions of quasi-transitive rationality.Meanwhile,some sufficient conditions are proven also.The main conclusions included as follows:Under the intuitive negation,if the fuzzy choice function is the normal,the necessary and sufficient conditions of the quasi-transitive rational are that the choice function satisfy the condition F? or condition FA1,and the sufficient conditions of T-quasi-transitive rationality are that one of the condition FA3,FA4,FA5,FA6,FA7 and FA8 is verified.Under the negation derived from any t-norm,a sufficient condition of T-quasi-transitive rationality is that the normal choice function satisfy the condition F?.And under the strong negation,the sufficient condition is that the normal choice function verify the condition FA9.In summary,this paper researches on the quasi-transitive rationality in the frame-work of Georgescu fuzzy choice function mainly.Eventually,some satisfactory conclu-sions are presented.It is worth noting that some of the results are the extension of the crisp choice function and Banerjee fuzzy choice function,and some are new conclusions that have not been investigated before in the framework of crisp choice function and Banerjee fuzzy choice function.