模糊选择函数拟传递合理性的研究
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摘要
本文在Georgescu模糊选择函数意义下,研究了一些模糊合理性条件之间的关系及模糊选择函数的拟传递合理性。首先,给出了模糊选择函数合理性条件FA1,条件FA2与条件Fγ的定义,研究了模糊选择函数G-合理性与条件FA1之间的关系。其次对合理性条件FA2,条件FPI及条件Fδ之间的关系进行了详细的讨论。最后得出了模糊选择函数拟传递合理的三个充分条件。
In this paper,we deal with the fuzzy rationality conditions and quasi-transitive rationality of fuzzy choice function in the framework of the Georgescu fuzzy choice functions.Firstly,the definitions of the rationality conditions of fuzzy choice functions FA1,FA2 and Fγare given,and the connections between the rationality of fuzzy choice function and FA1 are investigated.Then,the relationships between fuzzy rationality conditions FA1,FA2 and Fγare discussed detailedly.Lastly,three sufficient conditions on the quasi-transitive rationality of fuzzy choice function are made.
In this paper,we deal with the fuzzy rationality conditions and quasi-transitive rationality of fuzzy choice function in the framework of the Georgescu fuzzy choice functions.Firstly,the definitions of the rationality conditions of fuzzy choice functions FA1,FA2 and Fγare given,and the connections between the rationality of fuzzy choice function and FA1 are investigated.Then,the relationships between fuzzy rationality conditions FA1,FA2 and Fγare discussed detailedly.Lastly,three sufficient conditions on the quasi-transitive rationality of fuzzy choice function are made.
引文
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[12]Georgescu I.fuzzy choice functions[M].Berlin:Springer-Verlag,2007.
[13]Martinetti D,Montes S,Diaz S,De Baets B.On Arrow-Sen style equivalences between rationality conditions for fuzzy choice functions[J].Fuzzy Sets Syst,2014,239:35~50.
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[16]张会娟,王绪柱,麻晓波,郭元春.模糊选择函数的合理性及拟传递合理性的刻画[J].模糊系统与数学,2006,(4):68~73.
[2]Sen A K.Choice functions and revealed preference[J].Review of Economic Studies,1971,38:307~317.
[3]Aizerman M A,Malishevski A V.General theory of best variants choice:Some aspects[J].IEEE Transactions Automatic Control,1981,26:1030~1040.
[4]Nehring K.Choice and revealed preference without binariness[J].Social Choice and Welfare,1997,14:403~425.
[5]Jamison D T,Lau L J.Semiorders and the theory of choice[J].Econometrica,1973,41:901~912.
[6]Suzumura K.Rational choice,collective decisions and social welfare[M].Cambridge University Press,1993.
[7]Banerjee A.Fuzzy choice functions,revealed preference and rationality[J].Fuzzy Sets and Systems,1995,70:31~43.
[8]张会娟,张强,王绪柱.直觉非下模糊合理性选择函数的刻画[J].北京理工大学学报,2008,9:834~837.
[9]Georgescu I.Rational and congruous fuzzy consumers[C]//Proceeding of the International Conference on Fuzzy Information Proceedings,Theory and Applications,Beijing,2003:133~137.
[10]Hájek P.Metamathematics of fuzzy logic[M].Dordrecht/Boston/London:Kluwer Academic Publisher,1998.
[11]Baczyński M,Jayaram B.Fuzzy implications[M].Berlin/Heidelberg:Springer-Verlag,2008.
[12]Georgescu I.fuzzy choice functions[M].Berlin:Springer-Verlag,2007.
[13]Martinetti D,Montes S,Diaz S,De Baets B.On Arrow-Sen style equivalences between rationality conditions for fuzzy choice functions[J].Fuzzy Sets Syst,2014,239:35~50.
[14]于福生,罗承忠.模糊集差运算[J].北京师范大学学报,1998,1:45~47.
[15]Kaufmann A.Introduction to the theory of fuzzy subsets[M].New York:Academic Press,1975.
[16]张会娟,王绪柱,麻晓波,郭元春.模糊选择函数的合理性及拟传递合理性的刻画[J].模糊系统与数学,2006,(4):68~73.