Expected value of fuzzy variable and fuzzy expected value models

This paper will present a novel concept of expected values of fuzzy variables, which is essentially a type of Choquet integral and coincides with that of random variables. In order to calculate the expected value of general fuzzy variable, a fuzzy simulation technique is also designed. Finally, we construct a spectrum of fuzzy expected value models, and integrate fuzzy simulation, neural network, and genetic algorithms to produce a hybrid intelligent algorithm for solving general fuzzy expected value models.

[1]  Hans-Jürgen Zimmermann,et al.  Applications of fuzzy set theory to mathematical programming , 1985, Inf. Sci..

[2]  Martin Spott,et al.  A theory of possibility distributions , 1999, Fuzzy Sets Syst..

[3]  A. V. Yazenin,et al.  Fuzzy and stochastic programming , 1987 .

[4]  Baoding Liu,et al.  Chance constrained programming with fuzzy parameters , 1998, Fuzzy Sets Syst..

[5]  Masahiro Inuiguchi,et al.  Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem , 2000, Fuzzy Sets Syst..

[6]  George J. Klir,et al.  On fuzzy-set interpretation of possibility theory , 1999, Fuzzy Sets Syst..

[7]  M. K. Luhandjula Fuzzy optimization: an appraisal , 1989 .

[8]  L. Zadeh Fuzzy sets as a basis for a theory of possibility , 1999 .

[9]  Hans-Jürgen Zimmermann,et al.  Possibility distributions of fuzzy decision variables obtained from possibilistic linear programming problems , 2000, Fuzzy Sets Syst..

[10]  M. Sugeno,et al.  An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy , 1989 .

[11]  Hans-Jürgen Zimmermann,et al.  Applications of fuzzy set theory to mathematical programming , 1985, Inf. Sci..

[12]  Masatoshi Sakawa,et al.  Fuzzy Sets and Interactive Multiobjective Optimization , 1993 .

[13]  D. Dubois,et al.  The mean value of a fuzzy number , 1987 .

[14]  R. Yager On the specificity of a possibility distribution , 1992 .

[15]  Baoding Liu,et al.  Uncertain Programming , 1999 .

[16]  Baoding Liu,et al.  A note on chance constrained programming with fuzzy coefficients , 1998, Fuzzy Sets Syst..

[17]  Baoding Liu,et al.  Dependent-chance programming in fuzzy environments , 2000, Fuzzy Sets Syst..

[18]  M. K. Luhandjula Fuzziness and randomness in an optimization framework , 1996, Fuzzy Sets Syst..

[19]  G. Choquet Theory of capacities , 1954 .

[20]  Michio Sugeno,et al.  Regular fuzzy measure and representation of comonotonically additive functional , 2000, Fuzzy Sets Syst..

[21]  Baoding Liu,et al.  Dependent-chance programming with fuzzy decisions , 1999, IEEE Trans. Fuzzy Syst..

[22]  M. Sugeno,et al.  A theory of fuzzy measures: Representations, the Choquet integral, and null sets , 1991 .

[23]  Alexander V. Yazenin,et al.  On the problem of possibilistic optimization , 1996, Fuzzy Sets Syst..

[24]  D. Schmeidler Integral representation without additivity , 1986 .

[25]  M. Sugeno,et al.  Non-monotonic fuzzy measures and the Choquet integral , 1994 .