Primal fuzzy programming and inverse fuzzy programming problems

Fuzzy variable is a function from a possibility space to the real line. In this paper, two classes of fuzzy programming problems with fuzzy variable coefficients are presented. The first one is called primal fuzzy programming problem whose objective is a chance function defined by possibility measure, while the second one is called inverse fuzzy programming problem whose objective is a critical value function. Generally, the difficulties of solving the two fuzzy programming problems are different. Thus, to solve the problems effectively, we prove two main results which show solving one of the problems is equivalent to solving its counterpart.

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

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

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

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

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

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

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

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

[9]  Hidetomo Ichihashi,et al.  Relationships between modality constrained programming problems and various fuzzy mathematical programming problems , 1992 .

[10]  Mohammad L. Hussein,et al.  On convex vector optimization problems with possibilistic weights , 1992 .

[11]  Booding Liu,et al.  Minimax Chance Constrained Programming Models for Fuzzy Decision Systems , 1998, Inf. Sci..

[12]  Hidetomo Ichihashi,et al.  Modality constrained programming problems: A unified approach to fuzzy mathematical programming problems in the setting of possibility theory , 1993, Inf. Sci..

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

[14]  Andrey I. Kibzun,et al.  Stochastic Programming Problems with Probability and Quantile Functions , 1996 .

[15]  C. Hwang,et al.  Fuzzy Mathematical Programming: Methods and Applications , 1995 .

[16]  Yu. S. Kan,et al.  On the Equivalence in Stochastic Programming with Probability and Quantile Objectives , 1998 .

[17]  Vladik Kreinovich,et al.  On the formulation of optimization under elastic constraints (with control in mind) , 1996, Fuzzy Sets Syst..

[18]  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..

[19]  J. Buckley,et al.  Fuzzy genetic algorithm and applications , 1994 .

[20]  S. Orlovsky.  On formalization of a general fuzzy mathematical problem , 1980 .

[21]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

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

[23]  Yian-Kui Liu,et al.  Multicriteria expected value models in fuzzy decision systems , 2002, 2002 IEEE World Congress on Computational Intelligence. 2002 IEEE International Conference on Fuzzy Systems. FUZZ-IEEE'02. Proceedings (Cat. No.02CH37291).

[24]  Jaroslav Ramík,et al.  Fuzzy mathematical programming based on some new inequality relations , 1996, Fuzzy Sets Syst..

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

[26]  Peter Kall,et al.  Stochastic Programming , 1995 .