Saddle Point Optimality Conditions in Fuzzy Optimization Problems

The fuzzy-valued Lagrangian function of constrained fuzzy programming as well as its duality are proposed via a new concept of fuzzy ordering, and the duality theorems are given. At the same time, the sufficient condition for the optimal solution of the fuzzy optimization problem is obtained by virtue of the saddle point of fuzzyvalued Lagrangian function, and the necessary condition for the optimal solution of the convex fuzzy optimization problem is also presented.

[1]  Sudarsan Nanda,et al.  Convex fuzzy mapping with differentiability and its application in fuzzy optimization , 2008, Eur. J. Oper. Res..

[2]  R. Słowiński,et al.  Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty , 1990, Theory and Decision Library.

[3]  Hong Yan,et al.  A class of convex fuzzy mappings , 2002, Fuzzy Sets Syst..

[4]  Hsien-Chung Wu,et al.  Duality theorems and saddle point optimality conditions in fuzzy nonlinear programming problems based on different solution concepts , 2007, Fuzzy Sets Syst..

[5]  E. Lee,et al.  Duality theory in fuzzy mathematical programming problems with fuzzy coefficients , 2005 .

[6]  Hsien-Chung Wu,et al.  Saddle Point Optimality Conditions in Fuzzy Optimization Problems , 2003, Fuzzy Optim. Decis. Mak..

[7]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[8]  C. Hwang,et al.  Fuzzy Multiple Objective Decision Making: Methods And Applications , 1996 .

[9]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[10]  Yong Shi,et al.  Duality in fuzzy multi-criteria and multi-constraint level linear programming: a parametric approach , 2002, Fuzzy Sets Syst..

[11]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[12]  Hsien-Chung Wu,et al.  Duality Theory in Fuzzy Linear Programming Problems with Fuzzy Coefficients , 2003, Fuzzy Optim. Decis. Mak..

[13]  R. Goetschel,et al.  Elementary fuzzy calculus , 1986 .

[14]  R. Słowiński.  Fuzzy sets in decision analysis, operations research and statistics , 1999 .

[15]  H. Zimmermann,et al.  Duality in Fuzzy Linear Programming , 1980 .

[16]  H. Zimmermann.  Fuzzy programming and linear programming with several objective functions , 1978 .

[17]  José L. Verdegay,et al.  Fuzzy Optimization: Recent Advances , 1994 .

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

[19]  D. Dubois,et al.  Operations on fuzzy numbers , 1978 .