Optimality conditions in nondifferentiable fuzzy optimization

Abstract In the present paper, an optimal solution of a nondifferentiable fuzzy optimization problem is characterized to be fuzzy. We use the -cut to attack the fuzzy optimization problem. Then, a bicriterial optimization problem arises. Thus, the solution of the fuzzy optimization problem turns out to be Pareto optimal for the bicriterial optimization problem. This approach is used to derive necessary and sufficient optimality conditions for the optimal solution of the nondifferentiable fuzzy optimization problem.

[1]  丸山 徹.  Convex Analysisの二,三の進展について , 1977 .

[2]  H. Rommelfanger,et al.  Linear programming with fuzzy objectives , 1989 .

[3]  Jörg Fliege,et al.  Gap-free computation of Pareto-points by quadratic scalarizations , 2004, Math. Methods Oper. Res..

[4]  Hsien-Chung Wu,et al.  The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function , 2007, Eur. J. Oper. Res..

[5]  Janusz Kacprzyk,et al.  Management decision support systems using fuzzy sets and possibility theory , 1985 .

[6]  E. Polak,et al.  On Multicriteria Optimization , 1976 .

[7]  Stephan Dempe,et al.  On the calculation of a membership function for the solution of a fuzzy linear optimization problem , 2012, Fuzzy Sets Syst..

[8]  S. Chanas,et al.  Multiobjective programming in optimization of interval objective functions -- A generalized approach , 1996 .

[9]  Lotfi A. Zadeh,et al.  Optimality and non-scalar-valued performance criteria , 1963 .

[10]  Tapan Kumar Pal,et al.  Solving the Shortest Path Problem with Interval Arcs , 2006, Fuzzy Optim. Decis. Mak..

[11]  Jakub Duda,et al.  ON D.C. FUNCTIONS AND MAPPINGS , 2001 .

[12]  Hsien-Chung Wu.  The optimality conditions for optimization problems with fuzzy-valued objective functions , 2008 .

[13]  H. Ishibuchi,et al.  Multiobjective programming in optimization of the interval objective function , 1990 .

[14]  Charles Audet,et al.  Multiobjective Optimization Through a Series of Single-Objective Formulations , 2008, SIAM J. Optim..

[15]  Tapan Kumar Pal,et al.  On comparing interval numbers , 2000, Eur. J. Oper. Res..

[16]  Ying Xiong.  Nonlinear Optimization , 2014 .

[17]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[18]  M. Wiecek,et al.  Minimum Effort Approximation of the Pareto Space of Convex Bi-Criteria Problems , 2003 .

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

[20]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[21]  R. Rockafellar.  Convex Analysis: (pms-28) , 1970 .

[22]  Gordon Whyburn,et al.  Functions and Mappings , 1979 .

[23]  M. K. Luhandjula.  Fuzzy optimization: Milestones and perspectives , 2015, Fuzzy Sets Syst..

[24]  H. Zimmermann,et al.  Fuzzy Set Theory and Its Applications , 1993 .

[25]  Hsien-Chung Wu,et al.  An (α ,β)-Optimal solution concept in Fuzzy Optimization problems , 2004 .