Fuzzy Sets and Systems - Fuzzy mathematical programming
Fuzzy Optimization: Recent Advances
Fuzzy Optimization: Recent Advances
Stochastic vs. Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty
Stochastic vs. Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty
Fuzzy Mathematical Programming: Methods and Applications
Fuzzy Mathematical Programming: Methods and Applications
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Uncertain bimatrix game with applications
Fuzzy Optimization and Decision Making
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The KKT optimality conditions for multiobjective programming problems with fuzzy-valued objective functions are derived in this paper. The solution concepts are proposed by defining an ordering relation on the class of all fuzzy numbers. Owing to this ordering relation being a partial ordering, the solution concepts proposed in this paper will follow from the similar solution concept, called Pareto optimal solution, in the conventional multiobjective programming problems. In order to consider the differentiation of fuzzy-valued function, we invoke the Hausdorff metric to define the distance between two fuzzy numbers and the Hukuhara difference to define the difference of two fuzzy numbers. Under these settings, the KKT optimality conditions are elicited naturally by introducing the Lagrange function multipliers.