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
Duality Theory in Fuzzy Optimization Problems
Fuzzy Optimization and Decision Making
Scalarization of the fuzzy optimization problems
Fuzzy Optimization and Decision Making
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Duality theory in fuzzy optimization problems formulated by the Wolfe's primal and dual pair
Fuzzy Optimization and Decision Making
Fuzzy Optimization and Decision Making
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The optimality conditions for multiobjective programming problems with fuzzy-valued objective functions are derived in this paper. The solution concepts for these kinds of problems will follow the concept of nondominated solution adopted in the multiobjective programming problems. In order to consider the differentiation of fuzzy-valued functions, 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 optimality conditions for obtaining the (strongly, weakly) Pareto optimal solutions are elicited naturally by introducing the Lagrange multipliers.