Abstract
The fuzzy-valued Lagrangian function of fuzzy optimization problem via the concept of fuzzy scalar (inner) product is proposed. A solution concept of fuzzy optimization problem, which is essentially similar to the notion of Pareto solution in multiobjective optimization problems, is introduced by imposing a partial ordering on the set of all fuzzy numbers. Under these settings, the saddle point optimality conditions along with necessary and sufficient conditions for the absence of a duality gap are elicited.
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Wu, HC. Saddle Point Optimality Conditions in Fuzzy Optimization Problems. Fuzzy Optimization and Decision Making 2, 261–273 (2003). https://doi.org/10.1023/A:1025098722162
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DOI: https://doi.org/10.1023/A:1025098722162