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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.

@article{wu_karush-kuhn-tucker_2009, title = {The {Karush}-{Kuhn}-{Tucker} {Optimality} {Conditions} for {Multi}-{Objective} {Programming} {Problems} with {Fuzzy}-{Valued} {Objective} {Functions}}, volume = {8}, issn = {1568-4539, 1573-2908}, url = {http://link.springer.com/10.1007/s10700-009-9049-2}, doi = {10/cfx6xv}, abstract = {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.}, language = {en}, number = {1}, urldate = {2022-06-12}, journal = {Fuzzy Optimization and Decision Making}, author = {Wu, Hsien-Chung}, month = mar, year = {2009}, note = {38 citations (Semantic Scholar/DOI) [2022-06-12]}, keywords = {/unread}, pages = {1--28}, }

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