On Unconstrained Fuzzy-Valued Optimization Problems

Abstract In this paper, based on the parametric representation of fuzzy-valued function, an unconstrained fuzzy-valued optimization problem is converted to a general unconstrained optimization problem. Two solutions for the unconstrained fuzzy-valued optimization problem are proposed which are parallel to the concept of efficient solution in the case of multi-objective programming problem. Also it is proven that the optimal solution of its corresponding general unconstrained optimization problem is the optimal solution of original problem. Finally, some numerical examples are given to illustrate the discussed suitability scheme. In the first example, the various solutions are discussed in details and a classic motivating example in the mathematical study of variational inequalities, namely the Elliptic Obstacle Problem, is expressed in the second one. Non-convex Fuzzy Rosenbrock Function have been solved in third example.

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