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Optimality conditions in nondifferentiable fuzzy optimization. (English) Zbl 1342.90230

The study is concerned with a class of nondifferentiable fuzzy optimization problems described in the following form \[ f(x)\to \text{Min},\qquad g(x)\leq 0, \] where the objective function \(f\) assumes fuzzy values by mapping \(\mathbb{R}^n\) to the space of fuzzy numbers and the constraint \(g: \mathbb{R}^n\to\mathbb{R}^k\) is a numeric mapping. The nondifferentiability of the problem stems from the fact that objective function or constraints are nondifferentiable.
The objective function is described by a collection of \(\alpha\)-cuts. A set of optimal solutions to the fuzzy optimization problem is presented through the set of Pareto optimal solutions of the corresponding bicriterial optimization problem. The question of local optimality of the optimal solution is discussed. Necessary and sufficient optimality conditions for the solution to the nondiferentiable fuzzy optimization problem are also provided. An illustrative numeric example is presented as well.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C46 Optimality conditions and duality in mathematical programming
90C30 Nonlinear programming
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