Optimality Criteria for Fuzzy Pseudo Convex Functions

Behera, Sanjaya Kumar

doi:10.17485/ijst/2014/v7i7.3

Cited by 4 publications

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“…Although convexity notion plays a key role in fuzzy optimization theory, however, this concept is very strict and, therefore, the area of its applications is limited. Recently, therefore, different types of generalized convexity notions for fuzzy mappings have been defined and used also for proving optimality and duality results for various classes of nonconvex fuzzy optimization problems (see, for example, Behera and Nayak 2014;Arana-Jiménez et al 2015;Mishra et al 2006;Noor 1994;Osuna-Gómez et al 2016;Rufián-Lizana et al 2012;Syau 1999Syau , 2000Syau , 2001.…”

Section: Introductionmentioning

confidence: 99%

Optimality conditions for invex nonsmooth optimization problems with fuzzy objective functions

Antczak

2022

Fuzzy Optim Decis Making

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In this paper, the definitions of Clarke generalized directional $$\alpha $$ α -derivative and Clarke generalized gradient are introduced for a locally Lipschitz fuzzy function. Further, a nonconvex nonsmooth optimization problem with fuzzy objective function and both inequality and equality constraints is considered. The Karush-Kuhn-Tucker optimality conditions are established for such a nonsmooth extremum problem. For proving these conditions, the approach is used in which, for the considered nonsmooth fuzzy optimization problem, its associated bi-objective optimization problem is constructed. The bi-objective optimization problem is solved by its associated scalarized problem constructed in the weighting method. Then, under invexity hypotheses, (weakly) nondominated solutions in the considered nonsmooth fuzzy minimization problem are characterized through Pareto solutions in its associated bi-objective optimization problem and Karush-Kuhn-Tucker points of the weighting problem.

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