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Convergence analysis of solution sets for fuzzy optimization problems

Authors: Nguyen Van Hung, Võ Minh Tâm, Nguyễn Huy Tuấn, Donal O'Regan, Nguyễn Huy Tuấn, Nguyen Van Hung, Donal O’Regan,

https://doi.org/10.1016/j.cam.2019.112615

Publisher, magazine: ,

Publication year: 2020

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Abstract

In this paper, we first consider fuzzy optimization problem (in short, (FOP)) and sequences of fuzzy optimization problems (in short, (FOP)). Then we establish the concept of -convergence of a sequence of fuzzy mappings and its characterizations. Finally, the Painlevé–Kuratowski lower convergence and the Painlevé–Kuratowski convergence of approximate solution sets for these problems are proposed using -convergence of a sequence of fuzzy mappings. Some examples are provided to illustrate the essentialness of the imposed assumptions.

Tags: fuzzy optimization problems; fuzzy mappings; approximate solution; the Painlevé-Kuratowski convergence; the D-convergence

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