Convergence analysis of solution sets for fuzzy optimization problems

Abstract

In this paper, we first consider fuzzy optimization problem (in short, (FOP)) and sequences of fuzzy optimization problems (in short, (FOP)n). Then we establish the concept of D-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 D-convergence of a sequence of fuzzy mappings. Some examples are provided to illustrate the essentialness of the imposed assumptions.