On semi-continuity and continuity of solution maps of parametric generalized multiobjective games in fuzzy environments

Abstract

The purpose of this article is to study new results on the continuity of solution maps for parametric generalized multiobjective games in fuzzy environments. Firstly, we revisit parametric fuzzy generalized multiobjective games. Secondly, we establish some sufficient conditions for upper semi-continuity, Hausdorff upper semi-continuity, closedness and compactness of solution maps for such problem under suitable conditions. Thirdly, we introduce the auxiliary problem of parametric fuzzy generalized multiobjective games and the concept of strong $K_i$-convexity of objective functions for these problems. Finally, results on the lower semi-continuity, Hausdorff lower semi-continuity, continuity and Hausdorff continuity of solution maps to parametric generalized multiobjective games in fuzzy environments are established and studied. Many examples are given to illustrate our results.