Upper semicontinuous selections for fuzzy mappings in noncompact WPH-spaces with applications

Abstract

In this paper, we introduce the concept of a WPH-space without linear structure and proceed to establish a new upper semicontinuous selection theorem for fuzzy mappings in the framework of noncompact WPH-spaces as well as a special form of this selection theorem in crisp settings. As applications, fuzzy collective coincidence point theorems, fuzzy collectively fixed point theorems, and existence theorems of equilibria for the generalized fuzzy games with three constraint set-valued mappings and generalized fuzzy qualitative games in WPH-spaces are obtained. As their special cases in crisp settings, we derive existence theorems of equilibria for generalized games and generalized qualitative games. Finally, we construct a multiobjective game model for water resource allocation and prove the existence of Pareto equilibria for this multiobjective game based on the existence theorem of equilibria for qualitative games.

Keywords

• wph-space
• fuzzy collective coincidence point
• generalized fuzzy game
• generalized fuzzy qualitative game
• equilibrium point
• water resource allocation