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

Haishu Lu; Xiaoqiu Liu; Rong Li; Haishu Lu; Xiaoqiu Liu; Rong Li

doi:10.3934/math.2022773

AIMS Mathematics

2022, Volume 7, Issue 8: 13994-14028. doi: 10.3934/math.2022773

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Research article

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

School of Business, Jiangsu University of Technology, Changzhou 213001, Jiangsu, China

Received: 13 October 2021 Revised: 17 May 2022 Accepted: 18 May 2022 Published: 26 May 2022
MSC : 47H04, 47H10, 91A10

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.
- $ WPH $-space,
- fuzzy collective coincidence point,
- generalized fuzzy game,
- generalized fuzzy qualitative game,
- equilibrium point,
- water resource allocation
Citation: Haishu Lu, Xiaoqiu Liu, Rong Li. Upper semicontinuous selections for fuzzy mappings in noncompact $ WPH $-spaces with applications[J]. AIMS Mathematics, 2022, 7(8): 13994-14028. doi: 10.3934/math.2022773

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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.

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