Hybrid Fixed Point Theorems of Fuzzy Soft Set-Valued Maps with Applications in Integral Inclusions and Decision Making

A lot of work has been completed in efforts to extend the notions of soft set and fuzzy soft set and their applications to other domains. However, neither of the two concepts has been examined in the study of functional equations in b-metric spaces. Given this background information, this paper proposes the idea of b-hybrid fuzzy soft contraction in b-metric space and investigates new criteria for the existence of fixed points for such mappings. The significance of the obtained principal result lies in the fact that the contractive inequalities can be specialized in various ways, depending on the choice of the parameters, thereby making it possible to unify, deduce, and refine several corresponding results. To motivate further studies in the directions studied herein, two applications regarding decision-making problems and an existence theorem of integral inclusion are considered, using fuzzy soft set-valued maps.

Automated summary

A new concept called b-hybrid fuzzy soft contraction in b-metric space is proposed in this study, and new criteria for the existence of fixed points for such mappings are investigated. The significance of the obtained principal result lies in the ability to specialize the contractive inequalities in various ways, depending on the choice of parameters, thereby unifying, deducing, and refining several corresponding results. Two applications regarding decision-making problems and an existence theorem of integral inclusion using fuzzy soft set-valued maps are considered to motivate further studies.