Set-Theoretic Inequalities Based on Convex Multi-Argument Approximate Functions via Set Inclusion

Abstract

Hypersoft set is a novel area of study which is established as an extension of soft set to handle its limitations. It employs a new approximate mapping called multi-argument approximate function which considers the Cartesian product of attribute-valued disjoint sets as its domain and the power set of universe as its co-domain. The domain of this function is broader as compared to the domain of soft approximate function. It is capable of handling the scenario where sub-attribute-valued sets are considered more significant than taking merely single set of attributes. In this study, notions of set inclusion, convex (concave) sets, strongly convex (concave) sets, strictly convex (concave) sets, convex hull, and convex cone are conceptualized for the multi-argument approximate function. Based on these characterized notions, some set-theoretic inequalities are established with generalized properties and results. The set-theoretic version of classical Jensen’s type inequalities is also discussed with the help of proposed notions.

An intelligent sv-neutrosophic parameterized MCDM approach to risk evaluation based on complex fuzzy hypersoft set for real estate investments

“…(2020b). Rahman et al. (2022a, b) discussed the several properties of convexity under HSS and FHSS environments.…”

An innovative decisive framework for optimized agri-automobile evaluation and HRM pattern recognition via possibility fuzzy hypersoft setting

“…Musa and Asaad 32 studied the bi-polarity of hs -set by developing a novel structure called bipolar hs -set and discussed its set-theoretic operations. Rahman et al 33–37 applied the concept of fhs -set in real world DM scenarios like medical diagnosis for heart diseases, set-theoretic and modular inequalities, supplier selection and risk analysis for real estate projects respectively. Ihsan et al 38,39 investigated various set-theoretic characteristics, set operations, and applications of hypersoft hybrids with an expert set environment to tackle with multi-decisive opinions of experts.…”

Retracted: Set-Theoretic Inequalities Based on Convex Multi-Argument Approximate Functions via Set Inclusion

“…This article has been retracted by Hindawi following an investigation undertaken by the publisher [1]. This investigation has uncovered evidence of one or more of the following indicators of systematic manipulation of the publication process:…”