An inclusive study on the fundamentals of interval-valued fuzzy hypersoft set

Abstract

When compared to its extension, hypersoft set, a soft set only deals with a single set of attributes, while a hypersoft set deals with several attribute-valued disjoint sets that correspond to various attributes. Several researchers have developed models based on soft sets, but the majority of these models suffer from limitations since they are inappropriate for interval-type data or uncertain data. In order to address these issues, a novel model interval-valued fuzzy hypersoft set (IV F HS -set) is presented in this research article. This model not only resolves the inadequacy of soft set for distinct attributes for non-overlapping attribute-valued sets, but also addresses the limitations of soft set-like models with having data in interval environment. This work modifies the current fuzzy hypersoft set concept and introduces certain fundamental ideas, such as subset, not set, whole set, and absolute relative null set, relative absolute set and aggregation operations e.g. intersection, union, extended intersection, restricted union, complement, OR, AND, difference, restricted difference are discussed under IV F HS -set environment with illustrated examples. Some new hybrids of fuzzy hypersoft set under interval-valued settings are also discussed. Moreover, some extensions of IV F HS -set are presented along with different operations.

Theoretical framework for a decision support system for micro-enterprise supermarket investment risk assessment using novel picture fuzzy hypersoft graph

“…The properties of HSS were developed by Saeed et al (i.e., HS subset, union, intersection, etc.) and developed hybrids of this HSS structure with structures from fuzzy and neutrosophic set theory [ 7 , 8 ]. Literature does revela some fuzzy hyperosft hybrid structures including Pythagorean fuzzy hypersoft set and Intuitionistic Fuzzy Hypersoft Set (IFHSS) which is a generalized version of the Intuitionistic Fuzzy Soft Set (IFSS) [ 9 , 10 ].…”

An Intelligent Multiattribute Decision-Support Framework Based on Parameterization of Neutrosophic Hypersoft Set

“…erefore, Smarandache [23] presented the notion of hypersoft set (hs-set) which is capable of handling such situations by using a new approximate mapping having multiargument domain. In order to utilize hs-set in other fields of study, its various basic properties, relations, and matrices have been investigated in [24] with the help of supporting examples. Debnath [25] discussed the decision-making application based on weightage operators of fuzzy hypersoft set.…”

An intelligent multiple-criteria decision-making approach based on sv-neutrosophic hypersoft set with possibility degree setting for investment selection

“…Since its development, HSS has earned the keen interest of many researchers so far. For the sake of its applicability in other branches and disciplines, its several elementary operational properties and axiomatic operations have been characterized in Saeed et al. (2021a).…”

“…Since its development, HSS has earned the keen interest of many researchers so far. For the sake of its applicability in other branches and disciplines, its several elementary operational properties and axiomatic operations have been characterized in Saeed et al (2021a). The ideas of neutrosophic hypersoft set (NHSS) and single-valued neutrosophic hypersoft set (sv-NHSS) (Smarandache, 2018) have been developed to adequate NSS with MAA-mapping environment.…”