An Algebraic Approach to Modular Inequalities Based on Interval-Valued Fuzzy Hypersoft Sets via Hypersoft Set-Inclusions

Abstract

Interval-valued fuzzy hypersoft set is an emerging field of study which is projected to address the limitations of interval-valued fuzzy soft set for the entitlement of multiargument approximate function. This kind of function maps the subparametric tuples to power set of universe. It emphasizes on the partitioning of attributes into their respective subattribute values in the form of disjoint sets. These features make it a completely new mathematical tool for solving problems dealing with uncertainties. In this study, after characterization of essential properties, operations, and set-inclusions (L-inclusion and J-inclusion) of interval-valued fuzzy hypersoft set, some of its modular inequalities are discussed via set-inclusions. It is proved that all set-inclusion-based properties and inequalities are preserved when ordinary approximate function of interval-valued fuzzy soft set is replaced with multiargument approximate function of interval-valued fuzzy hypersoft set.