Modeling uncertainties associated with decision-making algorithms based on similarity measures of possibility belief interval-valued fuzzy hypersoft setting

Hypersoft sets (HSSs) were initiated as an extension of soft sets (SSs) to address real-life scenarios involving multiple disjoint sets with di erent traits. One such extension is the interval-valued fuzzy hypersoft set (IVFHSS), which has proven e ective in decision-making (DM). However, the IVFHSS model lacks a mech anism to incorporate the degree of acceptance of DM opinions, which is crucial for accurate decision-making. To overcome this limitation, our work aims to develop a novel hyperstructure called a possibility interval-valued fuzzy hypersoft set (PIVFHS-set). We begin by introducing essential operations and their properties, such as PIVFHS-subset, PIVFHS-null set, PIVFHS-absolute set, and complement of a PIVFHS-set. These concepts are illustrated through numerical examples to demonstrate their practical applications. Next, we delve into set-theoretic operations of PIVFHS sets, including union, intersection, AND, OR, and relevant laws. These op erations are further elucidated through numerical examples, matrix representations, and graphical illustrations. Additionally, we present two algorithms based on AND and OR operations, providing step-by-step explana tions and showcasing their e ectiveness through illustrative examples. Furthermore, we introduce a similarity measure to facilitate pattern recognition in PIVFHS-sets, aiding users in recruitment processes. Alongside an analytical study of the advantages and disadvantages of this model, we provide suggestions for future research based on the identi ed limitations.