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

Mamika Ujianita Romdhini; Faisal Al-Sharqi; R.H. Al-Obaidi; Zahari Md. Rodzi

Authors

Mamika Ujianita Romdhini Department of Mathematics, Faculty of Mathematics and Natural Science, University of Mataram, Mataram, 83125,INDONESIA;
Faisal Al-Sharqi Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, 55431, Iraq;
R.H. Al-Obaidi Fuel and Energy Techniques Engineering Department, College of Engineering and Technologies, Al-mustaqbal University, 51001, Babylon, Iraq;
Zahari Md. Rodzi College of Computing, Informatics and Mathematics, UiTM Cawangan Negeri Sembilan, Kampus Seremban, 72000 Negeri Sembilan, Malaysia;

Keywords:

Interval-valued fuzzy set; soft set; hypersoft set; interval-valued fuzzy hypersoft set; similarity measures; decision-making ; possibility interval-valued fuzzy hypersoft set.

Abstract

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.

DOI: 10.5281/zenodo.14121031