N-bipolar hypersoft sets: Enhancing decision-making algorithms

Abstract

This paper introduces N-bipolar hypersoft (N-BHS) sets, a versatile extension of bipolar hypersoft (BHS) sets designed to effectively manage evaluations encompassing both binary and non-binary data, thereby exhibiting heightened versatility. The major contributions of this framework are twofold: Firstly, the N-BHS set introduces a parameterized representation of the universe, providing a nuanced and finite granularity in perceiving attributes, thereby distinguishing itself from conventional binary BHS sets and continuous fuzzy BHS sets. Secondly, this model signifies a new area of research aimed at overcoming limitations inherent in the N-bipolar soft set when handling multi-argument approximate functions. Through the strategic partitioning of attributes into distinct subattribute values using disjoint sets, the N-BHS set emerges as a powerful tool for effectively addressing uncertainty-related problems. In pursuit of these objectives, the paper outlines various algebraic definitions, including incomplete N-BHS sets, efficient N-BHS sets, normalized N-BHS sets, equivalence under normalization, N-BHS complements, and BHS sets derived from a threshold, exemplified through illustrative examples. Additionally, the article explores set-theoretic operations within the N-BHS sets framework, such as relative null/whole N-BHS sets, N-BHS subsets, and two distinct approaches to N-BHS extended/restricted union and intersection. Finally, it proposes and compares decision-making methodologies regarding N-BHS sets, including a comprehensive comparison with relevant existing models.

A progressive approach to multi-criteria group decision-making: N-bipolar hypersoft topology perspective

“…In addition to Musa’s significant contributions to HS sets, their groundbreaking work on the N -BHS set [ 51 ] is noteworthy. This innovative hybridization of N -HS sets and bipolarity settings enhances HS model capabilities, providing nuanced data representation solutions for non-binary and discrete data structures.…”

“…Definition 6 . [ 51 ] Let ¥ denote a collection of alternatives , ξ be a set representing attributes, and . Let R be a set of ordered grades, specifically R = {0, 1, …, N − 1}, where N ∈ {2, 3, …}.…”

“…Definition 7 [51]. Suppose ðF x ; G :x ; NÞ and ðF 1 NÞ, if ξ � z and Fð�ÞðZÞ � F 1 ð�ÞðZÞ and G 1 ð:�ÞðZÞ � Gð:�ÞðZÞ, 8 � 2 ξ and η 2 ￥.2.…”