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N-bipolar hypersoft sets: Enhancing decision-making algorithms

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  • Sagvan Y Musa

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.

Suggested Citation

  • Sagvan Y Musa, 2024. "N-bipolar hypersoft sets: Enhancing decision-making algorithms," PLOS ONE, Public Library of Science, vol. 19(1), pages 1-24, January.
    • Handle: RePEc:plo:pone00:0296396
    DOI: 10.1371/journal.pone.0296396
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    References listed on IDEAS

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    1. Muhammad Saeed & Muhammad Imran Harl & Muhammad Haris Saeed & Ibrahim Mekawy, 2023. "Theoretical framework for a decision support system for micro-enterprise supermarket investment risk assessment using novel picture fuzzy hypersoft graph," PLOS ONE, Public Library of Science, vol. 18(3), pages 1-26, March.
    2. Sagvan Y. Musa & Baravan A. Asaad, 2021. "Bipolar Hypersoft Sets," Mathematics, MDPI, vol. 9(15), pages 1-15, August.
    3. Haiyan Zhao & Qian Xiao & Zheng Liu & Yanhong Wang, 2022. "An approach in medical diagnosis based on Z-numbers soft set," PLOS ONE, Public Library of Science, vol. 17(8), pages 1-22, August.
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