Galoitica: Journal of Mathematical Structures and Applications

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Volume 12 , Issue 2 , PP: 24-39, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Extending Classical Uncertainty Models via Hyperpolar Structures: Fuzzy, Neutrosophic, and Soft Set Perspectives

Takaaki Fujita 1 * , Arif Mehmood 2

  • 1 Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan - (Takaaki.fujita060@gmail.com)
  • 2 Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan 29050, KPK, Pakistan - (mehdaniyal@gmail.com)
  • Doi: https://doi.org/10.54216/GJMSA.120202

    Received: February 13, 2025 Revised: June 05, 2025 Accepted: August 10, 2025
    Abstract

    Concepts such as the Fuzzy Set, Neutrosophic Set, and Soft Set are known for handling uncertainty. As extensions of Fuzzy Sets, Neutrosophic Sets, and Soft Sets, concepts such as Bipolar Fuzzy Sets, Bipolar Neutrosophic Sets, and Bipolar Soft Sets have been introduced. In this paper, we further extend these notions and explore Hyperpolar Fuzzy Sets, Hyperpolar Neutrosophic Sets, and Hyperpolar Soft Sets. These structures integrate multi-perspective or multi-agent evaluations into a unified framework by leveraging higher-dimensional mappings and hypercubic representations. This work lays a theoretical foundation for advanced uncertainty modeling in complex, multi-source environments.

    Keywords :

    Soft Set , Fuzzy Set , Neutrosophic Set , Hyperpolar Fuzzy Set , Hyperpolar Neutrosophic Set , Hyperpolar Soft Set

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    Cite This Article As :
    Fujita, Takaaki. , Mehmood, Arif. Extending Classical Uncertainty Models via Hyperpolar Structures: Fuzzy, Neutrosophic, and Soft Set Perspectives. Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , 2025, pp. 24-39. DOI: https://doi.org/10.54216/GJMSA.120202
    Fujita, T. Mehmood, A. (2025). Extending Classical Uncertainty Models via Hyperpolar Structures: Fuzzy, Neutrosophic, and Soft Set Perspectives. Galoitica: Journal of Mathematical Structures and Applications, (), 24-39. DOI: https://doi.org/10.54216/GJMSA.120202
    Fujita, Takaaki. Mehmood, Arif. Extending Classical Uncertainty Models via Hyperpolar Structures: Fuzzy, Neutrosophic, and Soft Set Perspectives. Galoitica: Journal of Mathematical Structures and Applications , no. (2025): 24-39. DOI: https://doi.org/10.54216/GJMSA.120202
    Fujita, T. , Mehmood, A. (2025) . Extending Classical Uncertainty Models via Hyperpolar Structures: Fuzzy, Neutrosophic, and Soft Set Perspectives. Galoitica: Journal of Mathematical Structures and Applications , () , 24-39 . DOI: https://doi.org/10.54216/GJMSA.120202
    Fujita T. , Mehmood A. [2025]. Extending Classical Uncertainty Models via Hyperpolar Structures: Fuzzy, Neutrosophic, and Soft Set Perspectives. Galoitica: Journal of Mathematical Structures and Applications. (): 24-39. DOI: https://doi.org/10.54216/GJMSA.120202
    Fujita, T. Mehmood, A. "Extending Classical Uncertainty Models via Hyperpolar Structures: Fuzzy, Neutrosophic, and Soft Set Perspectives," Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , pp. 24-39, 2025. DOI: https://doi.org/10.54216/GJMSA.120202