Extending Classical Uncertainty Models via Hyperpolar
Structures: Fuzzy, Neutrosophic, and Soft Set Perspectives
Takaaki Fujita1,∗, Arif Mehmood2
1Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan
2Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan 29050,
KPK, Pakistan
Emails: Takaaki.fujita060@gmail.com; mehdaniyal@gmail.com
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 Neu-
trosophic 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 in-
tegrate 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