Volume 27 , Issue 2 , PP: 204-222, 2026 | Cite this article as | XML | Html | PDF | Full Length Article
Takaaki Fujita 1 * , Florentin Smarandache 2
Doi: https://doi.org/10.54216/IJNS.270218
A variety of mathematical frameworks—such as fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, soft sets, rough sets, and plithogenic sets—have been developed to model uncertainty, with wide applications in decision making, data analysis, and artificial intelligence. Within soft set theory, extensions like hypersoft sets, indeterm-soft sets, indeterm-hypersoft sets, bipolar soft sets, and bipolar hypersoft sets have further enhanced its expressive power. In this paper, we introduce two new constructs: bipolar indeterm-soft sets and bipolar indeterm-hypersoft sets. We provide their formal definitions, establish key algebraic properties, and demonstrate how they naturally combine bipolar evaluation with inherent indeterminacy. These models offer a versatile toolkit for capturing complex forms of uncertainty and lay the groundwork for future theoretical advances and practical applications in soft set theory.
Soft Set , Indeterm-Soft Set , Hypersoft set , Indeterm-HyperSoft Set , Bipolar Soft Set , Bipolar Hypersoft Set
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