Branch Mathematics and Statistics Faculty and Staff Publications
Document Type
Article
Publication Date
2025
Abstract
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.
Language (ISO)
English
Keywords
Soft Set, Indeterm-Soft Set, Hypersoft set, Indeterm-HyperSoft Set, Bipolar Soft Set, Bipolar Hypersoft Set
Recommended Citation
Fujita, Takaaki and Florentin Smarandache. "Navigating Bipolar Indeterminacy: Bipolar IndetermSoft Sets and Bipolar IndetermHyperSoft Sets for Knowledge Representation." (2025). https://digitalrepository.unm.edu/math_fsp/808
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.