International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/4060 2020 2020 Navigating Bipolar Indeterminacy: Bipolar IndetermSoft Sets and Bipolar IndetermHyperSoft Sets for Knowledge Representation Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan Takaaki Takaaki University of New Mexico, Gallup Campus, NM 87301, USA Florentin Smarandache 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. 2026 2026 204 222 10.54216/IJNS.270218 https://www.americaspg.com/articleinfo/21/show/4060