DSm Fuzzy Vector Space, DSm Neutrosophic Vector Space, and DSm Plithogenic Vector Space - Takaaki Fujita (Magister Program of Mathematics, Universitas Lampung, 2026)
A wide range of formalisms has been developed to represent uncertainty across disciplines, including Fuzzy Sets, Rough Sets, Intuitionistic Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets, among others that continue to be active areas of research. A DSm Vector Space is defined as a linear space over refined DSm labels, where addition and scalar multiplication satisfy the classical axioms. In this paper, we newly introduce the extensions of DSm Vector Space using Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets, namely the DSm Fuzzy Vector Space, the DSm Neutrosophic Vector Space, and the DSm Plithogenic Vector Space, and investigate their structural properties.