2995-3162ISSN (Online)
Volume 5 , Issue 1 , PP: 48-61, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Takaaki Fujita 1 * , Arif Mehmood 2 , Arkan A. Ghaib 3
Doi: https://doi.org/10.54216/PMTCS.050105
A variety of uncertainty-handling frameworks—such as Fuzzy Sets,1 Hyperfuzzy Sets,2 Bipolar Fuzzy Sets,3 Neutrosophic Sets,4 Vague Set,5 Hesitant Fuzzy Sets,6, 7 Picture Fuzzy Sets,8 Soft Sets,9, 10 Rough Sets,11 and Plithogenic Sets12, 13—have been extensively studied for modeling and reasoning under vagueness and imprecision. A fuzzy set extends classical set theory by assigning each element a membership value in the unit interval [0, 1], thereby capturing partial inclusion.1 Neutrosophic Sets further generalize this idea by introducing three independent membership functions—truth, indeterminacy, and falsity—each mapping into [0, 1]. Many of these frameworks have been enriched by incorporating offset concepts, which permit membership degrees to take values beyond the unit interval. Similarly, D-numbers extend Dempster–Shafer belief functions by assigning to each subset B ⊆ X a mass D(B) ∈ [0, 1] with P B D(B) ≤ 1, thus accommodating incomplete uncertainty.14 In this work, we introduce and formally define four new constructs: D-OffNumber, D-OverNumber, D-UnderNumber, and Neutrosophic D-Number, and we investigate their mathematical foundations, structural properties, and interrelationships. The present study focuses exclusively on theoretical development, leaving potential applications—such as their integration into decision-making frameworks—for future research.
Fuzzy Offset , Neutrosophic OffSet , Fuzzy Set , Neutrosophic Set , D-Number , Neutrosophic D-Number
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