A Dynamic Survey of Fuzzy, Intuitionistic Fuzzy, Neutrosophic, Plithogenic, and Extensional Sets

Computer Science > Artificial Intelligence [Submitted on 12 Mar 2026] A Dynamic Survey of Fuzzy, Intuitionistic Fuzzy, Neutrosophic, Plithogenic, and Extensional Sets Takaaki Fujita, Florentin Smarandache Real-world phenomena often exhibit vagueness, partial truth, and incomplete information. To model such uncertainty in a mathematically rigorous way, many generalized set-theoretic frameworks have been introduced, including Fuzzy Sets [1], Intuitionistic Fuzzy Sets [2], Neutrosophic Sets [3,4], Vague Sets [5], Hesitant Fuzzy Sets [6], Picture Fuzzy Sets [7], Quadripartitioned Neutrosophic Sets [8], Penta-Partitioned Neutrosophic Sets [9], Plithogenic Sets [10], HyperFuzzy Sets [11], and HyperNeutrosophic Sets [12]. Within these frameworks, a wide range of notions has been proposed and studied, particularly in the settings of fuzzy, intuitionistic fuzzy, neutrosophic, and plithogenic set theories. This extensive literature underscores both the significance of these theories and the breadth of their application areas. As a result, many ideas, constructions, and structural patterns recur across these four major families of uncertainty-oriented models. In this book, we provide a comprehensive, large-scale survey of Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Sets. Our goal is to give readers a systematic overview of existing developments and, through a unified exposition, to stimulate new insights, further conceptual extensions, and additional applications across a wide range of disciplines. Comments: Book. Peer-reviewed. Publisher: Neutrosophic Science International Association (NSIA). ISBN: 978-1-59973-842-0 Subjects: Artificial Intelligence (cs.AI); Computational Engineering, Finance, and Science (cs.CE) MSC classes: 03B52, 68T27 Cite as: arXiv:2603.15667 [cs.AI]   (or arXiv:2603.15667v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2603.15667 Focus to learn more Journal reference: Publisher: Neutrosophic Science International Association (NSIA). ISBN: 978-1-59973-842-0. Year: 2026 Related DOI: https://doi.org/10.5281/zenodo.18973238 Focus to learn more Submission history From: Takaaki Fujita [view email] [v1] Thu, 12 Mar 2026 02:16:42 UTC (2,223 KB) Access Paper: view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.CE References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)