A Dynamic Survey of Fuzzy, Intuitionistic Fuzzy, Neutrosophic, Plithogenic, and Extensional Sets
arXiv:2603.15667v1 Announce Type: new Abstract: 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-orient
arXiv:2603.15667v1 Announce Type: new Abstract: 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.
Executive Summary
This comprehensive survey article provides an extensive overview of Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Sets, addressing the complexity of real-world phenomena characterized by vagueness, partial truth, and incomplete information. By examining the theoretical foundations, applications, and future directions of these frameworks, the authors aim to stimulate further conceptual developments and interdisciplinary collaborations. The survey's unified exposition facilitates a deeper understanding of the dynamics between these frameworks, fostering new insights and potential applications across various disciplines. This work contributes significantly to the advancement of uncertainty modeling and has far-reaching implications for decision-making, artificial intelligence, and mathematical modeling.
Key Points
- ▸ Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Sets are generalized set-theoretic frameworks for modeling uncertainty and vagueness.
- ▸ These frameworks have been extensively applied in various disciplines, including artificial intelligence, decision-making, and mathematical modeling.
- ▸ The survey provides a comprehensive analysis of the theoretical foundations, applications, and future directions of these frameworks.
Merits
Comprehensive Coverage
The survey provides an extensive overview of the Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Sets, covering their theoretical foundations, applications, and future directions.
Unified Exposition
The authors' unified approach facilitates a deeper understanding of the dynamics between these frameworks, enabling readers to appreciate the connections and potential applications.
Interdisciplinary Applications
The survey highlights the far-reaching implications of these frameworks for decision-making, artificial intelligence, and mathematical modeling, demonstrating their potential for interdisciplinary collaborations.
Demerits
Complexity of the Topic
The survey's comprehensive coverage of multiple frameworks may be overwhelming for readers without a background in fuzzy mathematics, potentially limiting its accessibility.
Limited Novelty
The survey primarily synthesizes existing knowledge, rather than introducing novel concepts or methodologies, which may limit its impact on the field.
Expert Commentary
The survey's comprehensive coverage of Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Sets provides a valuable resource for researchers and practitioners in the field of uncertainty modeling. However, the survey's limitations, including its complexity and limited novelty, highlight the need for future research to build upon and extend the existing knowledge in this area. Furthermore, the survey's emphasis on the potential applications and connections to other uncertainty-oriented models underscores the importance of interdisciplinary collaborations and further research on the relationships between these frameworks.
Recommendations
- ✓ Future research should focus on developing novel methodologies and applications for the Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Sets frameworks.
- ✓ Interdisciplinary collaborations should be encouraged to explore the connections and potential applications of these frameworks in various fields.
