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Hyperlattice-Valued And Superhyperlattice-Valued Uncertain Sets With Decision Applications, Takaaki Fujita, Ajoy Kanti Das, Sankar Prasad Mondal, Arif Mehmood, Arkan Ghaib
Hyperlattice-Valued And Superhyperlattice-Valued Uncertain Sets With Decision Applications, Takaaki Fujita, Ajoy Kanti Das, Sankar Prasad Mondal, Arif Mehmood, Arkan Ghaib
Neutrosophic Systems with Applications
Fuzzy set theory enriches classical sets by assigning to each element a graded membership in [0,1], thereby capturing partial inclusion and uncertainty. The notion of an Uncertain Set further abstracts this idea by allowing membership to take values in a general degree-domain, providing a unified language that subsumes fuzzy, intuitionistic fuzzy, neutrosophic, plithogenic, and related models. On the algebraic side, a hyperlattice replaces one lattice operation by a multivalued hyperoperation, enabling the representation of ambiguous or non-deterministic combinations, while a superhyperlattice iterates this structure through powerset lifting to obtain higher-order layers of interaction. Motivated by these developments, we introduce HyperLattice-valued …
Neutrosophic Sets In Neural Networks: Theory, Applications, And Challenges, Vladimir Simic, Dragan Pamucar, Hafiz Muhammad Athar Farid
Neutrosophic Sets In Neural Networks: Theory, Applications, And Challenges, Vladimir Simic, Dragan Pamucar, Hafiz Muhammad Athar Farid
Neutrosophic Systems with Applications
The integration of neutrosophic sets into neural networks presents a novel approach to handling uncertainty, indeterminacy, and falsity in data. Traditional neural networks typically operate under the assumption of precise and complete data, but real-world applications often involve noisy, incomplete, or ambiguous information. Neutrosophic sets extend fuzzy logic by incorporating three components: truth, indeterminacy, and falsity, allowing for a more nuanced representation of uncertain data. This paper explores the theoretical foundations of neutrosophic sets and their integration with neural networks, highlighting the challenges in computational complexity, training, and optimization. The paper also discusses the potential applications of neutrosophic neural networks …
Single-Valued, Double-Valued, Triple-Valued, Quadruple-Valued, And Quintuple-Valued Neutrosophic Graph, Takaaki Fujita, Arif Mehmood, Arkan A. Ghaib
Single-Valued, Double-Valued, Triple-Valued, Quadruple-Valued, And Quintuple-Valued Neutrosophic Graph, Takaaki Fujita, Arif Mehmood, Arkan A. Ghaib
Neutrosophic Systems with Applications
Concepts such as fuzzy sets, neutrosophic sets, rough sets, and plithogenic sets have been extensively studied as formal tools for modeling uncertainty, and they have found broad applications across many disciplines. A Double-Valued Neutrosophic Set (DVNS) extends the classical neutrosophic framework by splitting indeterminacy into two distinct components: one leaning toward truth and the other leaning toward falsity. In recent years, further refinements—namely Triple-Valued, Quadruple-Valued, and Quintuple-Valued Neutrosophic Sets—have also been introduced and investigated. These uncertainty models have naturally been lifted to graph-theoretic settings, where vertices and edges represent entities and relationships under ambiguity. Although fuzzy graphs and neutrosophic graphs …
New Measures Of Consistency And Coverage For Social Research Based On Neutrosophic Logic, Erick Gonzalez Caballero, Maikel Y. Leyva Vázquez, Noel Batista-Hernández, Florentin Smarandache
New Measures Of Consistency And Coverage For Social Research Based On Neutrosophic Logic, Erick Gonzalez Caballero, Maikel Y. Leyva Vázquez, Noel Batista-Hernández, Florentin Smarandache
Neutrosophic Sets and Systems
The mathematical methods systematically used in social sciences often rely on statistical tools like correlation, which may not optimally model social phenomena, frequently described using words. Set theory, as proposed by C.C. Ragin, provides a more suitable tool, leveraging set asymmetry to measure set-theoretic consistency and coverage, which were later generalized to fuzzy sets. Subsequent extensions into the neutrosophic field are significant because the underlying binary logic in traditional models often fails to capture the complexities and nuances of social realities, such as those found in Afro-Latin American and Caribbean cosmovisions that encompass ambiguity and indeterminacy. This paper proposes new, …
A Proposed Mathematical Framework For Fuzzy It Service Management (F-Itsm) And Neutrosophic It Service Management (N-Itsm), Takaaki Fujita
A Proposed Mathematical Framework For Fuzzy It Service Management (F-Itsm) And Neutrosophic It Service Management (N-Itsm), Takaaki Fujita
Neutrosophic Systems with Applications
Fuzzy sets, rough sets, hyperrough sets, intuitionistic fuzzy sets, neutrosophic sets, plithogenic sets , and other frameworks for handling uncertainty are under active research every day. These concepts can model a wide range of real-world phenomena and are frequently investigated to facilitate more efficient decision-making. IT Service Management is a systematic approach to designing, delivering, managing, and improving IT services in alignment with organizational objectives. In this paper, we explore the Mathematical Frameworks for Fuzzy IT Service Management (F-ITSM) and Neutrosophic IT Service Management (N-ITSM), which combine these uncertainty-based ideas with IT Service Management practices.
Triple-Valued Neutrosophic Set, Quadruple-Valued Neutrosophic Set, Quintuple-Valued Neutrosophic Set, And Double-Valued Indetermsoft Set, Takaaki Fujita
Triple-Valued Neutrosophic Set, Quadruple-Valued Neutrosophic Set, Quintuple-Valued Neutrosophic Set, And Double-Valued Indetermsoft Set, Takaaki Fujita
Neutrosophic Systems with Applications
Concepts such as Fuzzy Sets, Neutrosophic Sets, Rough Sets, and Plithogenic Sets have been extensively studied to address uncertainty, finding diverse applications across various fields. A Double-Valued Neutrosophic Set (DVNS) extends traditional neutrosophic sets by introducing two distinct indeterminacy components: one leaning towards truth and the other towards falsity. In this paper, we explore Triple-Valued Neutrosophic Sets, Quadruple-Valued Neutrosophic Sets, and Quintuple-Valued Neutrosophic Sets, as well as an extension of the Indetermsoft Set, termed the Double-Valued Indetermsoft Set. Note that related concepts such as the Multi-Valued Neutrosophic Set and the n-Valued Refined Neutrosophic Set have already been established.
Exploring Concepts Of Hyperfuzzy, Hyperneutrosophic, And Hyperplithogenic Sets (I), Florentin Smarandache, Takaaki Fujita
Exploring Concepts Of Hyperfuzzy, Hyperneutrosophic, And Hyperplithogenic Sets (I), Florentin Smarandache, Takaaki Fujita
Branch Mathematics and Statistics Faculty and Staff Publications
This work investigates the evolution of traditional set theory to address complex and ambiguous real-world phenomena. It introduces hierarchical hyperstructures and superhyperstructures, where superhyperstructures are formed by iteratively applying power sets to create nested abstractions. The focus is placed on three foundational set-based frameworks—Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets and their extensions into Hyperfuzzy Sets, HyperNeutrosophic Sets, and Hyperplithogenic Sets. These extensions are applied to various domains, including Statistics, TOPSIS, K-means Clustering, Evolutionary Theory, Topological Spaces, Decision Making, Probability, and Language Theory. By exploring these generalized forms, this paper seeks to guide and inspire further research and development in …
Exploring Concepts Of Hyperfuzzy, Hyperneutrosophic, And Hyperplithogenic Sets (Ii), Takaaki Fujita, Florentin Smarandache
Exploring Concepts Of Hyperfuzzy, Hyperneutrosophic, And Hyperplithogenic Sets (Ii), Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper delves into the advancements of classical set theory to address the complexities and uncertainties inherent in real-world phenomena. It highlights three major extensions of traditional set theory - Fuzzy Sets [288], Neutrosophic Sets [237], and Plithogenic Sets [243] - and examines their further generalizations into Hyperfuzzy [106], HyperNeutrosophic [90], and Hyperplithogenic Sets [90]. Building on previous research [83], this study explores the potential applications of HyperNeutrosophic Sets and SuperHyperNeutrosophic Sets across various domains. Specifically, it extends f undamental c oncepts such as Neutrosophic Logic, Cognitive Maps, Graph Neural Networks, Classifiers, and Triplet Groups through these advanced set structures …
Reconsideration Of Neutrosophic Social Science And Neutrosophic Phenomenology With Non-Classical Logic, Takaaki Fujita, Florentin Smarandache
Reconsideration Of Neutrosophic Social Science And Neutrosophic Phenomenology With Non-Classical Logic, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Body-Mind-Soul-Spirit Fluidity is a concept rooted in psychology and phenomenology, offering significant insights into human decision-making and well-being. Similarly, in social analysis and social sciences, frameworks such as PDCA, DMAIC, SWOT, and OODA have been established to enable structured evaluation and effective p roblem-solving. Furthermore, in phenomenology and social sciences, various logical systems have been developed to address specific objectives and practical applications. This paper extends these concepts using the Neutrosophic theory, revisiting their mathematical definitions and exploring their properties. The Neutrosophic Set, an extension of the Fuzzy Set, is a highly flexible framework that has been widely studied in …
Uncertain Automata And Uncertain Graph Grammar, Takaaki Fujita, Florentin Smarandache
Uncertain Automata And Uncertain Graph Grammar, Takaaki Fujita, Florentin Smarandache
Neutrosophic Sets and Systems
Graph theory has been widely studied, resulting in numerous applications across various felds. Among its many topics, Automata and Graph Grammar have emerged as signifcant areas ofresearch. This paper delves into these concepts, emphasizing their adaptation o uncertainframeworks likeFuzzy, Neutro- sophic, Vague, Turiyam Neutrosophic, and Plithogenic systems. By integrating uncertaintyinto traditional graph theoretical models, the paper aims to address ongoing researchchallengesand expand thescope of thesemodels.
Medical Diagnosis Via Refined Neutrosophic Fuzzy Logic: Detection Of Illness Using Neutrosophic Sets, K. Hemabala, B. Srinivasa Kumar, Florentin Smarandache
Medical Diagnosis Via Refined Neutrosophic Fuzzy Logic: Detection Of Illness Using Neutrosophic Sets, K. Hemabala, B. Srinivasa Kumar, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
The objective of the paper is to implement and validate diagnosis in the medical field via refined neutrosophic fuzzy logic (RNFL). As such, we have proposed a Max-Min composition (MMC) method in RNFL. This method deals with the diagnosis under certain constraints like uncertainty and indeterminacy. Further, we have considered the diagnosis problems to validate the sensitivity analysis of the novel multi attribute decision-making technique. Finally, we gave the graphical representations and compared the obtained results with other existing measures in refined neutrosophic fuzzy sets.
Introduction To The Special Issue On Advances In Neutrosophic And Plithogenic Sets For Engineering And Sciences: Theory, Models, And Applications, S. A. Edalatpanah, Florentin Smarandache
Introduction To The Special Issue On Advances In Neutrosophic And Plithogenic Sets For Engineering And Sciences: Theory, Models, And Applications, S. A. Edalatpanah, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Recently, research on uncertainty modeling has been progressing rapidly, and many essential and breakthrough studies have already been done. There are various ways to handle these uncertainties, such as fuzzy and intuitionistic fuzzy sets. Although these concepts can take incomplete information in various real-world issues, they cannot address all types of uncertainty, such as indeterminate and inconsistent information. The neutrosophic theory founded by Florentin Smarandache in 1998 constitutes a further generalization of fuzzy set, intuitionistic fuzzy set, picture fuzzy set, Pythagorean fuzzy set, spherical fuzzy set, etc. Since then, this logic has been applied in various science and engineering domains. …
The Lattice Of Intuitionistic Fuzzy Topologies Generated By Intuitionistic Fuzzy Relations, Soheyb Milles
The Lattice Of Intuitionistic Fuzzy Topologies Generated By Intuitionistic Fuzzy Relations, Soheyb Milles
Applications and Applied Mathematics: An International Journal (AAM)
We generalize the notion of fuzzy topology generated by fuzzy relation given by Mishra and Srivastava to the setting of intuitionistic fuzzy sets. Some fundamental properties and necessary examples are given. More specifically, we provide the lattice structure to a family of intuitionistic fuzzy topologies generated by intuitionistic fuzzy relations. To that end, we study necessary structural characteristics such as distributivity, modularity and complementary of this lattice.
A New Type Of Group Action Through The Applications Of Fuzzy Sets And Neutrosophic Sets, Florentin Smarandache, Mumtaz Ali
A New Type Of Group Action Through The Applications Of Fuzzy Sets And Neutrosophic Sets, Florentin Smarandache, Mumtaz Ali
Branch Mathematics and Statistics Faculty and Staff Publications
Fuzzy sets are the most significant tools to handle uncertain data while neutrosophic sets are the generalizations of fuzzy sets in the sense to handle uncertain, incomplete, inconsistent, indeterminate, false data. In this paper, we introduced fuzzy subspaces and neutrosophic subspaces (generalization of fuzzy subspaces) by applying group actions.Further, we define fuzzy transitivity and neutrosophic transitivty in this paper. Fuzzy orbits and neutrosophic orbits are introduced as well. We also studied some basic properties of fuzzy subspaces as well as neutrosophic subspaces.