Local Neutrosophic Logic And Local Neutrosophic Sets Incorporating Locality With Applications

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Local Neutrosophic Logic And Local Neutrosophic Sets Incorporating Locality With Applications

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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-01

Local Neutrosophic Logic And Local Neutrosophic Sets Incorporating Locality With Applications written by Takaaki Fujita and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-01 with Mathematics categories.

The study of uncertainty has been a significant area of research, with concepts such as fuzzy sets [87], fuzzy graphs [51], and neutrosophic sets [58] receiving extensive attention. In Neutrosophic Logic, indeterminacy often arises from real-world complexities. This paper explores the concept of locality as a key factor in determining indeterminacy, building upon the framework introduced by F. Smarandache in [73]. Locality refers to processes constrained within a specific region, where an object or system is directly influenced by its immediate s urroundings. In contrast, nonlocality involves effects that transcend spatial or temporal boundaries, where changes in one location have direct implications for another. This paper introduces the concepts of Local-Neutrosophic Logic and Local-Neutrosophic Set by integrating the notion of locality into Neutrosophic Logic. It provides their mathematical definitions and examines potential applications.

Neutrosophic Treesoft Expert Set And Forestsoft Set

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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-01

Neutrosophic Treesoft Expert Set And Forestsoft Set written by Takaaki Fujita and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-01 with Mathematics categories.

Concepts such as Fuzzy Sets [28,57],Neutrosophic Sets [42,44], and Plithogenic Sets [48] have been extensively studied to address uncertainty, finding diverse applications across various fields. The Soft Set provides a framework that associates each parameter with subsets of a universal set, enabling flexible approximations [31]. The TreeSoft Set extends the Soft Set by introducing hierarchical, tree-structured parameters, allowing for multi-level data representation [53]. In this paper, we revisit the concept of the Neutrosophic TreeSoft Set, which has been discussed in other studies [8, 34]. Additionally, we propose and examine the Neutrosophic TreeSoft Expert Set by incorporating the framework of the Neutrosophic Soft Expert Set. Furthermore, we revisit the ForestSoft Set, an extension of the TreeSoft Set, and explore related concepts, including the Neutrosophic ForestSoft Set.

Advancing Uncertain Combinatorics Through Graphization Hyperization And Uncertainization Fuzzy Neutrosophic Soft Rough And Beyond

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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-24

Advancing Uncertain Combinatorics Through Graphization Hyperization And Uncertainization Fuzzy Neutrosophic Soft Rough And Beyond written by Takaaki Fujita and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-24 with Mathematics categories.

This book is the sixth volume in the series of Collected Papers on Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. Building upon the foundational contributions of previous volumes, this edition focuses on the exploration and development of Various New Uncertain Concepts, further enriching the study of uncertainty and complexity through innovative theoretical advancements and practical applications. The volume is meticulously organized into 15 chapters, each presenting unique perspectives and contributions to the field. From theoretical explorations to real-world applications, these chapters provide a cohesive and comprehensive overview of the state of the art in uncertain combinatorics, emphasizing the versatility and power of the newly introduced concepts and methodologies. The first chapter (SuperHypertree-depth – Structural Analysis in SuperHyperGraphs) explores the concept of SuperHypertree-depth, an extension of the classical graph parameter Tree-depth and its hypergraph counterpart Hypertree-depth. By introducing hierarchical nesting within SuperHyperGraphs, where both vertices and edges can represent recursive subsets, this study investigates the mathematical properties and structural implications of these extended parameters. The findings highlight the relationships between SuperHypertree-depth and its traditional graph-theoretic equivalents, providing a deeper understanding of their applicability to hierarchical and complex systems. The second chapter (Obstructions for Hypertree-width and SuperHypertree-width) examines the role of ultrafilters as obstructions in determining Hypertree-width and extends the concept to SuperHypertree-width. Building on hypergraph theory, which abstracts traditional graph frameworks into more complex domains, the study investigates how recursive structures within SuperHyperGraphs redefine the computational and structural properties of these parameters. Ultrafilters, with their broad mathematical significance, serve as critical tools for understanding the limitations and potentials of these advanced graph metrics. The third chapter (SuperHypertree-Length and SuperHypertree-Breadth in SuperHyperGraphs) investigates the extension of the graph-theoretic parameters Tree-length and Tree-breadth to the realms of hypergraphs and SuperHyperGraphs. By leveraging the hierarchical nesting of SuperHyperGraphs, the study explores how these parameters adapt to increasingly complex and multi-level structures. Comparative analyses between these extended parameters and their classical counterparts reveal new insights into their relevance and utility in advanced graph and hypergraph theory. Plithogenic Sets, which generalize Fuzzy and Neutrosophic Sets, are extended in the fourth chapter (Extended HyperPlithogenic Sets and Generalized Plithogenic Graphs) to Extended Plithogenic Sets, HyperPlithogenic Sets, and SuperHyperPlithogenic Sets. This study further investigates their application to graph theory through the concepts of Extended Plithogenic Graphs and Generalized Extended Plithogenic Graphs. The chapter provides a concise exploration of these frameworks, offering insights into their potential for addressing uncertainty and complexity in graph structures. Soft Sets provide an effective framework for decision-making by mapping parameters to subsets of a universal set, addressing uncertainty and vagueness. The fifth chapter (Double-Framed Superhypersoft Set and Double-Framed Treesoft Set) introduces the Double-Framed SuperHypersoft Set and the Double-Framed Treesoft Set as extensions of traditional and advanced soft set frameworks, such as Hypersoft and SuperHypersoft Sets. The chapter explores their relationships with existing concepts, offering new tools to handle complex decision-making scenarios with enhanced structural flexibility. The sixth paper (HyperPlithogenic Cubic Set and SuperHyperPlithogenic Cubic Set) introduces the concepts of the HyperPlithogenic Cubic Set and SuperHyperPlithogenic Cubic Set, which extend the Plithogenic Cubic Set by integrating both interval-valued and single-valued fuzzy memberships. These sets leverage multi-attribute aggregation techniques inherent to plithogenic structures, allowing for nuanced representations of uncertainty. Additionally, related constructs such as the HyperPlithogenic Fuzzy Cubic Set, HyperPlithogenic Intuitionistic Fuzzy Cubic Set, and HyperPlithogenic Neutrosophic Cubic Set are explored, further enriching the theoretical and practical applications of this framework. The seventh chapter (L-Neutrosophic Sets and Nonstationary Neutrosophic Sets) extends the foundational concepts of fuzzy sets by integrating Neutrosophic and Plithogenic frameworks. By introducing L-Neutrosophic Sets and Nonstationary Neutrosophic Sets, the study enhances the representation of uncertainty through independent membership components: truth, indeterminacy, and falsity. These advanced constructs also incorporate multi-dimensional and contradictory attributes, providing a robust means of modeling complex decision-making and uncertain data. Plithogenic and Rough Sets, known for generalizing uncertainty modeling and classification, are extended in the eight chapter (Forest HyperPlithogenic and Forest HyperRough Sets) to Forest HyperPlithogenic Sets, Forest SuperHyperPlithogenic Sets, Forest HyperRough Sets, and Forest SuperHyperRough Sets. These frameworks incorporate hierarchical and recursive structures to advance existing set-theoretic paradigms. The chapter explores their applications in multi-level data analysis and uncertainty classification, demonstrating their adaptability to complex systems. Building on Fuzzy, Neutrosophic, and Plithogenic Sets, the tenth chapter (Symbolic HyperPlithogenic Sets) introduces Symbolic HyperPlithogenic Sets and Symbolic n-SuperHyperPlithogenic Sets. These sets incorporate symbolic components and algebraic coefficients, enabling flexible operations within a defined prevalence order. By extending symbolic representation into hyperplithogenic and superhyperplithogenic domains, the chapter opens new pathways for addressing uncertainty and hierarchical complexity in mathematical modeling. Soft Sets, designed to manage uncertainty and imprecision, have evolved through various extensions like Hypersoft Sets and SuperHypersoft Sets. The eleventh chapter (N-SuperHypersoft and Bijective SuperHypersoft Sets) introduces N-SuperHypersoft Sets, N-Treesoft Sets, Bijective SuperHypersoft Sets, and Bijective Treesoft Sets. These new constructs enhance decision-making frameworks by incorporating advanced hierarchical and bijective relationships, building on existing theories and expanding their applications. Plithogenic Sets, known for integrating multi-valued attributes and contradictions, and Rough Sets, which partition data into definable approximations, are combined in the twelfth chapter (Plithogenic Rough Sets) to form Plithogenic Rough Sets. This fusion provides a powerful framework for addressing uncertainty in dynamic and complex decision-making scenarios, offering a novel approach to uncertainty modeling. Expanding on Neutrosophic Sets, which represent truth, indeterminacy, and falsehood, this chapter introduces Plithogenic Duplets and Plithogenic Triplets. These constructs leverage the Plithogenic framework to incorporate attributes, values, and contradiction measures. The thirteenth chapter (Plithogenic Duplets and Triplets) examines their relationships with Neutrosophic Duplets and Triplets, offering new tools for multi-dimensional data representation and decision-making. Building on foundational concepts like Rough Sets and Vague Sets, the fourteenth chapter (SuperRough and SuperVague Sets) introduces SuperRough Sets and SuperVague Sets. These generalized frameworks extend uncertainty modeling by incorporating hierarchical structures. The study also demonstrates that SuperRough Sets can evolve into SuperHyperRough Sets, providing further generalizations for advanced data classification and analysis. The fifteenth chapter (Neutrosophic TreeSoft Expert and ForestSoft Sets) revisits the Neutrosophic TreeSoft Set, which combines the hierarchical structure of TreeSoft Sets with the Neutrosophic framework for uncertainty representation. Additionally, it introduces the Neutrosophic TreeSoft Expert Set, incorporating expert knowledge into the model. The chapter also explores the ForestSoft Set and its extension, the Neutrosophic ForestSoft Set, to provide multi-level, tree-structured approaches for complex data representation and analysis.

Some Types Of Hyperneutrosophic Set 5 Support Paraconsistent Faillibilist And Others

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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-01

Some Types Of Hyperneutrosophic Set 5 Support Paraconsistent Faillibilist And Others written by Takaaki Fujita and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-01 with Mathematics categories.

This paper builds upon the foundational advancements introduced in [14, 25–27]. The Neutrosophic Set offers a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to tackle increasingly sophisticated and multidimensional problems. Detailed formal definitions of these concepts can be found in [20]. In this paper, we extend various specialized classes of Neutrosophic Sets—namely, the Support Neutrosophic Set, Neutrosophic Intuitionistic Set (distinct from the Intuitionistic Fuzzy Set), Neutrosophic Paraconsistent Set, Neutrosophic Faillibilist Set, Neutrosophic Paradoxist Set, Neutrosophic Pseudo-Paradoxist Set, Neutrosophic Tautological Set, Neutrosophic Nihilist Set, Neutrosophic Dialetheist Set, and Neutrosophic Trivialist Set—by utilizing the frameworks of the Hyperneutrosophic Set and the SuperHyperneutrosophic Set.

Some Types Of Hyperneutrosophic Set 7 Type M Nonstationary Subset Valued And Complex Refined

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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-01

Some Types Of Hyperneutrosophic Set 7 Type M Nonstationary Subset Valued And Complex Refined written by Takaaki Fujita and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-01 with Mathematics categories.

This paper builds upon the foundational advancements introduced in [26,39–43]. TheNeutrosophic Set provides a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity [84]. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to address increasingly complex and multidimensional problems. Detailed formal definitions of these concepts can be found in [33]. In this paper, we extend the Type-𝑚, Nonstationary, Subset-Valued, and Complex Refined Neutrosophic Sets using the Hyperneutrosophic Set and the SuperHyperneutrosophic Set frameworks.

Some Types Of Hyperneutrosophic Set 3 Dynamic Quadripartitioned Pentapartitioned Heptapartitioned M Polar

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Author :
language : en
Publisher: Infinite Study
Release Date : 2025-01-01

Some Types Of Hyperneutrosophic Set 3 Dynamic Quadripartitioned Pentapartitioned Heptapartitioned M Polar written by and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-01 with Mathematics categories.

This paper builds upon the foundation established in [50, 51]. The Neutrosophic Set provides a robust mathematical framework for handling uncertainty, defined by three membership functions: truth, indeterminacy, and falsity. Recent developments have introduced extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set to tackle increasingly complex and multidimensional problems. In this study, we explore further extensions, including the Dynamic Neutrosophic Set, Quadripartitioned Neutrosophic Set, Pentapartitioned Neutrosophic Set, Heptapartitioned Neutrosophic Set, and m-Polar Neutrosophic Set, to address advanced challenges and applications.

Some Types Of Hyperneutrosophic Set 2 Complex Single Valued Triangular Fermatean And Linguistic Sets

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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-01

Some Types Of Hyperneutrosophic Set 2 Complex Single Valued Triangular Fermatean And Linguistic Sets written by Takaaki Fujita and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-01 with Mathematics categories.

This paper is a continuation of the work presented in [35]. The Neutrosophic Set provides a mathematical framework for managing uncertainty, characterized by three membership functions: truth, indeterminacy, and falsity. Recent advancements have introduced extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set to address more complex and multidimensional challenges. In this study, we extend the Complex Neutrosophic Set, Single-Valued Triangular Neutrosophic Set, Fermatean Neutrosophic Set, and Linguistic Neutrosophic Set within the frameworks of Hyperneutrosophic Sets and SuperHyperneutrosophic Sets. Furthermore, we investigate their mathematical structures and analyze their connections with other set-theoretic concepts.

Some Types Of Hyperneutrosophic Set 4 Cubic Trapozoidal Q Rung Orthopair Overset Underset And Offset

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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date :

Some Types Of Hyperneutrosophic Set 4 Cubic Trapozoidal Q Rung Orthopair Overset Underset And Offset written by Takaaki Fujita and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

This paper builds upon the foundational work presented in [38–40]. The Neutrosophic Set provides a comprehensive mathematical framework for managing uncertainty, defined by three membership functions: truth, indeterminacy, and falsity. Recent advancements have introduced extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set, which are specifically designed to address increasingly complex and multidimensional problems. The formal definitions of these sets are available in [30]. In this paper, we extend the Neutrosophic Cubic Set, Trapezoidal Neutrosophic Set, q-Rung Orthopair Neutrosophic Set, Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset using the frameworks of the Hyperneutrosophic Set and the SuperHyperneutrosophic Set. Furthermore, we briefly examine their properties and potential applications.

Forestfuzzy Forestneutrosophic Forestplithogenic And Forestrough Set

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Author : Takaaki Fujita
language : un
Publisher: Infinite Study
Release Date : 2025-01-01

Forestfuzzy Forestneutrosophic Forestplithogenic And Forestrough Set written by Takaaki Fujita and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-01 with Mathematics categories.

Concepts such as Fuzzy Sets [30, 72], Neutrosophic Sets [53, 55], Rough Sets [37], and Plithogenic Sets [59] have been extensively studied to address uncertainty, with diverse applications across various fields. Recently, TreeFuzzy, TreeNeutrosophic, TreePlithogenic, and TreeRough Sets have been defined [15]. This work examines their extensions: ForestFuzzy, ForestNeutrosophic, ForestPlithogenic, and ForestRough Sets.

Neutrosophic Systems With Applications Nswa Vol 5 2023

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2023-09-23

Neutrosophic Systems With Applications Nswa Vol 5 2023 written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-23 with Antiques & Collectibles categories.

Papers on neutrosophic and plithogenic sets, logics, probabilities and statistics, on NeutroAlgebra and AntiAlgebra, NeutroGeometry and AntiGeometry, SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra, etc…