Survey Of Planar And Outerplanar Graphs In Fuzzy And Neutrosophic Graphs
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Survey Of Planar And Outerplanar Graphs In Fuzzy And Neutrosophic Graphs
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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-01
Survey Of Planar And Outerplanar Graphs In Fuzzy And Neutrosophic Graphs 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.
As many readers may know, graph theory is a fundamental branch of mathematics that explores networks made up of nodes and edges, focusing on their paths, structures, and properties [196]. A planar graph is one that can be drawn on a plane without any edges intersecting, ensuring planarity. Outerplanar graphs, a subset of planar graphs, have all their vertices located on the boundary of the outer face in their planar embedding. In recent years, outerplanar graphs have been formally defined within the context of fuzzy graphs. To capture uncertain parameters and concepts, various graphs such as fuzzy, neutrosophic, Turiyam, and plithogenic graphs have been studied. In this paper, we investigate planar graphs, outerplanar graphs, apex graphs, and others within the frameworks of neutrosophic graphs, Turiyam Neutrosophic graphs, fuzzy graphs, and plithogenic graphs.
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 : 2024-10-01
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 2024-10-01 with Mathematics categories.
This book explores the advancement of uncertain combinatorics through innovative methods such as graphization, hyperization, and uncertainization, incorporating concepts from fuzzy, neutrosophic, soft, and rough set theory, among others. Combinatorics and set theory are fundamental mathematical disciplines that focus on counting, arrangement, and the study of collections under specified rules. While combinatorics excels at solving problems involving uncertainty, set theory has expanded to include advanced concepts like fuzzy and neutrosophic sets, which are capable of modeling complex real-world uncertainties by accounting for truth, indeterminacy, and falsehood. These developments intersect with graph theory, leading to novel forms of uncertain sets in "graphized" structures, such as hypergraphs and superhypergraphs. Innovations like Neutrosophic Oversets, Undersets, and Offsets, as well as the Nonstandard Real Set, build upon traditional graph concepts, pushing the boundaries of theoretical and practical advancements. This synthesis of combinatorics, set theory, and graph theory provides a strong foundation for addressing the complexities and uncertainties present in mathematical and real-world systems, paving the way for future research and application.
Neutrosophic Sets And Systems Vol 77 2025
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2025-01-31
Neutrosophic Sets And Systems Vol 77 2025 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 2025-01-31 with Mathematics categories.
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation
Neutrosophic Sets And Systems Vol 74 2024 Special Issue Advances In Superhyperstructures And Applied Neutrosophic Theories
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2024-12-16
Neutrosophic Sets And Systems Vol 74 2024 Special Issue Advances In Superhyperstructures And Applied Neutrosophic Theories 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 2024-12-16 with Mathematics categories.
This volume contains the proceedings of the conference held at the University of Guayaquil on November 28 and 29, 2024, featuring contributions from researchers representing Colombia, Cuba, Ecuador, Spain, the United States, Greece, Japan, Mexico, and Peru. The conference focused on SuperHyperStructures and Applied Neutrosophic Theories, commemorating the 30th anniversary of neutrosophic theories and their extensive applications. The topic of SuperHyperStructures and Neutrosophic SuperHyperStructures explores advanced mathematical frameworks built on powersets of a set 𝐻, extending to higher orders 𝑃𝑛(𝐻). SuperHyperStructures are constructed using all non-empty subsets of 𝐻, while Neutrosophic SuperHyperStructures incorporate the empty set 𝜙, representing indeterminacy. These structures model real-world systems where elements are organized hierarchically, from sets to sub-sets and beyond, enabling the analysis of complex and indeterminate relationships.
Superhypergraph Neural Networks And Plithogenic Graph Neural Networks Theoretical Foundations
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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-01
Superhypergraph Neural Networks And Plithogenic Graph Neural Networks Theoretical Foundations 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.
Hypergraphs extend traditional graphs by allowing edges to connect multiple nodes, while superhypergraphs further generalize this concept to represent even more complex relationships. Neural networks, inspired by biological systems, are widely used for tasks such as pattern recognition, data classification, and prediction. Graph Neural Networks (GNNs), a well-established framework, have recently been extended to Hypergraph Neural Networks (HGNNs), with their properties and applications being actively studied. The Plithogenic Graph framework enhances graph representations by integrating multi-valued attributes, as well as membership and contradiction functions, enabling the detailed modeling of complex relationships. In the context of handling uncertainty, concepts such as Fuzzy Graphs and Neutrosophic Graphs have gained prominence. It is well established that Plithogenic Graphs serve as a generalization of both Fuzzy Graphs and Neutrosophic Graphs. Furthermore, the Fuzzy Graph Neural Network has been proposed and is an active area of research. This paper establishes the theoretical foundation for the development of SuperHyperGraph Neural Networks (SHGNNs) and Plithogenic Graph Neural Networks, expanding the applicability of neural networks to these advanced graph structures. While mathematical generalizations and proofs are presented, future computational experiments are anticipated.
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.
A Concise Study Of Some Superhypergraph Classes
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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-15
A Concise Study Of Some Superhypergraph Classes 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 2025-01-15 with Mathematics categories.
In graph theory, the hypergraph [22] extends the traditional graph structure by allowing edges to connect multiple vertices, and this concept is further broadened by the superhypergraph [174,176]. Additionally, several types of uncertain graphs have been explored, including fuzzy graphs [136, 153], neutrosophic graphs [35, 36], and plithogenic graphs [66, 75, 185]. This study explores the SuperHyperGraph, Single-Valued Neutrosophic Quasi SuperHyperGraph, and Plithogenic Quasi SuperHyperGraph, analyzing their relationships with other graph classes. Future work will define the Semi Superhypergraph, Multi Superhypergraph, Pseudo Superhypergraph, Mixed Superhypergraph, and Bidirected Superhypergraph and examine their connections to existing classes in hypergraphs and graphs.
Neutrosophic Circular Arc Graphs And Proper Circular Arc Graphs
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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-01
Neutrosophic Circular Arc Graphs And Proper Circular Arc Graphs 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.
Graph theory is a fundamental branch of mathematics that studies networks made up of nodes (vertices) and connections (edges). A key concept in graph theory is the intersection graph, where vertices represent sets, and edges are drawn between vertices if their corresponding sets intersect. A circular-arc graph specifically models the intersections of arcs on a circle, with vertices corresponding to the arcs and edges existing between intersecting arcs. This paper delves into the study of circular-arc graphs within the frameworks of fuzzy, intuitionistic fuzzy, neutrosophic, and Turiyam Neutrosophic graphs, all of which incorporate uncertainty into graph structures. Additionally, we examine the concept of proper circular-arc graphs.
Neutrosophic Sets And Systems Vol 78 2025
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2025-02-15
Neutrosophic Sets And Systems Vol 78 2025 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 2025-02-15 with Mathematics categories.
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation
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.