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Product Operations on q-Rung Orthopair Fuzzy Graphs

Product Operations on q-Rung Orthopair Fuzzy Graphs
Author: Songyi Yin
Publisher: Infinite Study
Total Pages: 23
Release:
Genre: Mathematics
ISBN:
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The q-rung orthopair fuzzy graph is an extension of intuitionistic fuzzy graph and Pythagorean fuzzy graph. In this paper, the degree and total degree of a vertex in q-rung orthopair fuzzy graphs are firstly defined. Then, some product operations on q-rung orthopair fuzzy graphs, including direct product, Cartesian product, semi-strong product, strong product, and lexicographic product, are defined. Furthermore, some theorems about the degree and total degree under these product operations are put forward and elaborated with several examples. In particular, these theorems improve the similar results in single-valued neutrosophic graphs and Pythagorean fuzzy graphs.

Modern Trends in Fuzzy Graph Theory

Modern Trends in Fuzzy Graph Theory
Author: Madhumangal Pal
Publisher: Springer Nature
Total Pages: 323
Release: 2020-11-02
Genre: Mathematics
ISBN: 9811588031
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This book provides an extensive set of tools for applying fuzzy mathematics and graph theory to real-life problems. Balancing the basics and latest developments in fuzzy graph theory, this book starts with existing fundamental theories such as connectivity, isomorphism, products of fuzzy graphs, and different types of paths and arcs in fuzzy graphs to focus on advanced concepts such as planarity in fuzzy graphs, fuzzy competition graphs, fuzzy threshold graphs, fuzzy tolerance graphs, fuzzy trees, coloring in fuzzy graphs, bipolar fuzzy graphs, intuitionistic fuzzy graphs, m-polar fuzzy graphs, applications of fuzzy graphs, and more. Each chapter includes a number of key representative applications of the discussed concept. An authoritative, self-contained, and inspiring read on the theory and modern applications of fuzzy graphs, this book is of value to advanced undergraduate and graduate students of mathematics, engineering, and computer science, as well as researchers interested in new developments in fuzzy logic and applied mathematics.

q-Rung Orthopair Fuzzy Sets

q-Rung Orthopair Fuzzy Sets
Author: Harish Garg
Publisher: Springer Nature
Total Pages: 558
Release: 2022-09-08
Genre: Computers
ISBN: 9811914494
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This book collects chapters which discuss interdisciplinary solutions to complex problems by using different approaches in order to save money, time and resources. The book presents the results on the recent advancements in artificial intelligence, computational intelligence, decision-making problems, emerging problems and practical achievements in the broad knowledge management field. q-ROFS is one of the hot topics for all the researchers, industrialists as well as academicians. This book is of interest to professionals and researchers working in the field of decision making and computational intelligence, as well as postgraduate and undergraduate students studying applications of fuzzy sets. The book helps solve different kinds of the decision-making problems such as medical diagnosis, pattern recognition, construction problems and technology selection under the uncertain fuzzy environment. Containing 19 chapters, the book begins by giving a topology of the q-ROFSs and their applications. It then progresses in a logical fashion, dedicating a chapter to each approach, including the generalized information measures for q-ROFSs, implementation of q-ROFSs to medical diagnosis, inventory model, multi-attribute decision-making and approaches to real-life industrial problems such as green campus transportation, social responsibility evaluation pattern and extensions of the q-ROFSs.

Neutrosophic Sets and Systems, vol. 50/2022

Neutrosophic Sets and Systems, vol. 50/2022
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 674
Release: 2022-06-01
Genre: Mathematics
ISBN:
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“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 and with their spectrum of neutralities in between them (i.e. notions or ideas supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic).

Neutrosophic Sets and Systems, Vol. 43, 2021

Neutrosophic Sets and Systems, Vol. 43, 2021
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 311
Release:
Genre: Mathematics
ISBN:
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“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. In this issue: On Neutrosophic Crisp Sets and Neutrosophic Crisp Mathematical Morphology, New Results on Pythagorean Neutrosophic Open Sets in Pythagorean Neutrosophic Topological Spaces, Comparative Mathematical Model for Predicting of Financial Loans Default using Altman Z-Score and Neutrosophic AHP Methods.

Fuzzy Graph Theory

Fuzzy Graph Theory
Author: Sunil Mathew
Publisher: Springer
Total Pages: 331
Release: 2017-12-30
Genre: Technology & Engineering
ISBN: 3319714074
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This book provides a timely overview of fuzzy graph theory, laying the foundation for future applications in a broad range of areas. It introduces readers to fundamental theories, such as Craine’s work on fuzzy interval graphs, fuzzy analogs of Marczewski’s theorem, and the Gilmore and Hoffman characterization. It also introduces them to the Fulkerson and Gross characterization and Menger’s theorem, the applications of which will be discussed in a forthcoming book by the same authors. This book also discusses in detail important concepts such as connectivity, distance and saturation in fuzzy graphs. Thanks to the good balance between the basics of fuzzy graph theory and new findings obtained by the authors, the book offers an excellent reference guide for advanced undergraduate and graduate students in mathematics, engineering and computer science, and an inspiring read for all researchers interested in new developments in fuzzy logic and applied mathematics.

Pythagorean Fuzzy Sets

Pythagorean Fuzzy Sets
Author: Harish Garg
Publisher: Springer Nature
Total Pages: 443
Release: 2021-07-22
Genre: Mathematics
ISBN: 9811619891
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This book presents a collection of recent research on topics related to Pythagorean fuzzy set, dealing with dynamic and complex decision-making problems. It discusses a wide range of theoretical and practical information to the latest research on Pythagorean fuzzy sets, allowing readers to gain an extensive understanding of both fundamentals and applications. It aims at solving various decision-making problems such as medical diagnosis, pattern recognition, construction problems, technology selection, and more, under the Pythagorean fuzzy environment, making it of much value to students, researchers, and professionals associated with the field.

Decision Making with Spherical Fuzzy Sets

Decision Making with Spherical Fuzzy Sets
Author: Cengiz Kahraman
Publisher: Springer Nature
Total Pages: 551
Release: 2020-05-27
Genre: Technology & Engineering
ISBN: 3030454614
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This book introduces readers to the novel concept of spherical fuzzy sets, showing how these sets can be applied in practice to solve various decision-making problems. It also demonstrates that these sets provide a larger preference volume in 3D space for decision-makers. Written by authoritative researchers, the various chapters cover a large amount of theoretical and practical information, allowing readers to gain an extensive understanding of both the fundamentals and applications of spherical fuzzy sets in intelligent decision-making and mathematical programming.

Fuzzy Hypergraphs and Related Extensions

Fuzzy Hypergraphs and Related Extensions
Author: Muhammad Akram
Publisher: Springer Nature
Total Pages: 522
Release: 2020-02-01
Genre: Mathematics
ISBN: 9811524033
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This book presents the fundamental and technical concepts of fuzzy hypergraphs and explains their extensions and applications. It discusses applied generalized mathematical models of hypergraphs, including complex, intuitionistic, bipolar, m-polar fuzzy, Pythagorean, complex Pythagorean, and q-rung orthopair hypergraphs, as well as single-valued neutrosophic, complex neutrosophic and bipolar neutrosophic hypergraphs. In addition, the book also sheds light on real-world applications of these hypergraphs, making it a valuable resource for students and researchers in the field of mathematics, as well as computer and social scientists.