Topological And Algebraic Structures In Fuzzy Sets

Author : S.E. Rodabaugh,Erich Peter Klement
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 45,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401702317

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Topological and Algebraic Structures in Fuzzy Sets by S.E. Rodabaugh,Erich Peter Klement Pdf

This volume summarizes recent developments in the topological and algebraic structures in fuzzy sets and may be rightly viewed as a continuation of the stan dardization of the mathematics of fuzzy sets established in the "Handbook", namely the Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Volume 3 of The Handbooks of Fuzzy Sets Series (Kluwer Academic Publish ers, 1999). Many of the topological chapters of the present work are not only based upon the foundations and notation for topology laid down in the Hand book, but also upon Handbook developments in convergence, uniform spaces, compactness, separation axioms, and canonical examples; and thus this work is, with respect to topology, a continuation of the standardization of the Hand book. At the same time, this work significantly complements the Handbook in regard to algebraic structures. Thus the present volume is an extension of the content and role of the Handbook as a reference work. On the other hand, this volume, even as the Handbook, is a culmination of mathematical developments motivated by the renowned International Sem inar on Fuzzy Set Theory, also known as the Linz Seminar, held annually in Linz, Austria. Much of the material of this volume is related to the Twenti eth Seminar held in February 1999, material for which the Seminar played a crucial and stimulating role, especially in providing feedback, connections, and the necessary screening of ideas.

Author : S. E. Rodabaugh,Erich Peter Klement
Publisher : Unknown
Page : 484 pages
File Size : 52,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401702322

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Topological and Algebraic Structures in Fuzzy Sets by S. E. Rodabaugh,Erich Peter Klement Pdf

Author : Jana, Chiranjibe,Senapati, Tapan,Pal, Madhumangal
Publisher : IGI Global
Page : 439 pages
File Size : 52,5 Mb
Release : 2019-10-25
Category : Mathematics
ISBN : 9781799801924

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Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures by Jana, Chiranjibe,Senapati, Tapan,Pal, Madhumangal Pdf

In the world of mathematics, the study of fuzzy relations and its theories are well-documented and a staple in the area of calculative methods. What many researchers and scientists overlook is how fuzzy theory can be applied to industries outside of arithmetic. The framework of fuzzy logic is much broader than professionals realize. There is a lack of research on the full potential this theoretical model can reach. The Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures provides emerging research exploring the theoretical and practical aspects of fuzzy set theory and its real-life applications within the fields of engineering and science. Featuring coverage on a broad range of topics such as complex systems, topological spaces, and linear transformations, this book is ideally designed for academicians, professionals, and students seeking current research on innovations in fuzzy logic in algebra and other matrices.

Author : Ulrich Höhle,S.E. Rodabaugh
Publisher : Springer Science & Business Media
Page : 722 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461550792

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Mathematics of Fuzzy Sets by Ulrich Höhle,S.E. Rodabaugh Pdf

Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory is a major attempt to provide much-needed coherence for the mathematics of fuzzy sets. Much of this book is new material required to standardize this mathematics, making this volume a reference tool with broad appeal as well as a platform for future research. Fourteen chapters are organized into three parts: mathematical logic and foundations (Chapters 1-2), general topology (Chapters 3-10), and measure and probability theory (Chapters 11-14). Chapter 1 deals with non-classical logics and their syntactic and semantic foundations. Chapter 2 details the lattice-theoretic foundations of image and preimage powerset operators. Chapters 3 and 4 lay down the axiomatic and categorical foundations of general topology using lattice-valued mappings as a fundamental tool. Chapter 3 focuses on the fixed-basis case, including a convergence theory demonstrating the utility of the underlying axioms. Chapter 4 focuses on the more general variable-basis case, providing a categorical unification of locales, fixed-basis topological spaces, and variable-basis compactifications. Chapter 5 relates lattice-valued topologies to probabilistic topological spaces and fuzzy neighborhood spaces. Chapter 6 investigates the important role of separation axioms in lattice-valued topology from the perspective of space embedding and mapping extension problems, while Chapter 7 examines separation axioms from the perspective of Stone-Cech-compactification and Stone-representation theorems. Chapters 8 and 9 introduce the most important concepts and properties of uniformities, including the covering and entourage approaches and the basic theory of precompact or complete [0,1]-valued uniform spaces. Chapter 10 sets out the algebraic, topological, and uniform structures of the fundamentally important fuzzy real line and fuzzy unit interval. Chapter 11 lays the foundations of generalized measure theory and representation by Markov kernels. Chapter 12 develops the important theory of conditioning operators with applications to measure-free conditioning. Chapter 13 presents elements of pseudo-analysis with applications to the Hamilton–Jacobi equation and optimization problems. Chapter 14 surveys briefly the fundamentals of fuzzy random variables which are [0,1]-valued interpretations of random sets.

Author : Florentin Smarandache,Yanhui Guo
Publisher : Infinite Study
Page : 411 pages
File Size : 41,8 Mb
Release : 2022-09-01
Category : Mathematics
ISBN : 8210379456XXX

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New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic Plithogenic Optimizations by Florentin Smarandache,Yanhui Guo Pdf

This volume presents state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, and neutrosophic symmetry, as well as their applications in the real world.

Author : Ulrich Höhle,S.E. Rodabaugh
Publisher : Springer
Page : 716 pages
File Size : 48,6 Mb
Release : 2012-01-10
Category : Mathematics
ISBN : 1461550807

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Mathematics of Fuzzy Sets by Ulrich Höhle,S.E. Rodabaugh Pdf

Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory is a major attempt to provide much-needed coherence for the mathematics of fuzzy sets. Much of this book is new material required to standardize this mathematics, making this volume a reference tool with broad appeal as well as a platform for future research. Fourteen chapters are organized into three parts: mathematical logic and foundations (Chapters 1-2), general topology (Chapters 3-10), and measure and probability theory (Chapters 11-14). Chapter 1 deals with non-classical logics and their syntactic and semantic foundations. Chapter 2 details the lattice-theoretic foundations of image and preimage powerset operators. Chapters 3 and 4 lay down the axiomatic and categorical foundations of general topology using lattice-valued mappings as a fundamental tool. Chapter 3 focuses on the fixed-basis case, including a convergence theory demonstrating the utility of the underlying axioms. Chapter 4 focuses on the more general variable-basis case, providing a categorical unification of locales, fixed-basis topological spaces, and variable-basis compactifications. Chapter 5 relates lattice-valued topologies to probabilistic topological spaces and fuzzy neighborhood spaces. Chapter 6 investigates the important role of separation axioms in lattice-valued topology from the perspective of space embedding and mapping extension problems, while Chapter 7 examines separation axioms from the perspective of Stone-Cech-compactification and Stone-representation theorems. Chapters 8 and 9 introduce the most important concepts and properties of uniformities, including the covering and entourage approaches and the basic theory of precompact or complete [0,1]-valued uniform spaces. Chapter 10 sets out the algebraic, topological, and uniform structures of the fundamentally important fuzzy real line and fuzzy unit interval. Chapter 11 lays the foundations of generalized measure theory and representation by Markov kernels. Chapter 12 develops the important theory of conditioning operators with applications to measure-free conditioning. Chapter 13 presents elements of pseudo-analysis with applications to the Hamilton–Jacobi equation and optimization problems. Chapter 14 surveys briefly the fundamentals of fuzzy random variables which are [0,1]-valued interpretations of random sets.

Author : Mahouton Norbert Hounkonnou,Melanija Mitrović,Mujahid Abbas,Madad Khan
Publisher : Springer Nature
Page : 600 pages
File Size : 49,7 Mb
Release : 2023-12-01
Category : Mathematics
ISBN : 9783031393341

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Algebra without Borders – Classical and Constructive Nonassociative Algebraic Structures by Mahouton Norbert Hounkonnou,Melanija Mitrović,Mujahid Abbas,Madad Khan Pdf

This book gathers invited, peer-reviewed works presented at the 2021 edition of the Classical and Constructive Nonassociative Algebraic Structures: Foundations and Applications—CaCNAS: FA 2021, virtually held from June 30 to July 2, 2021, in dedication to the memory of Professor Nebojša Stevanović (1962-2009). The papers cover new trends in the field, focusing on the growing development of applications in other disciplines. These aspects interplay in the same cadence, promoting interactions between theory and applications, and between nonassociative algebraic structures and various fields in pure and applied mathematics. In this volume, the reader will find novel studies on topics such as left almost algebras, logical algebras, groupoids and their generalizations, algebraic geometry and its relations with quiver algebras, enumerative combinatorics, representation theory, fuzzy logic and foundation theory, fuzzy algebraic structures, group amalgams, computer-aided development and transformation of the theory of nonassociative algebraic structures, and applications within natural sciences and engineering. Researchers and graduate students in algebraic structures and their applications can hugely benefit from this book, which can also interest any researcher exploring multi-disciplinarity and complexity in the scientific realm.

Author : Etienne E. Kerre,John Mordeson
Publisher : MDPI
Page : 287 pages
File Size : 44,6 Mb
Release : 2018-11-28
Category : Electronic books
ISBN : 9783038973225

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Fuzzy Mathematics by Etienne E. Kerre,John Mordeson Pdf

This book is a printed edition of the Special Issue "Fuzzy Mathematics" that was published in Mathematics

Author : Liu Ying-Ming,Luo Mao-Kang
Publisher : World Scientific
Page : 364 pages
File Size : 49,8 Mb
Release : 1998-02-28
Category : Computers
ISBN : 9789814518208

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Fuzzy Topology by Liu Ying-Ming,Luo Mao-Kang Pdf

Fuzzy set theory provides us with a framework which is wider than that of classical set theory. Various mathematical structures, whose features emphasize the effects of ordered structure, can be developed on the theory. Fuzzy topology is one such branch, combining ordered structure with topological structure. This branch of mathematics, emerged from the background — processing fuzziness, and locale theory, proposed from the angle of pure mathematics by the great French mathematician Ehresmann, comprise the two most active aspects of topology on lattice, which affect each other. This book is the first monograph to systematically reflect the up-to-date state of fuzzy topology. It emphasizes the so-called “pointed approach” and the effects of stratification structure appearing in fuzzy sets. The monograph can serve as a reference book for mathematicians, researchers, and graduate students working in this branch of mathematics. After an appropriate rearrangements of the chapters and sections, it can also be used as a text for undergraduates. Contents:Fuzzy Topological SpacesOperations on Fuzzy Topological SpacesL-Valued Stratification SpacesConvergence TheoryConnectednessSome Properties Related to CardinalsSeparation (I)Separation (II)CompactnessCompactificationParacompactnessUniformity and ProximityMetric SpacesRelations Between Fuzzy Topological Spaces and Locales Readership: Senior undergraduates, graduate students, and researchers in mathematics and computer science. keywords:Fuzzy;Topology;Fuzzy Lattice;Lattice-valued Topology;Multiple Choice Principle;Coincident Neighborhood Structure;Level Structure;Pointlike Structure;Ordered Structure;Locale “This will be a very useful reference book for everyone working in this field.” Mathematical Reviews

Author : Michael Gr. Voskoglou
Publisher : MDPI
Page : 366 pages
File Size : 45,8 Mb
Release : 2020-03-25
Category : Mathematics
ISBN : 9783039285204

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Fuzzy Sets, Fuzzy Logic and Their Applications by Michael Gr. Voskoglou Pdf

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity.

Author : Dongsik Jo,S. Saleh,Jeong-Gon Lee, Kul Hur,Chen Xueyou
Publisher : Infinite Study
Page : 30 pages
File Size : 54,7 Mb
Release : 2024-06-02
Category : Mathematics
ISBN : 8210379456XXX

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Topological Structures via Interval-Valued Neutrosophic Crisp Sets by Dongsik Jo,S. Saleh,Jeong-Gon Lee, Kul Hur,Chen Xueyou Pdf

In this paper, we introduce the new notion of interval-valued neutrosophic crisp sets providing a tool for approximating undefinable or complex concepts in real world. First, we deal with some of its algebraic structures. We also define an interval-valued neutrosophic crisp (vanishing) point and obtain some of its properties. Next, we define an interval-valued neutrosophic crisp topology, base (subbase), neighborhood, and interior (closure), respectively and investigate some of each property, and give some examples. Finally, we define an interval-valued neutrosophic crisp continuity and quotient topology and study some of each property.

Author : Bijan Davvaz,Irina Cristea
Publisher : Unknown
Page : 254 pages
File Size : 53,6 Mb
Release : 2015-02-28
Category : Electronic
ISBN : 3319147633

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Fuzzy Algebraic Hyperstructures by Bijan Davvaz,Irina Cristea Pdf

Author : Florentin Smarandache,Memet Şahin,Derya Bakbak,Vakkas Uluçay,Abdullah Kargın
Publisher : Infinite Study
Page : 269 pages
File Size : 43,5 Mb
Release : 2022-08-01
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic Algebraic Structures and Their Applications by Florentin Smarandache,Memet Şahin,Derya Bakbak,Vakkas Uluçay,Abdullah Kargın Pdf

Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, medicine, social science, and some more.

Author : Dongsik Jo, S. Saleh,Jeong-Gon Lee, Kul Hur, Chen Xueyou
Publisher : Infinite Study
Page : 29 pages
File Size : 44,5 Mb
Release : 2024-06-02
Category : Mathematics
ISBN : 8210379456XXX

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Topological Structures via Interval-Valued Neutrosophic Crisp Sets by Dongsik Jo, S. Saleh,Jeong-Gon Lee, Kul Hur, Chen Xueyou Pdf

In this paper, we introduce the new notion of interval-valued neutrosophic crisp sets providing a tool for approximating undefinable or complex concepts in real world. First, we deal with some of its algebraic structures. We also define an interval-valued neutrosophic crisp (vanishing) point and obtain some of its properties. Next, we define an interval-valued neutrosophic crisp topology, base (subbase), neighborhood, and interior (closure), respectively and investigate some of each property, and give some examples. Finally, we define an interval-valued neutrosophic crisp continuity and quotient topology and study some of each property.

Author : István Á. Harmati,László T. Kóczy,Jesús Medina,Eloísa Ramírez-Poussa
Publisher : Springer Nature
Page : 223 pages
File Size : 50,6 Mb
Release : 2021-08-25
Category : Technology & Engineering
ISBN : 9783030749705

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Computational Intelligence and Mathematics for Tackling Complex Problems 3 by István Á. Harmati,László T. Kóczy,Jesús Medina,Eloísa Ramírez-Poussa Pdf

Complex problems and systems, which prevail in the real world, cannot often be tackled and solved either by traditional methods offered by mathematics or even the traditional computer science (CS) and and artificial intelligence (AI)..). What is the way out of this dilemma? Advanced methodologies, and tools and techniques, „mimicking” human reasoning or the behavior of animals, animal populations or certain parts of the living bod, based on traditional computer science science and the initial approaches of artificial intelligence are often referred to as biologically inspired methods, or often computational intelligence (CI). Computational intelligence offers effective and efficient solutions to many „unsolvable" problems problems. However, it is far from being a ready to use and complete collection of approaches, and is rather a continuously developing field without clear borders. The emerging new models and algorithms of computational intelligence are deeply rooted in the vast apparatus of traditional mathematics. Thus, the investigation of connections and synergy between mathematics and computational intelligence is an eminent goal which is periodically pursued by a group of mathematicians and computational intelligence researchers who regularly attand the annual European Symposia on Computational Intelligence and Mathematics (ESCIM). Some relevant papers from the last ESCIM-2020 are included in this volume.