Fuzzy Topology

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Author :
Publisher : World Scientific
ISBN 13 : 9814518204
Total Pages : 365 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Fuzzy Topology by : Ying-ming Liu

Download or read book Fuzzy Topology written by Ying-ming Liu and published by World Scientific. This book was released on 1998-02-28 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of the History of General Topology

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 9401704708
Total Pages : 418 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Handbook of the History of General Topology by : C.E. Aull

Download or read book Handbook of the History of General Topology written by C.E. Aull and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first one of a work in several volumes, treating the history of the development of topology. The work contains papers which can be classified into 4 main areas. Thus there are contributions dealing with the life and work of individual topologists, with specific schools of topology, with research in topology in various countries, and with the development of topology in different periods. The work is not restricted to topology in the strictest sense but also deals with applications and generalisations in a broad sense. Thus it also treats, e.g., categorical topology, interactions with functional analysis, convergence spaces, and uniform spaces. Written by specialists in the field, it contains a wealth of information which is not available anywhere else.

Fuzzy Topology

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Author :
Publisher : Chapman & Hall/CRC
ISBN 13 : 9780849324161
Total Pages : 0 pages
Book Rating : 4.3/5 (241 download)

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Book Synopsis Fuzzy Topology by : N. Palaniappan

Download or read book Fuzzy Topology written by N. Palaniappan and published by Chapman & Hall/CRC. This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, many concepts in mathematics, engineering, computer science, and many other disciplines have been in a sense redefined to incorporate the notion of fuzziness. Designed for graduate students and research scholars, Fuzzy Topology imparts the concepts and recent developments related to the various properties of fuzzy topology. The author first addresses fundamental problems, such as the idea of a fuzzy point and its neighborhood structure and the theory of convergence. He then studies the connection between fuzzy topological spaces and topological spaces and introduces fuzzy continuity and product induced spaces. Chapter Three examines fuzzy nets, fuzzy upper and lower limits, and fuzzy convergence and is followed by a study of fuzzy metric spaces. The treatment then introduces the concept of fuzzy compactness before moving to initial and final topologies and the fuzzy Tychnoff theorem. The final sections of the book cover connectedness, complements, separation axioms, and uniform spaces.

Mathematics of Fuzzy Sets

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Publisher : Springer Science & Business Media
ISBN 13 : 1461550793
Total Pages : 722 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Mathematics of Fuzzy Sets by : Ulrich Höhle

Download or read book Mathematics of Fuzzy Sets written by Ulrich Höhle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematics of Fuzziness—Basic Issues

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Publisher : Springer Science & Business Media
ISBN 13 : 3540783105
Total Pages : 227 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Mathematics of Fuzziness—Basic Issues by : Xuzhu Wang

Download or read book Mathematics of Fuzziness—Basic Issues written by Xuzhu Wang and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Fuzziness – Basic Issues introduces a basic notion of ‘fuzziness’ and provides a conceptual mathematical framework to characterize such fuzzy phenomena in Studies in Fuzziness and Soft Computing. The book systematically presents a self-contained introduction to the essentials of mathematics of fuzziness ranging from fuzzy sets, fuzzy relations, fuzzy numbers, fuzzy algebra, fuzzy measures, fuzzy integrals, and fuzzy topology to fuzzy control in a strictly mathematical manner. It contains most of the authors’ research results in the field of fuzzy set theory and has evolved from the authors’ lecture notes to both undergraduate and graduate students over the last three decades. A lot of exercises in each chapter of the book are particularly suitable as a textbook for any undergraduate and graduate student in mathematics, computer science and engineering. The reading of the book will surely lay a solid foundation for further research on fuzzy set theory and its applications.

Topological and Algebraic Structures in Fuzzy Sets

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Publisher : Springer Science & Business Media
ISBN 13 : 9401702314
Total Pages : 468 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Topological and Algebraic Structures in Fuzzy Sets by : S.E. Rodabaugh

Download or read book Topological and Algebraic Structures in Fuzzy Sets written by S.E. Rodabaugh and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Encyclopedia of General Topology

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Publisher : Elsevier
ISBN 13 : 0080530869
Total Pages : 537 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Encyclopedia of General Topology by : K.P. Hart

Download or read book Encyclopedia of General Topology written by K.P. Hart and published by Elsevier. This book was released on 2003-11-18 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book.Key features:• More terms from General Topology than any other book ever published• Short and informative articles• Authors include the majority of top researchers in the field• Extensive indexing of terms

Putting Crime in its Place

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Publisher : Springer Science & Business Media
ISBN 13 : 0387096876
Total Pages : 258 pages
Book Rating : 4.3/5 (87 download)

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Book Synopsis Putting Crime in its Place by : David Weisburd

Download or read book Putting Crime in its Place written by David Weisburd and published by Springer Science & Business Media. This book was released on 2008-10-20 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Putting Crime in its Place: Units of Analysis in Geographic Criminology focuses on the units of analysis used in geographic criminology. While crime and place studies have been a part of criminology from the early 19th century, growing interest in crime places over the last two decades demands critical reflection on the units of analysis that should form the focus of geographic analysis of crime. Should the focus be on very small units such as street addresses or street segments, or on larger aggregates such as census tracts or communities? Academic researchers, as well as practical crime analysts, are confronted routinely with the dilemma of deciding what the unit of analysis should be when reporting on trends in crime, when identifying crime hot spots or when mapping crime in cities. In place-based crime prevention, the choice of the level of aggregation plays a particularly critical role. This peer reviewed collection of essays aims to contribute to crime and place studies by making explicit the problems involved in choosing units of analysis in geographic criminology. Written by renowned experts in the field, the chapters in this book address basic academic questions, and also provide real-life examples and applications of how they are resolved in cutting-edge research. Crime analysts in police and law enforcement agencies as well as academic researchers studying the spatial distributions of crime and victimization will learn from the discussions and tools presented.

Aspects of Topology

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Publisher : Cambridge University Press
ISBN 13 : 0521278155
Total Pages : 357 pages
Book Rating : 4.5/5 (212 download)

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Book Synopsis Aspects of Topology by : Ioan Mackenzie James

Download or read book Aspects of Topology written by Ioan Mackenzie James and published by Cambridge University Press. This book was released on 1985-01-31 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a memorial volume to the distinguished Canadian-born mathematician Hugh Dowker, one of the most highly regarded topologists in the United Kingdom and sometime Professor at Birkbeck College, London. The volume comprises specially written articles on various topological topics by experts in many countries who worked with Dowker at one time or another. These include survey, expository and research articles on general topology, algebraic topology and related subjects such as knot theory and graph theory. The volume will be of great interest to graduate students and professional mathematicians whose speciality is topology, in all its aspects.

Metric Spaces of Fuzzy Sets

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Author :
Publisher : World Scientific
ISBN 13 : 9789810217310
Total Pages : 192 pages
Book Rating : 4.2/5 (173 download)

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Book Synopsis Metric Spaces of Fuzzy Sets by : Phil Diamond

Download or read book Metric Spaces of Fuzzy Sets written by Phil Diamond and published by World Scientific. This book was released on 1994 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary aim of the book is to provide a systematic development of the theory of metric spaces of normal, upper semicontinuous fuzzy convex fuzzy sets with compact support sets, mainly on the base space ?n. An additional aim is to sketch selected applications in which these metric space results and methods are essential for a thorough mathematical analysis.This book is distinctly mathematical in its orientation and style, in contrast with many of the other books now available on fuzzy sets, which, although all making use of mathematical formalism to some extent, are essentially motivated by and oriented towards more immediate applications and related practical issues. The reader is assumed to have some previous undergraduate level acquaintance with metric spaces and elementary functional analysis.

Fuzzy Topology

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Publisher : World Scientific
ISBN 13 : 9789810228620
Total Pages : 372 pages
Book Rating : 4.2/5 (286 download)

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Book Synopsis Fuzzy Topology by : Ying-ming Liu

Download or read book Fuzzy Topology written by Ying-ming Liu and published by World Scientific. This book was released on 1997 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

New types of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/Off-Set, Neutrosophic Refined Set, and their Extension to Plithogenic Set/Logic/Probability, with Applications

Download New types of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/Off-Set, Neutrosophic Refined Set, and their Extension to Plithogenic Set/Logic/Probability, with Applications PDF Online Free

Author :
Publisher : MDPI
ISBN 13 : 3039219383
Total Pages : 714 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis New types of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/Off-Set, Neutrosophic Refined Set, and their Extension to Plithogenic Set/Logic/Probability, with Applications by : Florentin Smarandache

Download or read book New types of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/Off-Set, Neutrosophic Refined Set, and their Extension to Plithogenic Set/Logic/Probability, with Applications written by Florentin Smarandache and published by MDPI. This book was released on 2019-11-27 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains 37 papers by 73 renowned experts from 13 countries around the world, on following topics: neutrosophic set; neutrosophic rings; neutrosophic quadruple rings; idempotents; neutrosophic extended triplet group; hypergroup; semihypergroup; neutrosophic extended triplet group; neutrosophic extended triplet semihypergroup and hypergroup; neutrosophic offset; uninorm; neutrosophic offuninorm and offnorm; neutrosophic offconorm; implicator; prospector; n-person cooperative game; ordinary single-valued neutrosophic (co)topology; ordinary single-valued neutrosophic subspace; α-level; ordinary single-valued neutrosophic neighborhood system; ordinary single-valued neutrosophic base and subbase; fuzzy numbers; neutrosophic numbers; neutrosophic symmetric scenarios; performance indicators; financial assets; neutrosophic extended triplet group; neutrosophic quadruple numbers; refined neutrosophic numbers; refined neutrosophic quadruple numbers; multigranulation neutrosophic rough set; nondual; two universes; multiattribute group decision making; nonstandard analysis; extended nonstandard analysis; monad; binad; left monad closed to the right; right monad closed to the left; pierced binad; unpierced binad; nonstandard neutrosophic mobinad set; neutrosophic topology; nonstandard neutrosophic topology; visual tracking; neutrosophic weight; objectness; weighted multiple instance learning; neutrosophic triangular norms; residuated lattices; representable neutrosophic t-norms; De Morgan neutrosophic triples; neutrosophic residual implications; infinitely ∨-distributive; probabilistic neutrosophic hesitant fuzzy set; decision-making; Choquet integral; e-marketing; Internet of Things; neutrosophic set; multicriteria decision making techniques; uncertainty modeling; neutrosophic goal programming approach; shale gas water management system.

Ordinary Single Valued Neutrosophic Topological Spaces

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Author :
Publisher : Infinite Study
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4./5 ( download)

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Book Synopsis Ordinary Single Valued Neutrosophic Topological Spaces by : Junhui Kim

Download or read book Ordinary Single Valued Neutrosophic Topological Spaces written by Junhui Kim and published by Infinite Study. This book was released on with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: We define an ordinary single valued neutrosophic topology and obtain some of its basic properties. In addition, we introduce the concept of an ordinary single valued neutrosophic subspace. Next, we define the ordinary single valued neutrosophic neighborhood system and we show that an ordinary single valued neutrosophic neighborhood system has the same properties in a classical neighborhood system. Finally, we introduce the concepts of an ordinary single valued neutrosophic base and an ordinary single valued neutrosophic subbase, and obtain two characterizations of an ordinary single valued neutrosophic base and one characterization of an ordinary single valued neutrosophic subbase.

Neutrosophic Crisp Set Theory

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Publisher : Infinite Study
ISBN 13 : 1599733234
Total Pages : 184 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Neutrosophic Crisp Set Theory by : A. A. Salama, Florentin Smarandache

Download or read book Neutrosophic Crisp Set Theory written by A. A. Salama, Florentin Smarandache and published by Infinite Study. This book was released on 2015-05-01 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:

New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic Plithogenic Optimizations

Download New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic Plithogenic Optimizations PDF Online Free

Author :
Publisher : Infinite Study
ISBN 13 :
Total Pages : 411 pages
Book Rating : 4./5 ( download)

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Book Synopsis New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic Plithogenic Optimizations by : Florentin Smarandache

Download or read book New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic Plithogenic Optimizations written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-09-01 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Modern Introduction to Fuzzy Mathematics

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 1119445280
Total Pages : 382 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis A Modern Introduction to Fuzzy Mathematics by : Apostolos Syropoulos

Download or read book A Modern Introduction to Fuzzy Mathematics written by Apostolos Syropoulos and published by John Wiley & Sons. This book was released on 2020-07-28 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides readers with the foundations of fuzzy mathematics as well as more advanced topics A Modern Introduction to Fuzzy Mathematics provides a concise presentation of fuzzy mathematics., moving from proofs of important results to more advanced topics, like fuzzy algebras, fuzzy graph theory, and fuzzy topologies. The authors take the reader through the development of the field of fuzzy mathematics, starting with the publication in 1965 of Lotfi Asker Zadeh's seminal paper, Fuzzy Sets. The book begins with the basics of fuzzy mathematics before moving on to more complex topics, including: Fuzzy sets Fuzzy numbers Fuzzy relations Possibility theory Fuzzy abstract algebra And more Perfect for advanced undergraduate students, graduate students, and researchers with an interest in the field of fuzzy mathematics, A Modern Introduction to Fuzzy Mathematics walks through both foundational concepts and cutting-edge, new mathematics in the field.

Neutrosophic Systems with Applications (NSWA), Vol. 1, 2023

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Author :
Publisher : Infinite Study
ISBN 13 :
Total Pages : 37 pages
Book Rating : 4./5 ( download)

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Book Synopsis Neutrosophic Systems with Applications (NSWA), Vol. 1, 2023 by : Florentin Smarandache

Download or read book Neutrosophic Systems with Applications (NSWA), Vol. 1, 2023 written by Florentin Smarandache and published by Infinite Study. This book was released on 2023-09-23 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers on neutrosophic and plithogenic sets, logics, probabilities and statistics.