Mathematics Behind Fuzzy Logic

Author : Esko Turunen
Publisher : Physica
ISBN 13 :
Total Pages : 212 pages
Book Rating : 4.25/5 ( download)

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Download or read book Mathematics Behind Fuzzy Logic written by Esko Turunen and published by Physica. This book was released on 1999-09-24 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many results in fuzzy logic depend on the mathematical structure the truth value set obeys. In this textbook the algebraic foundations of many-valued and fuzzy reasoning are introduced. The book is self-contained, thus no previous knowledge in algebra or in logic is required. It contains 134 exercises with complete answers, and can therefore be used as teaching material at universities for both undergraduated and post-graduated courses. Chapter 1 starts from such basic concepts as order, lattice, equivalence and residuated lattice. It contains a full section on BL-algebras. Chapter 2 concerns MV-algebra and its basic properties. Chapter 3 applies these mathematical results on Lukasiewicz-Pavelka style fuzzy logic, which is studied in details; besides semantics, syntax and completeness of this logic, a lot of examples are given. Chapter 4 shows the connection between fuzzy relations, approximate reasoning and fuzzy IF-THEN rules to residuated lattices.

Author : Petr Hájek
Publisher : Springer Science & Business Media
ISBN 13 : 9401153000
Total Pages : 304 pages
Book Rating : 4.03/5 ( download)

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Download or read book Metamathematics of Fuzzy Logic written by Petr Hájek and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. It aims to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named ‘fuzzy inference’ can be naturally understood as logical deduction. It is for mathematicians, logicians, computer scientists, specialists in artificial intelligence and knowledge engineering, and developers of fuzzy logic.

Author : Radim Bělohlávek
Publisher : Oxford University Press
ISBN 13 : 0190200014
Total Pages : 545 pages
Book Rating : 4.15/5 ( download)

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Download or read book Fuzzy Logic and Mathematics written by Radim Bělohlávek and published by Oxford University Press. This book was released on 2017 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main part of the book is a comprehensive overview of the development of fuzzy logic and its applications in various areas of human affair since its genesis in the mid 1960s. This overview is then employed for assessing the significance of fuzzy logic and mathematics based on fuzzy logic.

Author : Vilém Novák
Publisher : Springer Science & Business Media
ISBN 13 : 1461552176
Total Pages : 327 pages
Book Rating : 4.78/5 ( download)

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Download or read book Mathematical Principles of Fuzzy Logic written by Vilém Novák and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Principles of Fuzzy Logic provides a systematic study of the formal theory of fuzzy logic. The book is based on logical formalism demonstrating that fuzzy logic is a well-developed logical theory. It includes the theory of functional systems in fuzzy logic, providing an explanation of what can be represented, and how, by formulas of fuzzy logic calculi. It also presents a more general interpretation of fuzzy logic within the environment of other proper categories of fuzzy sets stemming either from the topos theory, or even generalizing the latter. This book presents fuzzy logic as the mathematical theory of vagueness as well as the theory of commonsense human reasoning, based on the use of natural language, the distinguishing feature of which is the vagueness of its semantics.

Author : Barnabas Bede
Publisher : Springer
ISBN 13 : 3642352219
Total Pages : 281 pages
Book Rating : 4.18/5 ( download)

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Download or read book Mathematics of Fuzzy Sets and Fuzzy Logic written by Barnabas Bede and published by Springer. This book was released on 2012-12-14 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a mathematically-based introduction into the fascinating topic of Fuzzy Sets and Fuzzy Logic and might be used as textbook at both undergraduate and graduate levels and also as reference guide for mathematician, scientists or engineers who would like to get an insight into Fuzzy Logic. Fuzzy Sets have been introduced by Lotfi Zadeh in 1965 and since then, they have been used in many applications. As a consequence, there is a vast literature on the practical applications of fuzzy sets, while theory has a more modest coverage. The main purpose of the present book is to reduce this gap by providing a theoretical introduction into Fuzzy Sets based on Mathematical Analysis and Approximation Theory. Well-known applications, as for example fuzzy control, are also discussed in this book and placed on new ground, a theoretical foundation. Moreover, a few advanced chapters and several new results are included. These comprise, among others, a new systematic and constructive approach for fuzzy inference systems of Mamdani and Takagi-Sugeno types, that investigates their approximation capability by providing new error estimates.

Author : Rahul Kar
Publisher : John Wiley & Sons
ISBN 13 : 1394175116
Total Pages : 265 pages
Book Rating : 4.16/5 ( download)

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Download or read book Fuzzy Logic Applications in Computer Science and Mathematics written by Rahul Kar and published by John Wiley & Sons. This book was released on 2023-09-15 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: FUZZY LOGIC APPLICATIONS IN COMPUTER SCIENCE AND MATHEMATICSTICS The prime objective of developing this book is to provide meticulous details about the basic and advanced concepts of fuzzy logic and its all-around applications to different fields of mathematics and engineering. The basic steps of fuzzy inference systems starting from the core foundation of the fuzzy concepts are presented in this book. The fuzzy theory is a mathematical concept and, at the same time, it is applied to many versatile engineering fields and research domains related to computer science. The fuzzy system offers some knowledge about uncertainty and is also related to the theory of probability. A fuzzy logic-based model acts as the classifier for many different types of data belonging to several classes. Covered in this book are topics such as the fundamental concepts of mathematics, fuzzy logic concepts, probability and possibility theories, and evolutionary computing to some extent. The combined fields of neural network and fuzzy domain (known as the neuro-fuzzy system) are explained and elaborated. Each chapter has been produced in a very lucid manner, with grading from simple to complex to accommodate the anticipated different audiences. The application-oriented approach is the unique feature of this book. Audience This book will be read and used by a broad audience including applied mathematicians, computer scientists, and industry engineers.

Author : Ulrich Höhle
Publisher : Springer Science & Business Media
ISBN 13 : 1461550793
Total Pages : 722 pages
Book Rating : 4.92/5 ( download)

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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.

Author : Bart Kosko
Publisher : Hyperion
ISBN 13 : 9780786880218
Total Pages : 0 pages
Book Rating : 4.1X/5 ( download)

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Download or read book Fuzzy Thinking written by Bart Kosko and published by Hyperion. This book was released on 1994-06-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A washing machine that gauges each load to determine how much soap to use An air conditioner that constantly adjusts cooling strength based on room temperature These "smart" products are possible with the advent of "fuzzy logic, " the principle that's revolutionizing science. Now, its chief proponent presents a brilliant, popular account of the field called the "new chaos.".

Author : G. Gerla
Publisher : Springer Science & Business Media
ISBN 13 : 9401596603
Total Pages : 276 pages
Book Rating : 4.02/5 ( download)

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Download or read book Fuzzy Logic written by G. Gerla and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy logic in narrow sense is a promising new chapter of formal logic whose basic ideas were formulated by Lotfi Zadeh (see Zadeh [1975]a). The aim of this theory is to formalize the "approximate reasoning" we use in everyday life, the object of investigation being the human aptitude to manage vague properties (as, for example, "beautiful", "small", "plausible", "believable", etc. ) that by their own nature can be satisfied to a degree different from 0 (false) and I (true). It is worth noting that the traditional deductive framework in many-valued logic is different from the one adopted in this book for fuzzy logic: in the former logics one always uses a "crisp" deduction apparatus, producing crisp sets of formulas, the formulas that are considered logically valid. By contrast, fuzzy logical deductive machinery is devised to produce a fuzzy set of formulas (the theorems) from a fuzzy set of formulas (the hypotheses). Approximate reasoning has generated a very interesting literature in recent years. However, in spite of several basic results, in our opinion, we are still far from a satisfactory setting of this very hard and mysterious subject. The aim of this book is to furnish some theoretical devices and to sketch a general framework for fuzzy logic. This is also in accordance with the non Fregean attitude of the book.

Author : Timothy J. Ross
Publisher : John Wiley & Sons
ISBN 13 : 1119235855
Total Pages : 584 pages
Book Rating : 4.59/5 ( download)

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Download or read book Fuzzy Logic with Engineering Applications written by Timothy J. Ross and published by John Wiley & Sons. This book was released on 2016-09-20 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: The latest update on this popular textbook The importance of concepts and methods based on fuzzy logic and fuzzy set theory has been rapidly growing since the early 1990s and all the indications are that this trend will continue in the foreseeable future. Fuzzy Logic with Engineering Applications, Fourth Edition is a new edition of the popular textbook with 15% of new and updated material. Updates have been made to most of the chapters and each chapter now includes new end-of-chapter problems. Key features: New edition of the popular textbook with 15% of new and updated material. Includes new examples and end-of-chapter problems. Has been made more concise with the removal of out of date material. Covers applications of fuzzy logic to engineering and science. Accompanied by a website hosting a solutions manual and software. The book is essential reading for graduates and senior undergraduate students in civil, chemical, mechanical and electrical engineering as wells as researchers and practitioners working with fuzzy logic in industry.