Mathematics Behind Fuzzy Logic
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Mathematics Behind Fuzzy Logic
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Author : Esko Turunen
language : en
Publisher: Physica
Release Date : 1999-09-24
Mathematics Behind Fuzzy Logic written by Esko Turunen and has been published by Physica this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-24 with Business & Economics categories.
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.
Fuzzy Logic And Mathematics
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Author : Radim Belohlavek
language : en
Publisher: Oxford University Press
Release Date : 2017-05-03
Fuzzy Logic And Mathematics written by Radim Belohlavek and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-03 with Philosophy categories.
The term "fuzzy logic," as it is understood in this book, stands for all aspects of representing and manipulating knowledge based on the rejection of the most fundamental principle of classical logic---the principle of bivalence. According to this principle, each declarative sentence is required to be either true or false. In fuzzy logic, these classical truth values are not abandoned. However, additional, intermediate truth values between true and false are allowed, which are interpreted as degrees of truth. This opens a new way of thinking---thinking in terms of degrees rather than absolutes. For example, it leads to the definition of a new kind of sets, referred to as fuzzy sets, in which membership is a matter of degree. The book examines the genesis and development of fuzzy logic. It surveys the prehistory of fuzzy logic and inspects circumstances that eventually lead to the emergence of fuzzy logic. The book explores in detail the development of propositional, predicate, and other calculi that admit degrees of truth, which are known as fuzzy logic in the narrow sense. Fuzzy logic in the broad sense, whose primary aim is to utilize degrees of truth for emulating common-sense human reasoning in natural language, is scrutinized as well. The book also examines principles for developing mathematics based on fuzzy logic and provides overviews of areas in which this has been done most effectively. It also presents a detailed survey of established and prospective applications of fuzzy logic in various areas of human affairs, and provides an assessment of the significance of fuzzy logic as a new paradigm.
Fuzzy Logic Applications In Computer Science And Mathematics
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Author : Rahul Kar
language : en
Publisher: John Wiley & Sons
Release Date : 2023-09-15
Fuzzy Logic Applications In Computer Science And Mathematics written by Rahul Kar and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-15 with Mathematics categories.
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.
Metamathematics Of Fuzzy Logic
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Author : Petr Hájek
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Metamathematics Of Fuzzy Logic written by Petr Hájek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Philosophy categories.
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.
Fuzzy Logic
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Author :
language : en
Publisher: BoD – Books on Demand
Release Date : 2020-02-05
Fuzzy Logic written by and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-05 with Mathematics categories.
This book promotes new research results in the field of advanced fuzzy logic applications. The book has eight chapters, with the following thematic areas: fuzzy mathematics, adaptive neuro-fuzzy inference system, inference methods, expert systems, electrical systems, and application in management and field-programmable gate array. The introductory chapter aims to recall some algebraic relations that describe fuzzy rule bases and fuzzy blocks as algebraic applications. Other works presented are: a study on the convergence of sequence spaces with respect to intuitionistic fuzzy norms and their topological and algebraic properties; an ANFIS application to identifying the online bearing fault; methods of conditional inference for fuzzy control systems; an application of fuzzy logic and fuzzy expert systems in material synthesis methods; control of electrical systems in conditions of incomplete information regarding the values of diagnostic parameters; a methodology for evaluating the causality of factors in organization management; and a technical study on the functional safety of an FPGA fuzzy logic controller. The authors have published worked examples and case studies resulting from their research in the field. Readers will have access to new solutions and answers to questions related to the emerging field of theoretical fuzzy logic applications and their implementation.
Fuzzy Logic
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Author : G. Gerla
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Fuzzy Logic written by G. Gerla and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.
An Introduction To Fuzzy Logic And Fuzzy Sets
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Author : James J. Buckley
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
An Introduction To Fuzzy Logic And Fuzzy Sets written by James J. Buckley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Computers categories.
This book is an excellent starting point for any curriculum in fuzzy systems fields such as computer science, mathematics, business/economics and engineering. It covers the basics leading to: fuzzy clustering, fuzzy pattern recognition, fuzzy database, fuzzy image processing, soft computing, fuzzy applications in operations research, fuzzy decision making, fuzzy rule based systems, fuzzy systems modeling, fuzzy mathematics. It is not a book designed for researchers - it is where you really learn the "basics" needed for any of the above-mentioned applications. It includes many figures and problem sets at the end of sections.
Fuzzy Sets Fuzzy Logic And Fuzzy Systems
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Author : Lotfi Asker Zadeh
language : en
Publisher: World Scientific
Release Date : 1996
Fuzzy Sets Fuzzy Logic And Fuzzy Systems written by Lotfi Asker Zadeh and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Computers categories.
This book consists of selected papers written by the founder of fuzzy set theory, Lotfi A Zadeh. Since Zadeh is not only the founder of this field, but has also been the principal contributor to its development over the last 30 years, the papers contain virtually all the major ideas in fuzzy set theory, fuzzy logic, and fuzzy systems in their historical context. Many of the ideas presented in the papers are still open to further development. The book is thus an important resource for anyone interested in the areas of fuzzy set theory, fuzzy logic, and fuzzy systems, as well as their applications. Moreover, the book is also intended to play a useful role in higher education, as a rich source of supplementary reading in relevant courses and seminars.The book contains a bibliography of all papers published by Zadeh in the period 1949-1995. It also contains an introduction that traces the development of Zadeh's ideas pertaining to fuzzy sets, fuzzy logic, and fuzzy systems via his papers. The ideas range from his 1965 seminal idea of the concept of a fuzzy set to ideas reflecting his current interest in computing with words ? a computing in which linguistic expressions are used in place of numbers.Places in the papers, where each idea is presented can easily be found by the reader via the Subject Index.
A First Course In Fuzzy Logic
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Author : Hung T. Nguyen
language : en
Publisher: CRC Press
Release Date : 2018-12-07
A First Course In Fuzzy Logic written by Hung T. Nguyen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-07 with Mathematics categories.
A First Course in Fuzzy Logic, Fourth Edition is an expanded version of the successful third edition. It provides a comprehensive introduction to the theory and applications of fuzzy logic. This popular text offers a firm mathematical basis for the calculus of fuzzy concepts necessary for designing intelligent systems and a solid background for readers to pursue further studies and real-world applications. New in the Fourth Edition: Features new results on fuzzy sets of type-2 Provides more information on copulas for modeling dependence structures Includes quantum probability for uncertainty modeling in social sciences, especially in economics With its comprehensive updates, this new edition presents all the background necessary for students, instructors and professionals to begin using fuzzy logic in its many—applications in computer science, mathematics, statistics, and engineering. About the Authors: Hung T. Nguyen is a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University. He is also an Adjunct Professor of Economics at Chiang Mai University, Thailand. Carol L. Walker is also a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University. Elbert A. Walker is a Professor Emeritus, Department of Mathematical Sciences, New Mexico State University.
Mathematics Of Fuzzy Sets And Fuzzy Logic
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Author : Barnabas Bede
language : en
Publisher: Springer
Release Date : 2012-12-14
Mathematics Of Fuzzy Sets And Fuzzy Logic written by Barnabas Bede and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Technology & Engineering categories.
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.