Mathematical Principles Of Fuzzy Logic Pdf
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, ...
Author: Barnabas Bede
Publisher: Springer
ISBN: 9783642352218
Category: Technology & Engineering
Page: 276
View: 839
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.
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.
Author: Radim Belohlavek
Publisher: Oxford University Press
ISBN: 9780190665708
Category: Philosophy
Page: 544
View: 995
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.
This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work.
Author: Franco Montagna
Publisher: Springer
ISBN: 9783319062334
Category: Mathematics
Page: 318
View: 656
This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work. The book opens with a discussion on Hájek's contribution to mathematical fuzzy logic and with a scientific biography of him, progresses to include two articles with a foundation flavour, that demonstrate some important aspects of Hájek's production, namely, a paper on the development of fuzzy sets and another paper on some fuzzy versions of set theory and arithmetic. Articles in the volume also focus on the treatment of vagueness, building connections between Hájek's favorite fuzzy logic and linguistic models of vagueness. Other articles introduce alternative notions of consequence relation, namely, the preservation of truth degrees, which is discussed in a general context, and the differential semantics. For the latter, a surprisingly strong standard completeness theorem is proved. Another contribution also looks at two principles valid in classical logic and characterize the three main t-norm logics in terms of these principles. Other articles, with an algebraic flavour, offer a summary of the applications of lattice ordered-groups to many-valued logic and to quantum logic, as well as an investigation of prelinearity in varieties of pointed lattice ordered algebras that satisfy a weak form of distributivity and have a very weak implication. The last part of the volume contains an article on possibilistic modal logics defined over MTL chains, a topic that Hájek discussed in his celebrated work, Metamathematics of Fuzzy Logic, and another one where the authors, besides offering unexpected premises such as proposing to call Hájek's basic fuzzy logic HL, instead of BL, propose a very weak system, called SL as a candidate for the role of the really basic fuzzy logic. The paper also provides a generalization of the prelinearity axiom, which was investigated by Hájek in the context of fuzzy logic.
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: Vilém Novák
Publisher: Springer Science & Business Media
ISBN: 9781461552178
Category: Mathematics
Page: 320
View: 653
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.
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: G. Gerla
Publisher: Springer Science & Business Media
ISBN: 9789401596602
Category: Mathematics
Page: 271
View: 866
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.
This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis.
Author: Petr Hájek
Publisher: Springer Science & Business Media
ISBN: 9789401153003
Category: Philosophy
Page: 299
View: 208
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 technology has emerged as one of the most exciting new concepts available.
Author: Zeungnam Bien
Publisher: Springer Science & Business Media
ISBN: 9789400901254
Category: Mathematics
Page: 483
View: 375
Fuzzy technology has emerged as one of the most exciting new concepts available. Fuzzy Logic and its Applications... covers a wide range of the theory and applications of fuzzy logic and related systems, including industrial applications of fuzzy technology, implementing human intelligence in machines and systems. There are four main themes: intelligent systems, engineering, mathematical foundations, and information sciences. Both academics and the technical community will learn how and why fuzzy logic is appreciated in the conceptual, design and manufacturing stages of intelligent systems, gaining an improved understanding of the basic science and the foundations of human reasoning.
This best-selling text provides 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 a
Author: Hung T. Nguyen
Publisher: CRC Press
ISBN: 9781420057102
Category: Mathematics
Page: 440
View: 996
A First Course in Fuzzy Logic, Third Edition continues to provide the ideal introduction to the theory and applications of fuzzy logic. This best-selling text provides 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 Third Edition: A section on type-2 fuzzy sets - a topic that has received much attention in the past few years Additional material on copulas and t-norms More discussions on generalized modus ponens and the compositional rule of inference Complete revision to the chapter on possibility theory Significant expansion of the chapter on fuzzy integrals Many new exercises With its comprehensive updates, this new edition presents all the background necessary for students and professionals to begin using fuzzy logic in its many-and rapidly growing- applications in computer science, mathematics, statistics, and engineering.
See fuzzy logic fuzzy necessity modal (FN), 220 fuzzy probability modal (FP), 219 generalized necessity, 214 Gödel (G). ... See many-valued logic mathematical, 453 minimal, 133 modal. See modal logic monoidal (ML), 186 monoidal t-norm ...
Author: Radim Belohlávek
Publisher: Oxford University Press
ISBN: 9780190200015
Category: Mathematics
Page: 544
View: 218
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.
Their role is significant when applied to complex phenomena not easily described by traditional mathematics.The unique feature of the book is twofold: 1) It is the first introductory course (with examples and exercises) which brings in a ...
Author: George Bojadziev
Publisher: World Scientific
ISBN: 9789814499941
Category: Computers
Page: 300
View: 571
Fuzzy sets and fuzzy logic are powerful mathematical tools for modeling and controlling uncertain systems in industry, humanity, and nature; they are facilitators for approximate reasoning in decision making in the absence of complete and precise information. Their role is significant when applied to complex phenomena not easily described by traditional mathematics.The unique feature of the book is twofold: 1) It is the first introductory course (with examples and exercises) which brings in a systematic way fuzzy sets and fuzzy logic into the educational university and college system. 2) It is designed to serve as a basic text for introducing engineers and scientists from various fields to the theory of fuzzy sets and fuzzy logic, thus enabling them to initiate projects and make applications.
This book introduces readers to fundamental concepts in fuzzy logic.
Author: Enric Trillas
Publisher: Springer
ISBN: 9783319142036
Category: Technology & Engineering
Page: 204
View: 278
This book introduces readers to fundamental concepts in fuzzy logic. It describes the necessary theoretical background and a number of basic mathematical models. Moreover, it makes them familiar with fuzzy control, an important topic in the engineering field. The book offers an unconventional introductory textbook on fuzzy logic, presenting theory together with examples and not always following the typical mathematical style of theorem-corollaries. Primarily intended to support engineers during their university studies, and to spark their curiosity about fuzzy logic and its applications, the book is also suitable for self-study, providing a valuable resource for engineers and professionals who deal with imprecision and non-random uncertainty in real-world applications.
This book is an excellent starting point for any curriculum in fuzzy systems fields such as computer science, mathematics, business/economics and engineering.
Author: James J. Buckley
Publisher: Springer Science & Business Media
ISBN: 9783790817997
Category: Computers
Page: 285
View: 963
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.
This volume demonstrates that there are many different views of the theory of fuzzy sets and systems and of their interpretation and applications in diverse areas of our cultural and social life.
Author: Rudolf Seising
Publisher: Springer
ISBN: 9783540938026
Category: Technology & Engineering
Page: 580
View: 425
In our new century, the theory of fuzzy sets and systems is in the core of "Soft Computing" and "Computational Intelligence" and has become a normal scientific theory in the fields of exact sciences and engineering and it is well on its way to becoming normal in the soft sciences as well. This book is a collection of the views of numerous scholars in different parts of the world who are involved in various research projects concerning fuzziness in science, technology, economic systems, social sciences, logics and philosophy. This volume demonstrates that there are many different views of the theory of fuzzy sets and systems and of their interpretation and applications in diverse areas of our cultural and social life.
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.
Author: Esko Turunen
Publisher: Physica
ISBN: UCSC:32106015489625
Category: Business & Economics
Page: 191
View: 487
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.
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online.
Author: Source Wikipedia
Publisher: University-Press.org
ISBN: 1230502831
Category:
Page: 100
View: 514
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 60. Chapters: Adaptive neuro fuzzy inference system, Bate's chip, BL (logic), Combs method, Construction of t-norms, Defuzzification, Degree of truth, European Society for Fuzzy Logic and Technology, Fuzzy architectural spatial analysis, Fuzzy associative matrix, Fuzzy associative memory, Fuzzy classification, Fuzzy cognitive map, Fuzzy Control Language, Fuzzy control system, Fuzzy electronics, Fuzzy finite element, Fuzzy markup language, Fuzzy mathematics, Fuzzy measure theory, Fuzzy number, Fuzzy pay-off method for real option valuation, Fuzzy routing, Fuzzy rule, Fuzzy set, Fuzzy Sets and Systems, Fuzzy set operations, Fuzzy subalgebra, Fuzzy transportation, High Performance Fuzzy Computing, Linear partial information, Membership function (mathematics), Monoidal t-norm logic, MV-algebra, Noise-based logic, Ordered weighted averaging aggregation operator, Perceptual computing, Possibility theory, Predicate (mathematical logic), Residuated Boolean algebra, Residuated lattice, Rough fuzzy hybridization, Sugeno integral, T-norm fuzzy logics, Type-1 OWA operators, Type-2 fuzzy sets and systems, Uncertainty theory, Vagueness, ukasiewicz logic. Excerpt: A fuzzy control system is a control system based on fuzzy logic-a mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in contrast to classical or digital logic, which operates on discrete values of either 1 or 0 (true or false, respectively). Fuzzy logic is widely used in machine control. The term itself inspires a certain skepticism, sounding equivalent to "half-baked logic" or "bogus logic," but the "fuzzy" part does not refer to a lack of rigour in the method, rather to the fact that the logic involved can deal with concepts that cannot be expressed as "true" or "false" but rather as "partially...
Designed primarily as a text for senior undergraduate students of Computer Science and Engineering, and postgraduate students of Mathematics and Applied Mathematics, this compact book describes the theoretical aspects of fuzzy set theory ...
Author: RAJJAN SHINGHAL
Publisher: PHI Learning Pvt. Ltd.
ISBN: 9788120346994
Category: Computers
Page: 144
View: 932
Designed primarily as a text for senior undergraduate students of Computer Science and Engineering, and postgraduate students of Mathematics and Applied Mathematics, this compact book describes the theoretical aspects of fuzzy set theory and fuzzy logic. Based on his many years of experience, Professor Rajjan Shinghal gives a succinct analysis of the procedures for fuzzy sets complementation, intersection, and union. He also explains clearly how arithmetic operations are carried out on approximate numbers, how fuzzy sets are used for reasoning, and how they are employed for unsupervised learning. Finally, the book shows how fuzzy sets are utilized in applications such as logic control, databases, information retrieval, ordering of objects, and satisfying multiple goals. Besides students, professionals working in research organizations should find the book quite useful.
Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides a comprehensive study of fuzzy social choice theory.The book explains the concept of a fuzzy max
Author: John N. Mordeson
Publisher: CRC Press
ISBN: 9781482250992
Category: Mathematics
Page: 352
View: 655
Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences. Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides a comprehensive study of fuzzy social choice theory. The book explains the concept of a fuzzy maximal subset of a set of alternatives, fuzzy choice functions, the factorization of a fuzzy preference relation into the "union" (conorm) of a strict fuzzy relation and an indifference operator, fuzzy non-Arrowian results, fuzzy versions of Arrow's theorem, and Black's median voter theorem for fuzzy preferences. It examines how unambiguous and exact choices are generated by fuzzy preferences and whether exact choices induced by fuzzy preferences satisfy certain plausible rationality relations. The authors also extend known Arrowian results involving fuzzy set theory to results involving intuitionistic fuzzy sets as well as the Gibbard–Satterthwaite theorem to the case of fuzzy weak preference relations. The final chapter discusses Georgescu's degree of similarity of two fuzzy choice functions.
This book provides an essential introduction to the field of dynamical models.
Author: Laécio Carvalho de Barros
Publisher: Springer
ISBN: 9783662533246
Category: Computers
Page: 299
View: 111
This book provides an essential introduction to the field of dynamical models. Starting from classical theories such as set theory and probability, it allows readers to draw near to the fuzzy case. On one hand, the book equips readers with a fundamental understanding of the theoretical underpinnings of fuzzy sets and fuzzy dynamical systems. On the other, it demonstrates how these theories are used to solve modeling problems in biomathematics, and presents existing derivatives and integrals applied to the context of fuzzy functions. Each of the major topics is accompanied by examples, worked-out exercises, and exercises to be completed. Moreover, many applications to real problems are presented. The book has been developed on the basis of the authors' lectures to university students and is accordingly primarily intended as a textbook for both upper-level undergraduates and graduates in applied mathematics, statistics, and engineering. It also offers a valuable resource for practitioners such as mathematical consultants and modelers, and for researchers alike, as it may provide both groups with new ideas and inspirations for projects in the fields of fuzzy logic and biomathematics.
The term 'fuzzy logic' (FL), 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.
Author: Belohlavek
Publisher:
ISBN: 0190200030
Category:
Page:
View: 854
With this book, you can find out. The authors of this updated edition have extended Klir's work by taking fuzzy logic into even more areas of application.
Author: Paul P. Wang
Publisher: Springer
ISBN: 9783540712589
Category: Technology & Engineering
Page: 459
View: 312
How far can you take fuzzy logic, the brilliant conceptual framework made famous by George Klir? With this book, you can find out. The authors of this updated edition have extended Klir's work by taking fuzzy logic into even more areas of application. It serves a number of functions, from an introductory text on the concept of fuzzy logic to a treatment of cutting-edge research problems suitable for a fully paid-up member of the fuzzy logic community.
Mathematical Principles Of Fuzzy Logic Pdf
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