Mathematical Principles Of Fuzzy Logic

Author : Vilém Novák,Irina Perfilieva,J. Mockor
Publisher : Springer Science & Business Media
Page : 327 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461552178

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Mathematical Principles of Fuzzy Logic by Vilém Novák,Irina Perfilieva,J. Mockor Pdf

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 : Radim Belohlavek,Joseph W. Dauben,George J. Klir
Publisher : Oxford University Press
Page : 544 pages
File Size : 47,7 Mb
Release : 2017-05-03
Category : Philosophy
ISBN : 9780190665708

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Fuzzy Logic and Mathematics by Radim Belohlavek,Joseph W. Dauben,George J. Klir Pdf

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.

Author : Abhijit Pandit
Publisher : CRC Press
Page : 195 pages
File Size : 40,9 Mb
Release : 2021-05-20
Category : Business & Economics
ISBN : 9780429751714

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Mathematical Modeling using Fuzzy Logic by Abhijit Pandit Pdf

Mathematical Modeling using Fuzzy Logic has been a dream project for the author. Fuzzy logic provides a unique method of approximate reasoning in an imperfect world. This text is a bridge to the principles of fuzzy logic through an application-focused approach to selected topics in engineering and management. The many examples point to the richer solutions obtained through fuzzy logic and to the possibilities of much wider applications. There are relatively very few texts available at present in fuzzy logic applications. The style and content of this text is complementary to those already available. New areas of application, like application of fuzzy logic in modeling of sustainability, are presented in a graded approach in which the underlying concepts are first described. The text is broadly divided into two parts: the first treats processes, materials, and system applications related to fuzzy logic, and the second delves into the modeling of sustainability with the help of fuzzy logic. This book offers comprehensive coverage of the most essential topics, including: Treating processes, materials, system applications related to fuzzy logic Highlighting new areas of application of fuzzy logic Identifying possibilities of much wider applications of fuzzy logic Modeling of sustainability with the help of fuzzy logic The level enables a selection of the text to be made for the substance of undergraduate-, graduate-, and postgraduate-level courses. There is also sufficient volume and quality for the basis of a postgraduate course. A more restricted and judicious selection can provide the material for a professional short course and various university-level courses.

Author : Rahul Kar,Dac-Nhuong Le,Gunjan Mukherjee,Biswadip Basu Mallik,Ashok Kumar Shaw
Publisher : John Wiley & Sons
Page : 265 pages
File Size : 46,6 Mb
Release : 2023-09-15
Category : Mathematics
ISBN : 9781394175116

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Fuzzy Logic Applications in Computer Science and Mathematics by Rahul Kar,Dac-Nhuong Le,Gunjan Mukherjee,Biswadip Basu Mallik,Ashok Kumar Shaw Pdf

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 : G. Gerla
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 44,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401596602

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Fuzzy Logic by G. Gerla Pdf

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 : Lotfi Asker Zadeh,George J. Klir,Bo Yuan
Publisher : World Scientific
Page : 848 pages
File Size : 50,9 Mb
Release : 1996
Category : Computers
ISBN : 9810224214

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Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems by Lotfi Asker Zadeh,George J. Klir,Bo Yuan Pdf

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.

Author : Anonim
Publisher : BoD – Books on Demand
Page : 186 pages
File Size : 48,8 Mb
Release : 2020-02-05
Category : Mathematics
ISBN : 9781789842319

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Fuzzy Logic by Anonim Pdf

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.

Author : James J. Buckley,Esfandiar Eslami
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 42,6 Mb
Release : 2013-11-11
Category : Computers
ISBN : 9783790817997

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An Introduction to Fuzzy Logic and Fuzzy Sets by James J. Buckley,Esfandiar Eslami Pdf

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.

Author : H. J. Zimmerman
Publisher : Allied Publishers
Page : 430 pages
File Size : 46,8 Mb
Release : 1996
Category : Fuzzy sets
ISBN : 8170235251

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Fuzzy Set Theory and Its Applications by H. J. Zimmerman Pdf

Author : Petr Cintula,Christian G Fermueller,Carles Noguera
Publisher : Unknown
Page : 384 pages
File Size : 47,9 Mb
Release : 2015-12-31
Category : Mathematics
ISBN : 1848901933

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Handbook of Mathematical Fuzzy Logic by Petr Cintula,Christian G Fermueller,Carles Noguera Pdf

Originating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, Mathematical Fuzzy Logic (MFL) has become a significant subfield of mathematical logic. Research in this area focuses on many-valued logics with linearly ordered truth values and has yielded elegant and deep mathematical theories and challenging problems, thus continuing to attract an ever increasing number of researchers. This handbook provides, through its several volumes, an up-to-date systematic presentation of the best-developed areas of MFL. Its intended audience is researchers working on MFL or related fields, that may use the text as a reference book, and anyone looking for a comprehensive introduction to MFL. This handbook will be useful not only for readers interested in pure mathematical logic, but also for those interested in logical foundations of fuzzy set theory or in a mathematical apparatus suitable for dealing with some philosophical and linguistic issues related to vagueness. This third volume starts with three chapters on semantics of fuzzy logics, namely, on the structure of linearly ordered algebras, on semantic games, and on Ulam-Renyi games; it continues with an introduction to fuzzy logics with evaluated syntax, a survey of fuzzy description logics, and a study of probability on MV-algebras; and it ends with a philosophical chapter on the role of fuzzy logics in theories of vagueness."

Author : Franco Montagna
Publisher : Springer
Page : 318 pages
File Size : 43,6 Mb
Release : 2014-09-23
Category : Mathematics
ISBN : 9783319062334

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Petr Hájek on Mathematical Fuzzy Logic by Franco Montagna Pdf

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.

Author : Michael Gr. Voskoglou
Publisher : MDPI
Page : 366 pages
File Size : 52,5 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 : Hung T. Nguyen,Carol L. Walker,Elbert A. Walker
Publisher : CRC Press
Page : 448 pages
File Size : 47,5 Mb
Release : 2018-12-07
Category : Mathematics
ISBN : 9780429012617

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A First Course in Fuzzy Logic by Hung T. Nguyen,Carol L. Walker,Elbert A. Walker Pdf

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.

Author : S.N. Sivanandam,S. Sumathi,S. N. Deepa
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 42,8 Mb
Release : 2006-10-28
Category : Technology & Engineering
ISBN : 9783540357810

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Introduction to Fuzzy Logic using MATLAB by S.N. Sivanandam,S. Sumathi,S. N. Deepa Pdf

This book provides a broad-ranging, but detailed overview of the basics of Fuzzy Logic. The fundamentals of Fuzzy Logic are discussed in detail, and illustrated with various solved examples. The book also deals with applications of Fuzzy Logic, to help readers more fully understand the concepts involved. Solutions to the problems are programmed using MATLAB 6.0, with simulated results. The MATLAB Fuzzy Logic toolbox is provided for easy reference.

Author : M. GANESH
Publisher : PHI Learning Pvt. Ltd.
Page : 256 pages
File Size : 50,6 Mb
Release : 2006-01-01
Category : Mathematics
ISBN : 9788120328617

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INTRODUCTION TO FUZZY SETS AND FUZZY LOGIC by M. GANESH Pdf

Reflecting the tremendous advances that have taken place in the study of fuzzy set theory and fuzzy logic, this book not only details the theoretical advances in these areas, but also considers a broad variety of applications of fuzzy sets and fuzzy logic. This comprehensive and up-to-date text is organized in three parts. The concepts pertaining to the “crisp” situation such as Set Theory, Logic, Switching Function Theory and Boolean Algebra are covered in Part I of the text. Part II is devoted to fuzzy Set Theory, Fuzzy Relations and Fuzzy Logic. The applications of fuzzy set theory and fuzzy logic to Control Theory and Decision Making are designated Part III of the text. Designed as a textbook for the undergraduate and postgraduate students of Science and Engineering, the book will also be immensely useful to practicing engineers and computer scientists.