35 Years of Fuzzy Set Theory

by Chris Cornelis

Author	: Chris Cornelis
Publisher	: Springer Science & Business Media
Total Pages	: 296
Release	: 2010-10-14
Genre	: Computers
ISBN	: 3642166288

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This book is a tribute to Etienne E. Kerre on the occasion of his retirement on October 1st, 2010, after being active for 35 years in the field of fuzzy set theory. It gathers contributions from researchers that have been close to him in one way or another during his long and fruitful career. Besides a foreword by Lotfi A. Zadeh, it contains 13 chapters on both theoretical and applied topics in fuzzy set theory, divided in three parts: 1) logics and connectives, 2) data analysis, and 3) media applications. The first part deals with fuzzy logics and with operators on (extensions of) fuzzy sets. Part 2 deals with fuzzy methods in rough set theory, formal concept analysis, decision making and classification. The last part discusses the use of fuzzy methods for representing and manipulating media objects, such as images and text documents. The diversity of the topics that are covered reflect the diversity of Etienne's research interests, and indeed, the diversity of current research in the area of fuzzy set theory.

Intuitionistic Fuzzy Sets

by Krassimir T. Atanassov

Author	: Krassimir T. Atanassov
Publisher	: Physica
Total Pages	: 336
Release	: 2013-03-20
Genre	: Mathematics
ISBN	: 3790818704

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In the beginning of 1983, I came across A. Kaufmann's book "Introduction to the theory of fuzzy sets" (Academic Press, New York, 1975). This was my first acquaintance with the fuzzy set theory. Then I tried to introduce a new component (which determines the degree of non-membership) in the definition of these sets and to study the properties of the new objects so defined. I defined ordinary operations as "n", "U", "+" and "." over the new sets, but I had began to look more seriously at them since April 1983, when I defined operators analogous to the modal operators of "necessity" and "possibility". The late George Gargov (7 April 1947 - 9 November 1996) is the "god father" of the sets I introduced - in fact, he has invented the name "intu itionistic fuzzy", motivated by the fact that the law of the excluded middle does not hold for them. Presently, intuitionistic fuzzy sets are an object of intensive research by scholars and scientists from over ten countries. This book is the first attempt for a more comprehensive and complete report on the intuitionistic fuzzy set theory and its more relevant applications in a variety of diverse fields. In this sense, it has also a referential character.

Generalized Measure Theory

by Zhenyuan Wang

Author	: Zhenyuan Wang
Publisher	: Springer Science & Business Media
Total Pages	: 392
Release	: 2010-07-07
Genre	: Mathematics
ISBN	: 0387768521

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Generalized Measure Theory examines the relatively new mathematical area of generalized measure theory. The exposition unfolds systematically, beginning with preliminaries and new concepts, followed by a detailed treatment of important new results regarding various types of nonadditive measures and the associated integration theory. The latter involves several types of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and lower and upper integrals. All of the topics are motivated by numerous examples, culminating in a final chapter on applications of generalized measure theory. Some key features of the book include: many exercises at the end of each chapter along with relevant historical and bibliographical notes, an extensive bibliography, and name and subject indices. The work is suitable for a classroom setting at the graduate level in courses or seminars in applied mathematics, computer science, engineering, and some areas of science. A sound background in mathematical analysis is required. Since the book contains many original results by the authors, it will also appeal to researchers working in the emerging area of generalized measure theory.

Fuzzy Sets, Fuzzy Logic, And Fuzzy Systems: Selected Papers By Lotfi A Zadeh

by George J Klir

Author	: George J Klir
Publisher	: World Scientific
Total Pages	: 842
Release	: 1996-05-30
Genre	: Computers
ISBN	: 9814499811

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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.

Fuzzy Set Theory

by Michael Smithson

Author	: Michael Smithson
Publisher	: SAGE
Total Pages	: 116
Release	: 2006-02-17
Genre	: Mathematics
ISBN	: 9780761929864

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This book introduces fuzzy set theory to social science researchers. Fuzzy sets are categories with blurred boundaries. With classical sets, objects are either in the set or not, but objects can belong partially to more than one fuzzy set at a time. Many concepts in the social sciences have this characteristic, and fuzzy set theory provides methods for systematically dealing with them. A primary reason for not going beyond programmatic statements and rather unsophisticated uses of fuzzy set theory has been the lack of practical methods for combining fuzzy set concepts with statistical methods. This monograph takes that topic as its major focus, and provides explicit guides for researchers who would like to harness fuzzy set concepts while being able to make statistical inferences and test their models. Real examples and data-sets from several disciplines illustrate the techniques and applications, demonstrating how a combination of fuzzy sets and statistics enable researchers to analyze their data in new ways.

Combining Experimentation and Theory

by Enric Trillas

Author	: Enric Trillas
Publisher	: Springer
Total Pages	: 424
Release	: 2012-01-10
Genre	: Technology & Engineering
ISBN	: 3642246664

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The unexpected and premature passing away of Professor Ebrahim H. "Abe" Mamdani on January, 22, 2010, was a big shock to the scientific community, to all his friends and colleagues around the world, and to his close relatives. Professor Mamdani was a remarkable figure in the academic world, as he contributed to so many areas of science and technology. Of great relevance are his latest thoughts and ideas on the study of language and its handling by computers. The fuzzy logic community is particularly indebted to Abe Mamdani (1941-2010) who, in 1975, in his famous paper An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller, jointly written with his student Sedrak Assilian, introduced the novel idea of fuzzy control. This was an elegant engineering approach to the modeling and control of complex processes for which mathematical models were unknown or too difficult to build, yet they could effectively and efficiently be controlled by human operators. This ground-breaking idea has found innumerable applications and can be considered as one of the main factors for the proliferation and adoption of fuzzy logic technology. Professor Mamdani's own life and vital experience are illustrative of his “never surrendering” attitude while facing adversaries, which is normal for a person proposing any novel solution, and represent a great example for everybody. His subtle sense of humor, his joy for life, and his will to critically help people, especially young people, were characteristics deeply appreciated by all the people who enjoyed and benefited from his friendship and advice. This book constitutes a posthumous homage to Abe Mamdani. It is a collection of original papers related in some way to his works, ideas and vision, and especially written by researchers directly acquainted with him or with his work. The underlying goal of this book will be fulfilled if, in the very spirit of Mamdani's legacy, the papers will trigger a scientific or philosophical debate on the issues covered, or contribute to a cross-fertilization of ideas in the various fields.

Fuzzy Evidence in Identification, Forecasting and Diagnosis

by Alexander P. Rotshtein

Author	: Alexander P. Rotshtein
Publisher	: Springer Science & Business Media
Total Pages	: 323
Release	: 2012-01-27
Genre	: Computers
ISBN	: 3642257852

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The purpose of this book is to present a methodology for designing and tuning fuzzy expert systems in order to identify nonlinear objects; that is, to build input-output models using expert and experimental information. The results of these identifications are used for direct and inverse fuzzy evidence in forecasting and diagnosis problem solving. The book is organised as follows: Chapter 1 presents the basic knowledge about fuzzy sets, genetic algorithms and neural nets necessary for a clear understanding of the rest of this book. Chapter 2 analyzes direct fuzzy inference based on fuzzy if-then rules. Chapter 3 is devoted to the tuning of fuzzy rules for direct inference using genetic algorithms and neural nets. Chapter 4 presents models and algorithms for extracting fuzzy rules from experimental data. Chapter 5 describes a method for solving fuzzy logic equations necessary for the inverse fuzzy inference in diagnostic systems. Chapters 6 and 7 are devoted to inverse fuzzy inference based on fuzzy relations and fuzzy rules. Chapter 8 presents a method for extracting fuzzy relations from data. All the algorithms presented in Chapters 2-8 are validated by computer experiments and illustrated by solving medical and technical forecasting and diagnosis problems. Finally, Chapter 9 includes applications of the proposed methodology in dynamic and inventory control systems, prediction of results of football games, decision making in road accident investigations, project management and reliability analysis.

Type-2 Fuzzy Logic in Intelligent Control Applications

by Oscar Castillo

Author	: Oscar Castillo
Publisher	: Springer
Total Pages	: 187
Release	: 2011-11-08
Genre	: Technology & Engineering
ISBN	: 364224663X

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We describe in this book, hybrid intelligent systems based mainly on type-2 fuzzy logic for intelligent control. Hybrid intelligent systems combine several intelligent computing paradigms, including fuzzy logic, and bio-inspired optimization algorithms, which can be used to produce powerful automatic control systems. The book is organized in three main parts, which contain a group of chapters around a similar subject. The first part consists of chapters with the main theme of theory and design algorithms, which are basically chapters that propose new models and concepts, which can be the basis for achieving intelligent control with interval type-2 fuzzy logic. The second part of the book is comprised of chapters with the main theme of evolutionary optimization of type-2 fuzzy systems in intelligent control with the aim of designing optimal type-2 fuzzy controllers for complex control problems in diverse areas of application, including mobile robotics, aircraft dynamics systems and hardware implementations. The third part of the book is formed with chapters dealing with the theme of bio-inspired optimization of type-2 fuzzy systems in intelligent control, which includes the application of particle swarm intelligence and ant colony optimization algorithms for obtaining optimal type-2 fuzzy controllers.

Fuzzy Logic in Its 50th Year

by Cengiz Kahraman

Author	: Cengiz Kahraman
Publisher	: Springer
Total Pages	: 406
Release	: 2016-05-17
Genre	: Technology & Engineering
ISBN	: 3319310933

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This book offers a multifaceted perspective on fuzzy set theory, discussing its developments over the last 50 years. It reports on all types of fuzzy sets, from ordinary to hesitant fuzzy sets, with each one explained by its own developers, authoritative scientists well known for their previous works. Highlighting recent theorems and proofs, the book also explores how fuzzy set theory has come to be extensively used in almost all branches of science, including the health sciences, decision science, earth science and the social sciences alike. It presents a wealth of real-world sample applications, from routing problem to robotics, and from agriculture to engineering. By offering a comprehensive, timely and detailed portrait of the field, the book represents an excellent reference guide for researchers, lecturers and postgraduate students pursuing research on new fuzzy set extensions.