Fuzzy Set Theory

Foundations and Applications

Author: George J. Klir,Ute H. St. Clair,Bo Yuan

Publisher: N.A

ISBN: 9780133410587

Category: Computers

Page: 245

View: 2472

This book is designed to help anyone understand the basics of fuzzy sets, whether or not they have a mathematical background. The book first presents a basic grounding in information theory, classical logic and set theories. Next, it introduces the basics of fuzzy sets, distinguishing them from traditional crisp sets, and introducing the concept of membership function. The distinctions between classical and fuzzy relations are introduced, as are representations of fuzzy relations; fuzzy equivalence relations; fuzzy partial orderings, and related topics. The book introduces fuzzy arithmetic and fuzzy numbers. It also presents a detailed introduction to fuzzy logic, multivalued logics, fuzzy propositions, quantifiers, linguistic hedges and approximate reasoning. Several basic and advanced applications for fuzzy set theory are presented as well. Any non-technical reader interested in fuzzy sets and fuzzy logic. Also ideal for introductory level-students, whether they are planning a technical or non-technical course of study.

Fuzzy Logic Foundations and Industrial Applications

Author: Da Ruan

Publisher: Springer Science & Business Media

ISBN: 1461314410

Category: Mathematics

Page: 330

View: 8668

Fuzzy Logic Foundations and Industrial Applications is an organized edited collection of contributed chapters covering basic fuzzy logic theory, fuzzy linear programming, and applications. Special emphasis has been given to coverage of recent research results, and to industrial applications of fuzzy logic. The chapters are new works that have been written exclusively for this book by many of the leading and prominent researchers (such as Ronald Yager, Ellen Hisdal, Etienne Kerre, and others) in this field. The contributions are original and each chapter is self-contained. The authors have been careful to indicate direct links between fuzzy set theory and its industrial applications. Fuzzy Logic Foundations and Industrial Applications is an invaluable work that provides researchers and industrial engineers with up-to-date coverage of new results on fuzzy logic and relates these results to their industrial use.

Qualitative Comparative Analysis (QCA) und Fuzzy Sets

Author: Carsten Q. Schneider,Claudius Wagemann

Publisher: Barbara Budrich

ISBN: 3866490682

Category: Computers

Page: 287

View: 4492

Dieses Buch führt in ,Qualitative Comparative Analysis' (QCA) ein, eine neuartige Methode zum systematischen qualitativen Fallvergleich. Dabei werden die ältere QCA-Version, die Fuzzy-Set-Variante und jüngste Neuerungen mit theoretischen Darstellungen, Beispielen aus der Forschungspraxis und �bungsaufgaben ausführlich und verständlich dargestellt. Im Buch werden die mathematischen Grundlagen der Methode, die auf Boolescher Algebra und Fuzzy-Algebra basieren, auf einfach verständliche Weise erklärt, die computergestützte Durchführung der Analysen anschaulich vorgestellt, und die Nützlichkeit der Methode an mehreren Beispielen aus der empirischen Forschungspraxis demonstriert. �bungsaufgaben zu allen Kapiteln runden die Darstellung ab. Dabei gehen die Autoren auf neueste Entwicklungen innerhalb von QCA und fsQCA wie Evaluationsparameter, Zwei-Schritt-Ansätze und den Wahrheitstafelalgorithmus ein. Das Buch von Schneider und Wagemann - beide mit langjähriger Erfahrung in Forschung und Lehre auf dem Gebiet - stellt damit den aktuellen Stand der Entwicklung von QCA und fsQCA dar und wendet sich sowohl an Studenten als auch an ForschungspraktikerInnen. THIS BOOK IS IN GERMAN ONLY.

Soft Computing and Its Applications

Author: Rafik Aziz ogly Aliev,R. R. Aliev

Publisher: World Scientific

ISBN: 9789810247003

Category: Computers

Page: 444

View: 8406

The concept of soft computing is still in its initial stages of crystallization. Presently available books on soft computing are merely collections of chapters or articles about different aspects of the field. This book is the first to provide a systematic account of the major concepts and methodologies of soft computing, presenting a unified framework that makes the subject more accessible to students and practitioners. Particularly worthy of note is the inclusion of a wealth of information about neuro-fuzzy, neuro-genetic, fuzzy-genetic and neuro-fuzzy-genetic systems, with many illuminating applications and examples.

Entropy Measures, Maximum Entropy Principle and Emerging Applications

Author: Karmeshu,Jawaharlal Karmeshu

Publisher: Springer Science & Business Media

ISBN: 9783540002420

Category: Computers

Page: 297

View: 2462

This book is dedicated to Prof. J. Kapur and his contributions to the field of entropy measures and maximum entropy applications. Eminent scholars in various fields of applied information theory have been invited to contribute to this Festschrift, collected on the occasion of his 75th birthday. The articles cover topics in the areas of physical, biological, engineering and social sciences such as information technology, soft computing, nonlinear systems or molecular biology with a thematic coherence. The volume will be useful to researchers working in these different fields enabling them to see the underlying unity and power of entropy optimization frameworks.

Fuzzy Set Theory and Advanced Mathematical Applications

Author: Da Ruan

Publisher: Springer Science & Business Media

ISBN: 1461523575

Category: Mathematics

Page: 324

View: 7579

Fuzzy Set Theory and Advanced Mathematical Applications contains contributions by many of the leading experts in the field, including coverage of the mathematical foundations of the theory, decision making and systems science, and recent developments in fuzzy neural control. The book supplies a readable, practical toolkit with a clear introduction to fuzzy set theory and its evolution in mathematics and new results on foundations of fuzzy set theory, decision making and systems science, and fuzzy control and neural systems. Each chapter is self-contained, providing up-to-date coverage of its subject. Audience: An important reference work for university students, and researchers and engineers working in both industrial and academic settings.

Mathematics of Fuzzy Sets

Logic, Topology, and Measure Theory

Author: Ulrich Höhle,S.E. Rodabaugh

Publisher: Springer Science & Business Media

ISBN: 1461550793

Category: Mathematics

Page: 716

View: 6312

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: Frank Klawonn,Jörg Gebhardt

Publisher: Springer-Verlag

ISBN: 3322867846

Category: Technology & Engineering

Page: 276

View: 3942


Views on Fuzzy Sets and Systems from Different Perspectives

Philosophy and Logic, Criticisms and Applications

Author: Rudolf Seising

Publisher: Springer Science & Business Media

ISBN: 354093801X

Category: Computers

Page: 580

View: 8602

This book presents the complete philosophy of Fuzzy Set Theory. It offers a collection of views from scholars involved in various research projects concerning fuzziness in science, technology, economic systems, social sciences, logics and philosophy.

Similarity and Compatibility in Fuzzy Set Theory

Assessment and Applications

Author: Valerie V. Cross,Thomas A. Sudkamp

Publisher: Physica

ISBN: 3790817937

Category: Mathematics

Page: 209

View: 7517

Assessing the degree to which two objects, an object and a query, or two concepts are similar or compatible is a fundamental component of human reasoning and consequently is critical in the development of automated diagnosis, classification, information retrieval and decision systems. The assessment of similarity has played an important role in such diverse disciplines such as taxonomy, psychology, and the social sciences. Each discipline has proposed methods for quantifying similarity judgments suitable for its particular applications. This book presents a unified approach to quantifying similarity and compatibility within the framework of fuzzy set theory and examines the primary importance of these concepts in approximate reasoning. Examples of the application of similarity measures in various areas including expert systems, information retrieval, and intelligent database systems are provided.

Fuzzy sets and fuzzy logic

the foundations of application--from a mathematical point of view

Author: Siegfried Gottwald

Publisher: N.A

ISBN: 9783528053116

Category: Mathematics

Page: 216

View: 9957


Fuzzy Sets and Fuzzy Decision-Making

Author: Hongxing Li,Vincent C. Yen

Publisher: CRC Press

ISBN: 9780849389313

Category: Computers

Page: 288

View: 589

The increasing number of applications of fuzzy mathematics has generated interest in widely ranging fields, from engineering and medicine to the humanities and management sciences. Fuzzy Sets and Fuzzy Decision-Making provides an introduction to fuzzy set theory and lays the foundation of fuzzy mathematics and its applications to decision-making. New concepts are simplified with the use of figures and diagrams, and methods are discussed in terms of their direct applications in obtaining solutions to real problems, particularly to decision-related problems. The first chapter presents the current state of knowledge of fuzzy set theory, using pan-Venn-diagrams to illustrate mathematical concepts. The second chapter clearly describes the theory of factor spaces, on which fuzzy decision-making is based. The remainder of the book is devoted to the methods, applications, techniques, and examples of this fuzzy decision-making, and includes methods for determining membership functions and for treating multifactorial and variable weights analyses.

Foundations of Fuzzy Logic and Soft Computing

12th International Fuzzy Systems Association World Congress, IFSA 2007, Cancun, Mexico, Junw 18-21, 2007, Proceedings

Author: Patricia Melin,Oscar Castillo,Luis T. Aguilar,Witold Pedrycz

Publisher: Springer Science & Business Media

ISBN: 354072950X

Category: Computers

Page: 832

View: 2286

This book comprises a selection of papers from IFSA 2007 on new methods and theories that contribute to the foundations of fuzzy logic and soft computing. Coverage includes the application of fuzzy logic and soft computing in flexible querying, philosophical and human-scientific aspects of soft computing, search engine and information processing and retrieval, as well as intelligent agents and knowledge ant colony.

An Ontological and Epistemological Perspective of Fuzzy Set Theory

Author: I. Burhan Türksen

Publisher: Elsevier

ISBN: 9780080525716

Category: Computers

Page: 542

View: 1498

Fuzzy set and logic theory suggest that all natural language linguistic expressions are imprecise and must be assessed as a matter of degree. But in general membership degree is an imprecise notion which requires that Type 2 membership degrees be considered in most applications related to human decision making schemas. Even if the membership functions are restricted to be Type1, their combinations generate an interval – valued Type 2 membership. This is part of the general result that Classical equivalences breakdown in Fuzzy theory. Thus all classical formulas must be reassessed with an upper and lower expression that are generated by the breakdown of classical formulas. Key features: - Ontological grounding - Epistemological justification - Measurement of Membership - Breakdown of equivalences - FDCF is not equivalent to FCCF - Fuzzy Beliefs - Meta-Linguistic axioms - Ontological grounding - Epistemological justification - Measurement of Membership - Breakdown of equivalences - FDCF is not equivalent to FCCF - Fuzzy Beliefs - Meta-Linguistic axioms

Fuzzy Image Processing and Applications with MATLAB

Author: Tamalika Chaira,Ajoy Kumar Ray

Publisher: CRC Press

ISBN: 1351834215

Category: Technology & Engineering

Page: 237

View: 1335

In contrast to classical image analysis methods that employ "crisp" mathematics, fuzzy set techniques provide an elegant foundation and a set of rich methodologies for diverse image-processing tasks. However, a solid understanding of fuzzy processing requires a firm grasp of essential principles and background knowledge. Fuzzy Image Processing and Applications with MATLAB® presents the integral science and essential mathematics behind this exciting and dynamic branch of image processing, which is becoming increasingly important to applications in areas such as remote sensing, medical imaging, and video surveillance, to name a few. Many texts cover the use of crisp sets, but this book stands apart by exploring the explosion of interest and significant growth in fuzzy set image processing. The distinguished authors clearly lay out theoretical concepts and applications of fuzzy set theory and their impact on areas such as enhancement, segmentation, filtering, edge detection, content-based image retrieval, pattern recognition, and clustering. They describe all components of fuzzy, detailing preprocessing, threshold detection, and match-based segmentation. Minimize Processing Errors Using Dynamic Fuzzy Set Theory This book serves as a primer on MATLAB and demonstrates how to implement it in fuzzy image processing methods. It illustrates how the code can be used to improve calculations that help prevent or deal with imprecision—whether it is in the grey level of the image, geometry of an object, definition of an object’s edges or boundaries, or in knowledge representation, object recognition, or image interpretation. The text addresses these considerations by applying fuzzy set theory to image thresholding, segmentation, edge detection, enhancement, clustering, color retrieval, clustering in pattern recognition, and other image processing operations. Highlighting key ideas, the authors present the experimental results of their own new fuzzy approaches and those suggested by different authors, offering data and insights that will be useful to teachers, scientists, and engineers, among others.

Advances in Type-2 Fuzzy Sets and Systems

Theory and Applications

Author: Alireza Sadeghian,Jerry M Mendel,Hooman Tahayori

Publisher: Springer

ISBN: 1461466660

Category: Computers

Page: 262

View: 4067

This book explores recent developments in the theoretical foundations and novel applications of general and interval type-2 fuzzy sets and systems, including: algebraic properties of type-2 fuzzy sets, geometric-based definition of type-2 fuzzy set operators, generalizations of the continuous KM algorithm, adaptiveness and novelty of interval type-2 fuzzy logic controllers, relations between conceptual spaces and type-2 fuzzy sets, type-2 fuzzy logic systems versus perceptual computers; modeling human perception of real world concepts with type-2 fuzzy sets, different methods for generating membership functions of interval and general type-2 fuzzy sets, and applications of interval type-2 fuzzy sets to control, machine tooling, image processing and diet. The applications demonstrate the appropriateness of using type-2 fuzzy sets and systems in real world problems that are characterized by different degrees of uncertainty.

Rough Fuzzy Image Analysis

Foundations and Methodologies

Author: Sankar K. Pal,James F. Peters

Publisher: CRC Press

ISBN: 9781439803301

Category: Mathematics

Page: 266

View: 4783

Fuzzy sets, near sets, and rough sets are useful and important stepping stones in a variety of approaches to image analysis. These three types of sets and their various hybridizations provide powerful frameworks for image analysis. Emphasizing the utility of fuzzy, near, and rough sets in image analysis, Rough Fuzzy Image Analysis: Foundations and Methodologies introduces the fundamentals and applications in the state of the art of rough fuzzy image analysis. In the first chapter, the distinguished editors explain how fuzzy, near, and rough sets provide the basis for the stages of pictorial pattern recognition: image transformation, feature extraction, and classification. The text then discusses hybrid approaches that combine fuzzy sets and rough sets in image analysis, illustrates how to perform image analysis using only rough sets, and describes tolerance spaces and a perceptual systems approach to image analysis. It also presents a free, downloadable implementation of near sets using the Near Set Evaluation and Recognition (NEAR) system, which visualizes concepts from near set theory. In addition, the book covers an array of applications, particularly in medical imaging involving breast cancer diagnosis, laryngeal pathology diagnosis, and brain MR segmentation. Edited by two leading researchers and with contributions from some of the best in the field, this volume fully reflects the diversity and richness of rough fuzzy image analysis. It deftly examines the underlying set theories as well as the diverse methods and applications.


Author: N.A

Publisher: N.A


Category: Cybernetics

Page: N.A

View: 790