# An Introduction to Fuzzy Sets: Analysis and Design (Complex Adaptive Systems)

By: Witold Pedrycz (author), Fernando Gomide (author)Hardback

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### Description

The concept of fuzzy sets is one of the most fundamental and influential tools in computational intelligence. Fuzzy sets can provide solutions to a broad range of problems of control, pattern classification, reasoning, planning, and computer vision. This book bridges the gap that has developed between theory and practice. The authors explain what fuzzy sets are, why they work, when they should be used (and when they shouldn't), and how to design systems using them. The authors take an unusual top-down approach to the design of detailed algorithms. They begin with illustrative examples, explain the fundamental theory and design methodologies, and then present more advanced case studies dealing with practical tasks. While they use mathematics to introduce concepts, they ground them in examples of real-world problems that can be solved through fuzzy set technology. The only mathematics prerequisites are a basic knowledge of introductory calculus and linear algebra.

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Witold Pedrycz is Professor and Chair of Electrical and Computer Engineering at the University of Alberta.

### Contents

Part 1 Fundamentals of fuzzy sets: basic notions and concepts of fuzzy sets - set membership and fuzzy sets, basic definitions of a fuzzy set, types of membership functions, characteristics of a fuzzy set, basic relationships between fuzzy sets - equality and inclusion, fuzzy sets and sets - the representation theorem, the extension principles, membership function determination, generalizations of fuzzy sets, chapter summary, problems, references; fuzzy set operations - set theory operations and their properties, triangular norms, aggregation operations on fuzzy sets, sensitivity of fuzzy sets operators, negations, comparison operations on fuzzy sets, chapter summary, problems, references; information-based characterization of fuzzy sets -entropy measures of fuzziness, energy measures of fuzziness, specificity of a fuzzy set, frames of cognition, information encoding and decoding using linguistic landmarks, decoding mechanisms for pointwise data, decoding using membership functions of the linguistic terms of the codebook, general possibility-necessity decoding, distance between fuzzy sets based on their internal, linguistic representation, chapter summary, problems, references; fuzzy relations and their calculus -relations and fuzzy relations, operations on fuzzy relations, compositions of fuzzy relations, projections and cylindric extensions of fuzzy relations, binary fuzzy relations, some classes of fuzzy relations, fuzzy-relational equations, estimation and inverse problem in fuzzy relational equations, solving fuzzy-relational equations with the sup-t composition, solutions to dual fuzzy-relational equations, adjoint fuzzy-relational equations, generaliations of fuzzy relational equations, approximate solutions to fuzzy-relational equations, chapter summary, problems, references; fuzzy numbers - defining fuzzy numbers, interval analysis and fuzzy numbers, computing with fuzzy numbers, triangular fuzzy numbers and basic operations, general formulas for LR fuzzy numbers, accumulation of fuzziness in computing with fuzzy numbers, inverse problem in computation with fuzzy numbers, fuzzy numbers and approximate operations, chapter summary, problems, references; fuzzy modelling - fuzzy models - beyond numerical computations, main phases of system modelling, fundamental design objectives in system modelling, general topology of fuzzy models, compatibility of encoding and decoding modules, classes of fuzzy models, verification and validation of fuzzy models, chapter summary, problems, references. Part 3 Problem solving with fuzzy sets: methodology -analysis and design, fuzzy controllers and fuzzy control, mathematical programming and fuzzy optimization, chapter summary, problems, references; case studies - traffic intersection control, distributed traffic control, elevator group control, induction motor control, communication network planning, neurocomputation in fault diagnosis of dynamic systems, multicommodity transportation planning in railways.

### Product Details

• ISBN13: 9780262161718
• Format: Hardback
• Number Of Pages: 490
• ID: 9780262161718
• weight: 1230
• ISBN10: 0262161710

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