Fuzzy Set And Its Extension
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Fuzzy Set and Its Extension
Provides detailed mathematical exposition of the fundamentals of fuzzy set theory, including intuitionistic fuzzy sets This book examines fuzzy and intuitionistic fuzzy mathematics and unifies the latest existing works in literature. It enables readers to fully understand the mathematics of both fuzzy set and intuitionistic fuzzy set so that they can use either one in their applications. Each chapter of Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set begins with an introduction, theory, and several examples to guide readers along. The first one starts by laying the groundwork of fuzzy/intuitionistic fuzzy sets, fuzzy hedges, and fuzzy relations. The next covers fuzzy numbers and explains Zadeh's extension principle. Then comes chapters looking at fuzzy operators; fuzzy similarity measures and measures of fuzziness; and fuzzy/intuitionistic fuzzy measures and fuzzy integrals. The book also: discusses the definition and properties of fuzzy measures; examines matrices and determinants of a fuzzy matrix; and teaches about fuzzy linear equations. Readers will also learn about fuzzy subgroups. The second to last chapter examines the application of fuzzy and intuitionistic fuzzy mathematics in image enhancement, segmentation, and retrieval. Finally, the book concludes with coverage the extension of fuzzy sets. This book: Covers both fuzzy and intuitionistic fuzzy sets and includes examples and practical applications Discusses intuitionistic fuzzy integrals and recent aggregation operators using Choquet integral, with examples Includes a chapter on applications in image processing using fuzzy and intuitionistic fuzzy sets Explains fuzzy matrix operations and features examples Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set is an ideal text for graduate and research students, as well as professionals, in image processing, decision-making, pattern recognition, and control system design.
Fuzzy Set Theory—and Its Applications
Author: Hans-Jürgen Zimmermann
language: en
Publisher: Springer Science & Business Media
Release Date: 2001-11-30
This introduction to fuzzy set theory and its multitude of applications seeks to balance the character of the book with the dynamic nature of the research. This edition includes new chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. Existing material has been updated, and extended exercises are included.
Hesitant Fuzzy Set
Covering a wide range of notions concerning hesitant fuzzy set and its extensions, this book provides a comprehensive reference to the topic. In the case where different sources of vagueness appear simultaneously, the concept of fuzzy set is not able to properly model the uncertainty, imprecise and vague information. In order to overcome such a limitation, different types of fuzzy extension have been introduced so far. Among them, hesitant fuzzy set was first introduced in 2010, and the existing extensions of hesitant fuzzy set have been encountering an increasing interest and attracting more and more attentions up to now. It is not an exaggeration to say that the recent decade has seen the blossoming of a larger set of techniques and theoretical outcomes for hesitant fuzzy set together with its extensions as well as applications. As the research has moved beyond its infancy, and now it is entering a maturing phase with increased numbers and types of extensions, this book aims to give a comprehensive review of such researches. Presenting the review of many and important types of hesitant fuzzy extensions, and including references to a large number of related publications, this book will serve as a useful reference book for researchers in this field.