Synopses & Reviews
This book introduces the reader to basic concepts and techniques in the field of fuzzy sets and gives a vast and up-to-date account of the literature. It distinguishes itself from most other works in this field in that it does not treat applications but rather provides a good theoretical foundation for applying fuzzy set theory. The main topics which are treated are: basic set theory, basic lattice theory, operations on fuzzy sets, t-norms and t-conorms, special types of fuzzy sets, fuzzy relations, functions working on fuzzy sets, fuzzy real numbers (both probabilistic and non-probabilistic), basic classical logic and fundamentals concerning fuzzy logic. Audience: This volume will be of interest to researchers working in the areas of engineering, data analysis, control theory, pattern recognition, neural networks, clustering, expert systems, information retrieval, operations research, decision making, image and signal processing, and who require more information on the set-theoretical basics on which fuzzy set theory is founded.
Synopsis
This text introduces the reader to basic concepts and techniques in the field of fuzzy sets and gives an account of the literature. It does not treat applications, but rather provides a theoretical foundation for applying fuzzy set theory.
Description
Includes bibliographical references (p. 241-404) and index.
Table of Contents
List of Figures. Preface.
1: Elementary Set Theory. 1. Sets and subsets.
2. Functions and relations.
3. Partially ordered sets.
4. The lattice of subsets of a set.
5. Characteristic functions.
6. Notes.
2: Fuzzy Sets. 1. Definitions and examples.
2. Lattice theoretical operations on fuzzy sets.
3. Pseudocomplementation.
4. Fuzzy sets, functions and fuzzy relations.
5. alpha-levels.
6. Notes.
3: t-Norms, t-Conorms and Negations. 1. Pointwise extensions.
2. t-Norms and t-Conorms.
3. Negations.
4. Notes.
4: Special Types of Fuzzy Sets. 1. Normal fuzzy sets.
2. Convex fuzzy sets.
3. Piecewise linear fuzzy sets.
4. Compact fuzzy sets.
5. Notes.
5: Fuzzy Real Numbers. 1. The probabilistic view.
2. The non-probabilistic view.
3. Interpolation.
4. Notes.
6: Fuzzy Logic. 1. Connectives in classical logic.
2. Fundamental classical theorems.
3. Basic principles of fuzzy logic.
4. Lattice generated fuzzy connectives.
5. t-Norm generated fuzzy connectives.
6. Probabilistically generated fuzzy connectives.
7. Notes.
7: Bibliography. 1. Books.
2. Articles. Index.