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Fuzzy Implications

  • Authors
  • Michał Baczyński
  • Balasubramaniam Jayaram

Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 231)

Table of contents

  1. Front Matter
  2. An Introduction to Fuzzy Implications

    1. Michał Baczyński, Balasubramaniam Jayaram
      Pages 1-35
  3. Part I: Analytical Study of Fuzzy Implications

    1. Front Matter
      Pages 37-37
    2. Michał Baczyński, Balasubramaniam Jayaram
      Pages 39-107
    3. Michał Baczyński, Balasubramaniam Jayaram
      Pages 109-125
    4. Michał Baczyński, Balasubramaniam Jayaram
      Pages 127-143
    5. Michał Baczyński, Balasubramaniam Jayaram
      Pages 145-177
  4. Part II: Algebraic Study of Fuzzy Implications

    1. Front Matter
      Pages 179-179
    2. Michał Baczyński, Balasubramaniam Jayaram
      Pages 181-204
    3. Michał Baczyński, Balasubramaniam Jayaram
      Pages 207-240
  5. Part III: Applicational Study of Fuzzy Implications

    1. Front Matter
      Pages 241-241
    2. Michał Baczyński, Balasubramaniam Jayaram
      Pages 243-277
  6. Back Matter

About this book

Introduction

Fuzzy Implications (FIs) generalize the classical implication and play a similar important role in Fuzzy Logic (FL), both in FL_n and FL_w in the sense of Zadeh. Their importance in applications of FL, viz., Approximate Reasoning (AR), Decision Support Systems, Fuzzy Control (FC), etc., is hard to exaggerate. This treatise is perhaps the first attempt at dealing exclusively with this class of operations.

The book begins with an introduction to FIs along with their desirable properties and investigates their inter-relationships. The reminder of the book is divided into 3 parts. Part I is an analytical study of FIs, detailing the different ways of obtaining FIs, generally called as families of FIs, the various properties they satisfy and the overlaps that exist among them. Part II is an algebraic exploration into the structures that exist on the set of all FIs, while the final part highlights the effecting role FIs with their myriad properties play in the inference schemes in AR.

This book is intended for any researcher in FL operations and it can serve as an auxiliary textbook for different courses on FL or FC. Parts of this book may also be of interest to practitioners in applications of FL, especially in AR or FC, where FIs play a central role.

Keywords

Approximate Reasoning Functional Equations Fuzzy Implications Fuzzy Logic Connectivess algebra computer-aided design (CAD) fuzzy fuzzy logic

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-69082-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-540-69080-1
  • Online ISBN 978-3-540-69082-5
  • Series Print ISSN 1434-9922
  • Series Online ISSN 1860-0808
  • Buy this book on publisher's site