Fuzzy implications

Michał Baczyński, Balasubramaniam Jayaram (auth.)9783540690801, 3540690808

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.

Table of contents :
Front Matter….Pages –
An Introduction to Fuzzy Implications….Pages 1-35
Front Matter….Pages 37-37
Fuzzy Implications from Fuzzy Logic Operations….Pages 39-107
Fuzzy Implications from Generator Functions….Pages 109-125
Intersections between Families of Fuzzy Implications….Pages 127-143
Fuzzy Implications from Uninorms….Pages 145-177
Front Matter….Pages 179-179
Algebraic Structures of Fuzzy Implications….Pages 181-204
Fuzzy Implications and Some Functional Equations….Pages 207-240
Front Matter….Pages 241-241
Fuzzy Implications in Approximate Reasoning….Pages 243-277
Back Matter….Pages –