Fuzzy Implications

by Michal Baczynski, Balasubramaniam Jayaram

Overview

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.

Product Details

ISBN-13:	9783540690801
Publisher:	Springer Berlin Heidelberg
Publication date:	10/10/2008
Series:	Studies in Fuzziness and Soft Computing , #231
Edition description:	2008
Pages:	310
Product dimensions:	5.90(w) x 9.40(h) x 0.90(d)

Table of Contents

An Introduction to Fuzzy Implications.- An Introduction to Fuzzy Implications.- I: Analytical Study of Fuzzy Implications.- Fuzzy Implications from Fuzzy Logic Operations.- Fuzzy Implications from Generator Functions.- Intersections between Families of Fuzzy Implications.- Fuzzy Implications from Uninorms.- II: Algebraic Study of Fuzzy Implications.- Algebraic Structures of Fuzzy Implications.- Fuzzy Implications and Some Functional Equations.- III: Applicational Study of Fuzzy Implications.- Fuzzy Implications in Approximate Reasoning.