Intuitionistic Fuzzy Sets: Theory and Applications

✍ Scribed by Krassimir T. Atanassov

• Publisher: Physica-Verlag Heidelberg
• Year: 1999
• Tongue: English
• Leaves: 335
• Series: Studies in Fuzziness and Soft Computing 35
• Edition: 1
• Category: Library

✦ Synopsis

In the beginning of 1983, I came across A. Kaufmann's book "Introduction to the theory of fuzzy sets" (Academic Press, New York, 1975). This was my first acquaintance with the fuzzy set theory. Then I tried to introduce a new component (which determines the degree of non-membership) in the definition of these sets and to study the properties of the new objects so defined. I defined ordinary operations as "n", "U", "+" and "." over the new sets, but I had began to look more seriously at them since April 1983, when I defined operators analogous to the modal operators of "necessity" and "possibility". The late George Gargov (7 April 1947 - 9 November 1996) is the "god­ father" of the sets I introduced - in fact, he has invented the name "intu­ itionistic fuzzy", motivated by the fact that the law of the excluded middle does not hold for them. Presently, intuitionistic fuzzy sets are an object of intensive research by scholars and scientists from over ten countries. This book is the first attempt for a more comprehensive and complete report on the intuitionistic fuzzy set theory and its more relevant applications in a variety of diverse fields. In this sense, it has also a referential character.

✦ Table of Contents

Front Matter....Pages I-XVIII
Intuitionistic Fuzzy Sets....Pages 1-137
Interval Valued Intuitionistic Fuzzy Sets....Pages 139-177
Other Extensions of Intuitionistic Fuzzy Sets....Pages 179-198
Elements of Intuitionistic Fuzzy Logics....Pages 199-236
Applications of Intuitionistic Fuzzy Sets....Pages 237-288
Open Problems in Intuitionistic Fuzzy Sets Theory....Pages 289-291
Back Matter....Pages 293-324

✦ Subjects

Artificial Intelligence (incl. Robotics); Mathematical Logic and Foundations; Economic Theory