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Intuitionistic Fuzzy Sets: Theory and Applications by Krassimir T. Atanassov (Paperback, 2010)

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ISBN-13: 9783790824636, 978-3790824636. This was my first acquaintance with the fuzzy set theory. 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".

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The basic definitions and properties of the Intuitionistic Fuzzy Sets (IFSs) are introduced in the book. The IFSs are substantial extensions of the ordinary fuzzy sets. IFSs are objects having degrees of membership and of non-membership, such that their sum is exactly 1. The most important property of IFS not shared by the fuzzy sets is that modal-like operators can be defined over IFSs. The IFSs have essentially higher describing possibilities than fuzzy sets. In this book, readers will find discussions on some of the IFS extensions (for example, interval-values IFSs, temporal IFSs and others) and applications (e.g. intuitionistic fuzzy expert systems, intuitionistic fuzzy neural networks, intuitionistic fuzzy systems, intuitionistic fuzzy generalized nets, and other).