Quantities And Applications Of Intuitionistic Fuzzy Sets

Since L.A.Zadeh introduced fuzzy sets in 1965, a lot of new theories treating imprecision and uncertainty have been introduced. Some of them are extensions of fuzzy set theory. K.T.Atanassov extended this theory, proposed the definition of intuitionistic fuzzy sets (IFS, for short) and interval-valued intuitionistic fuzzy sets (IVIFS, for short), which have been found to be highly useful to deal with vagueness out of several higher order fuzzy sets. And then, in the year 1999, Atanassov defined a Lattice-intuitionistic fuzzy set.This dissertation focuses on intuitionistic fuzzy sets, which covers quantities of VIFS and discuss the relation between VIFS and some other sets, extend entropy and subsethood onto VIFS, discuss the relation between them and then give idiographic functions of entropy and subsethood. The main research work is as follows:1. The definition of VIFS is proposed, then discuss the relation between them, and then discuss the relation between them.2. Entropy and subsethood are extended onto VIFS and given idiographic functions of entropy and subsethood.3. By discussing the relation between entropy, subsethood and entropy on VIFS, there comes idiographic functions of similarity this will be very important in the field of pattern recognition.Finally, after summarizing the works done in the dissertation some problems to be solved in future are pointed out.