Quantities And Applications Of Intuitionistic Fuzzy Sets

The scope of study and application of mathematics has extended from accuracy into fuzzy since Professor Zadeh established fuzzy sets theory in 1965. Because the intuitionistic fuzzy sets theory, which was introduced by Atanassov in 1986, considers both information of the membership and non-membership, it has stronger ability to express uncertainty than Zadeh's fuzzy sets, so it can depict the fuzzy essence of the realistic world. Therefore, more and more scholars pay attention to the new theory.This paper focused on intuitionistic fuzzy sets. First, on the basis of the analysis for current intuitionistic fuzzy sets theory, the qualities of the operators were discussed, and some new theorems and deductions were constructed.Second, based on the existing operation principle, some elementary equations for intuitionistic fuzzy sets were proposed, which made the basic theory of intuitionistic fuzzy sets extended.Third, owing to the importance and high efficiency of similarity measure in data processing and analysis, the similarity measure for intutionistic fuzzy sets was discussed in this paper. Comparing two original similarity measures for intuitionistic fuzzy sets, a new similarity measure for intuitionistic fuzzy sets was introduced, and some of its qualities were discussed. In addition, the weighted similarity measure was presented. Then the new similarity was used on medical diagnosis successfully.In the end, after summarizing the whole paper, we pointed out some problems to be solved in the future.