Study On Similarities And Its Application In Intuitionistic Fuzzy Sets,Interval-Valued Intuitionistic Fuzzy Sets

The similarity measures of intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets aim to describe the closeness or similarity of two intuitionistic fuzzy sets and two interval intuitionistic fuzzy sets.It is a very important research direction in intuitionistic fuzzy sets,interval intuitionistic fuzzy sets theory and its application in recent years.Its theory is widely used in multi-attribute decision-making,fuzzy pattern recognition and other fields.At present,the existing problems in the similarity measures of intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets mainly include: the calculation results of similarity measures are inconsistent with intuition,and the similarity measures have poor recognition effect in fuzzy pattern recognition.Therefore,this article has mainly completed the following two aspects of research work:Firstly,the similarity measure of intuitionistic fuzzy sets is proposed.Based on the similarities of the existing intuitionistic fuzzy sets,In this paper,considering the degree of hesitation,a kind of intuitionistic fuzzy set similarity degree is given based on the arithmetic average.Compared with the existing intuitionistic fuzzy sets similarities,it shows that the similarity measure has good distinction.Finally,an example is used to illustrate that the method has better recognition effect.Secondly,the four types similarity measures of interval-valued intuitionistic fuzzy sets are proposed.Based on the existing interval-valued intuitionistic fuzzy sets similarity degrees,this paper presents the similarity measure of interval-valued intuitionistic fuzzy sets based on the arithmetic mean.Based on the existing fuzzy closeness degrees,interval value fuzzy closeness degrees,and intuitionistic fuzzy set similarity measures,three types interval-valued intuitionistic fuzzy sets similarity measures are proposed.These four types similarity measures satisfy the similarity axioms.Finally,an example is used to illustrate these methods have good recognition effect.