Research On Interval Valued Intuitionistic Fuzzy Sets

The technology of analyzing and judging uncertainty and imprecise events through fuzzy knowledge has gradually tended to mature,and the limitations that accompany it are also presented.So,in the meantime,in the rapid development of the fuzzy set theory,there have been all sorts of forms of expansion,and the like intuitionistic fuzzy sets,interval form fuzzy sets and interval value intuitionistic fuzzy sets.On the one hand,it embodies the frequency of the application and development of fuzzy set theory in real life.On the other hand,it reflects the restriction and challenge of the interlaced objective things on the theory of fuzzy sets.We can see that the intuitionistic fuzzy set is the most representative and the fastest growing form in the numerous fuzzy set expansion forms.Fuzzy set is a kind of special form of intuitionistic fuzzy sets,while intuitionistic fuzzy sets are the generalization and application of fuzzy sets.The development of intuitionistic fuzzy sets is initially only in the perspective of pure mathematics.In recent years,in addition to further research in mathematics field,relevant application hotspots are slowly appearing.For example,the distance between intuitionistic fuzzy sets,intuitionistic fuzzy entropy,similarity measure and application,intuitionistic fuzzy clustering analysis,intuitionistic fuzzy reasoning and application,intuitionistic fuzzy set in decision making field,etc.And the interval value intuitionistic fuzzy set is an extension and generalization of intuitionistic fuzzy sets.Based on the theory of interval valued intuitionistic fuzzy sets,and in terms of the theory and the application,this article from the following three aspects of interval-valued intuitionistic fuzzy sets is studied:Cartesian product of interval valued intuitionistic fuzzy sets.Firstly,based on the intuition-istic fuzzy sets of interval values,in view of the interval-valued intuitionistic fuzzy sets of the existing five kinds of Cartesian product,and combines the knowledge of Cartesian prod-uct with intuitionistic fuzzy sets,then gives the definition of the sixth,seventh and eighth Cartesian products of the interval valued intuitionistic fuzzy sets.It given that geometric interpretation of the sixth Cartesian product of the interval value intuitionistic fuzzy sets by the geometrical interpretation of the sixth Cartesian product of the intuitional fuzzy sets.Similarity measure and application of interval valued intuitionistic fuzzy sets.Secondly,based on the four distances of the intuitionistic fuzzy sets defined by Szmidt and Kacprzyk and the distance formula of the interval value intuitionistic fuzzy sets given by Szmidt,the distance of the weighted interval value intuitionistic fuzzy sets is defined,then the similarity measure of the interval value intuitionistic fuzzy sets is given by the relation of distance and similarity measure,and it is applied to the field of pattern recognition.Sort of interval-valued intuitionistic fuzzy numbers.Then,based on the sorting of intuition-istic fuzzy numbers,this paper compares and analyzes the sorting methods of the existing interval value intuitionistic fuzzy numbers,and defines three new functions,namely,the s-coring function,the exact function and the similarity function,and proposes a new sorting method for the intuitionistic fuzzy number of the interval value.Then three propositions and two theorems are given,and the proofs are given respectively.This paper describes the three steps to sort the interval value intuitionistic fuzzy numbers.In the end,a scheme for the sorting of an interval valued intuitionistic fuzzy number is given.