Intuitionistic Fuzzy Sets And Their Applications Based On Interval-valued Level Cut Sets

As a generalization of fuzzy sets,intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets are widely used in dealing with uncertain problems.And in the study of fuzzy theory and fuzzy system,cut set plays an important role and has been widely concerned by scholars at home and abroad.In this paper,the definition of interval-valued level cut sets of intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets is given by the generalization of the interval-valued level cuts of fuzzy sets.What is more,based on the interval-valued level cut sets the decomposition theorem and representation theorem of intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets are established.And the intuitionistic fuzzy rough sets and interval-valued intuitionistic fuzzy rough sets are constructed by representation theorem.The main contents of this paper are as follows:1.The interval-valued level cut sets of intuitionistic fuzzy sets are regarded as three valued fuzzy sets,and four kinds of interval-valued level cut sets of intuitionistic fuzzy sets are defined,which has exactly the same properties with the cut sets of fuzzy set.Then based on the interval-valued level cut sets,four kinds of new decomposition theorem of intuitionistic fuzzy sets are established.Using the triple valued order nested sets and inverse order nested sets,four kinds of new representation theorem of the intuitionistic fuzzy sets are established.2.The interval-valued level cut sets of intuitionistic fuzzy set is extended to interval-valued intuitionistic fuzzy set.Five valued fuzzy sets are selected as the interval-valued level cut sets to introduce four kinds of the definition of interval-valued level cut sets of interval-valued intuitionistic fuzzy sets.The properties of the interval-valued level cut sets of interval-valued intuitionistic fuzzy sets are researched and four kinds of new decomposition theorem and representation theorem of interval-valued intuitionistic fuzzy sets are obtained.3.The application of the representation theorem in intuitionistic fuzzy rough sets and interval-valued intuitionistic fuzzy rough sets is studied.Nested sets are constructed by selecting the interval-valued level cut sets of intuitionistic fuzzy sets and the corresponding intuitionistic fuzzy interval-valued level cut relations of intuitionistic fuzzy equivalence relations,and intuitionistic fuzzy rough sets are studied by using the representation theorem.Furthermore,nested sets are established by selecting the interval-valued level cut sets of interval-valued intuitionistic fuzzy sets and the corresponding intuitionistic fuzzy interval-valued level cut relations of interval-valued intuitionistic fuzzy equivalence relations,and interval-valued intuitionistic fuzzy rough sets are studied by using the representation theorem.The upper and lower approximate membership functions of two kinds of intuitionistic fuzzy sets are obtained.