Research Of Intuitionistic Fuzzy Rough Approximation Operators

Rough set is a mathematical tool to deal with uncertainty knowledge, it can be better analyze and dealwith imprecise, inconsistent and incomplete information and it was widely used in the field of knowledgeacquisition, machine learning, intelligent control, expert systems, granular computing and achieved fruitfulresults. Intuitionistic fuzzy set is an extension of Zadeh fuzzy set theory, increase the non-membershipfunction, it can not only describe "He also vital vague concept of", but also can be described neither thisnor the neutral state. But, it strongly depend on people’s subjective cognition when the intuitionistic fuzzyset expresses the fuzzy concept and the max-min operation makes the calculation error growth too fast.Rough set theory without any prior information required to deal with the problem of data set, but also failedto include rough set to deal with imprecise or uncertainty of the original data mechanism, so intuitionisticfuzzy sets and rough sets in theory with highly complementary, the two fusion research not only promotedthe theory of rough set and intuitionistic fuzzy set but also has obtained the ideal effect in application, but itrelatively weak on the study of intuitionistic fuzzy rough logic and its reasoning. Therefore, it is verynecessary to study of intuitionistic fuzzy rough logic. Fuzzy equivalence relation and rough approximationoperators is the emphasis and difficulty in intuitionistic fuzzy rough logic, so their are a key study ofintuituionstic fuzzy rough approximation operator in the intuitionistic fuzzy rough logic. While on the basisof notion of implication, the research on constructive intuitionstic fuzzy rough approximation operators islittle. Therefore, in this paper, based on the existing concept of implication, using intuitionistic fuzzy setsand rough set theory, a new intuitionistic fuzzy rough approximation operators is constructed and important properties of approximation operators are proved, and an example is verified. This study enriches andperfects the intuitionstic fuzzy rough set theory, provides the theoretical basis for intuitionstic fuzzy roughset reasoning. The innovation of this paper is as follows:Firstly, based on the rough sets and intuitionstic fuzzy sets, combined with the basic concepts ofimplication, the operator and the surplus co-operators (ψ*) are put forward and proved the basicproperties. Intuitionistic fuzzy rough approximation operators are constructed based on the operator ψand the surplus co-operator (ψ*), Some properties of the intuitionistic fuzzy rough approximation operatorsare detailedly proved.Secondly, based on the intutitionstic fuzzy sets and rough approximation operators, combined with theψ operator and the surplus co-operator (ψ*), the γ operator and the surplus co-operator γ aredefined, and basic properties are proved. Based on the operator γ and the surplus co-operator (γ*),intuitionistic fuzzy rough approximation operators are constructed, some properties of the intuitionisticfuzzy rough approximation operators are detailedly proved.Thirdly, based on the concept of the approximation operator and cut sets, the intuitionistic fuzzy cutset upper (lower) approximation operator are defined, intuitionistic fuzzy cut set upper (lower) roughdegree are given. A series of important properties are proved. The application of approximation operatorand rough degree of intuitionstic fuzzy rough set is illustrated.