Intuitionistic Fuzzy Granular Structures And Uncertainty Research In Intuitionistic Fuzzy Information Systems

Interval-valued intuitionistic fuzzy sets use the form of interval numbers to indicate the degree of membership, non-membership and hesitation. However, the degree of membership, non-membership and hesitation are generally given by the experts based on experience, often with a strong subjective. In dealing with the ambiguity of the problem, Rough Sets depends on the knowledge base. Thus it can objective reflect the fuzziness of the knowledge. These two theories are highly complementary when they deal with uncertainty and fuzzy process. With the continuous development of database technology, facing a lot of fuzzy and complex information, how to characterize the imprecise information has become a growing concern. This paper investigates these key problems of interval-valued intuitionistic fuzzy rough sets, intuitionistic fuzzy information granularity and interval-valued intuitionistic fuzzy information granularity. Main results obtained are as follows.Firstly, by using two interval-valued intuitionistic fuzzy implicators, intuitionistic fuzzy rough sets is generalized to interval-valued intuitionistic fuzzy sets. An interval-valued intuitionistic fuzzy approximation space and (I.J)-interval-valued intuitionistic fuzzy rough sets are defined. That is, the concept of rough sets and interval-valued intuitionistic fuzzy implicators is combined. And the properties of (I,J)-interval-valued intuitionistic fuzzy rough sets are investigated.Secondly, intuitionistic fuzzy information granularity is defined and its properties are investigated. In the interval-valued intuitionistic fuzzy information systems, operators of intersection, union, subtraction and complement in interval-valued intuitionistic fuzzy granular structures are studied. Three new partial order relations in interval-valued intuitionistic fuzzy information systems are introduced and the relationships among them are established. Finally, an interval-valued intuitionistic fuzzy information granularity is defined, and an axiomatic approach to interval-valued intuitionistic fuzzy information granularity is constructed. Their properties are investigated.