Granularity Structure of Type II Intuitionistic Fuzzy Information Systems and their Information Measures

In order to solve the problem of hierarchical granularity structure and its information metrics involved in type II intuitionistic fuzzy information system. Firstly, the information granularity structure of type II intuitionistic fuzzy sets is defined, the basic operation of type II intuitionistic fuzzy information granularity structure is given, and three partial order relations on the type II intuitionistic fuzzy granularity structure are proposed, aiming to reveal the organisation and expression of different granularities of type II intuitionistic fuzzy information. Secondly, two metric forms of information granularity and roughness entropy of type II intuitionistic fuzzy information are defined, and their relationships with the three partial order relations are investigated. Finally, based on the application requirements of type II intuitionistic fuzzy information in multi-attribute decision making, the applicability and effectiveness of the type II intuitionistic fuzzy information system granularity structure and its information metrics in practical applications are demonstrated through application examples.