Distance-based Information Granularity and Hierarchical Structure for an Intuitionistic Fuzzy Granular Space

Information granularity and hierarchical structures in granular computing are the two main aspects for investigating the uncertainty and structure of all types of granular spaces. This study presents a distance-based information granularity for IF and multi-granulation IF granular spaces and use it to construct a novel hierarchical structure on such spaces. First, we propose a distance and a relative distance between two IF granular structures to differentiate them and use these two distances to generalize the axiomatic approach of fuzzy information granularity to the IF context. Second, we construct a hierarchical structure based on the relative distance between two IF granular structures to organize the IF granular space hierarchically. Third, we provide the multi-granulation IF granular space and study its relative-distance based axiomatic approach of IF information granularity. Fourth, we propose a relative-distance-based hierarchical structure on multi-granulation IF granular space.