Information granulation and uncertainty measures in interval-valued intuitionistic fuzzy information systems

highlights
• Operations of IIFGS are proposed.
• Information granularity is introduced to depict the distinguishment ability of an IIFGS.
• How to scale the uncertainty of the uncertainty among IIFGSs are discussed.
• The relationship between entropy and granularity of IIFGSs is discovered.

Information granulation and entropy are main approaches for investigating the uncertainty of information systems, which have been widely employed in many practical domains. In this paper, information granulation and uncertainty measures for interval-valued intuitionistic fuzzy binary granular structures are addressed. First, we propose the representation of interval-valued intuitionistic fuzzy information granules and examine some operations of interval-valued intuitionistic fuzzy granular structures. Second, the interval-valued intuitionistic fuzzy information granularity is introduced to depict the distinguishment ability of an interval-valued intuitionistic fuzzy granular structure (IIFGS), which is a natural extension of fuzzy information granularity. Third, we discuss how to scale the uncertainty of an IIFGS using the extended information entropy and the uncertainty among interval-valued intuitionistic fuzzy granular structures using the expanded mutual information derived from the presented intuitionistic fuzzy information entropy. Fourth, we discovery the relationship between the developed interval-valued intuitionistic fuzzy information entropy and the intuitionistic fuzzy information granularity presented in this paper.