Information Granularity in Fuzzy Binary GrC Model

Abstract—Zadeh’s seminal work in theory of fuzzy-information granulation in human reasoning is inspired by the ways in which humans granulate information and reason with it. This has led to an interesting research topic: granular computing (GrC). Al-though many excellent research contributions have been made, there remains an important issue to be addressed: What is the essence of measuring a fuzzy-information granularity of a fuzzy-granular structure? What is needed to answer this question is an axiomatic constraint with a partial-order relation that is de-fined in terms of the size of each fuzzy-information granule from a fuzzy-binary granular structure. This viewpoint is demonstrated for fuzzy-binary granular structure, which is called the binary GrC model by Lin. We study this viewpoint from from five aspects in this study, which are fuzzy BINARY-granular-structure operators, partial-order relations, measures for fuzzy-information granular-ity, an axiomatic approach to fuzzy-information granularity, and fuzzy-information entropies. Index Terms—Fuzzy-information entropy, fuzzy-information granularity, granular computing (GrC), partial-order relation