Granule, granular set and granular system

This paper, based on the author's new model of granular computing — the theory of granular set, offers firstly the definition of granule, and describes the form of four-tuple array of granule, then puts forward the concept of object granular set, description granular set, granular set, object granular system, description granular system, granular system, through upgrading the mapping from the Point Set to the Power Set and mapping from one-way to two-way. It further describes those concept s respectively, of which the description of granular set and granular system are in the form of five-tuple array, that is, (U, D, L, H, J), where U is the universe of the problem discussed, D describes all the elements in U, L and H are the operators of the opposite direction, and J restricts the L and H. The difference between granular set and granular system is that the operator in the granular set is from the Point Set to the Point Set, while the operator in the granular system is from the Power Set to the Power Set. Thus it expands and improves the granular set theory.