Towards the definition of spatial granules.

Three basic issues of granular computing are construction or definition of granules, measures of granules, and computation or reasoning with granules. This paper reviews the main theories of granular computing and introduces the definition of spatial granules. A granule is composed of one or more atomic granules. The rationality of this definition is explained from the four aspects: simplicity, applicability, measurability and visualization. A one-to-one correspondence is established between the granules and the points in the unit hypercube, and the coarsening and refining of the granules are the descending and ascending dimensions of the points, respectively. The weak fuzzy tolerance relation and weak fuzzy equivalence relation are defined so as to study on all fuzzy binary relations. The notion of layer granularity/fineness is introduced and each granule can be easily denoted by two numbers, which can be used to pre-process macro knowledge space and greatly improve the search speed. This paper also discusses the main properties of granules including the necessary and sufficient conditions of coarse-fine relation and the main principles of granular space. • Introduce the definition of spatial granules and explain its rationality. • Define coarse-fine relation and all the granules can be hierarchicalized. • Adopt a one-to-one mapping between the granules and the points. • Discuss the main properties of spatial granules. • Layer granularity/fineness is used to pre-process macro knowledge space. [ABSTRACT FROM AUTHOR]