When granules are not enough in a Theory of Granularities

Abstract

Several approaches have been proposed to model spatiotemporal phenome- na at multiple LoDs, in particularly, under the granular computing research area, where a granularities-based model was proposed. Such model stands out from the related literature, but has two major limitations. On one hand, it has difficulties for describing regions, intervals of time, among others complex descriptions, and on the other hand, the generalization process is the same whether it is generalizing spatial, temporal or other features of a phenomenon. These problems reduce its applicability. To overcome such limitations, this paper extends the granularities-based model by introducing the granular term concept. We apply this concept to represent time in- stants and intervals as well as cells and raster regions. For each granular term, gener- alization rules are defined so that a phenomenon can be expressed from one LoD to a coarser one in an automatic way. Changing a phenomenon’s LoD can simplify granu- lar terms, transforming for instance a time interval into a time instant or a raster re- gion into a cell. Our contributions are shown based on a real dataset about tornadoes in the USA. The results obtained show an enhancement of application scenarios from the extended granularities-based model to its ability of providing different phenome- non's representations in each LoD, while keeping its original strengths.