Modeling Fuzzy Topological Relations Between Uncertain Objects in a GIS

Abstract

This paper presents a study on modeling fuzzy topological relations between uncertain objects in GIS. Quasi-coincidence and quasi-difference, which are used to distinguish the topological relations between fuzzy objects, and to indicate the effect of one fuzzy object on another in a fuzzy topology adopted for the development. Geometrically, features in GIS can be classified as point features, linear features, and polygon or region features. In this paper, we first introduce several basic concepts in fuzzy topology that will be used in this study. This is followed by several definitions of fuzzy points, fuzzy lines, and fuzzy regions for GIS objects. Next, the level at which one fuzzy object affects the other is modeled based on the sum and difference of the membership functions that are quasi-coincident and quasi-different, respectively. Finally, an applicable example of using quasi-coincidence and quasi-difference based on the new definitions of fuzzy point, line and polygon is given.