A method to obtain fuzzy relations between uncertain objects using similarity measure

Abstract

Topological relation between geographical objects is one of the key components of geographical information system (GIS). Considering the objects to be exact with sharp boundaries, 4 intersection and 9 intersection matrices initiated the study of calculating the topological relations. Due to the extensive existence of vague spatial phenomenons, the study of uncertainty object modeling has grown rapidly. Parallelly, the relationship calculating tools have been upgraded to handle the vague concepts. The fuzzy 9 intersection matrix and Egg yolk methods are such popular tools. Although the geographical objects are themselves uncertain, surprisingly, most of these tools generate certain relations between the objects. Thereby, the qualitative nature of these tools overlook the very essence of their uncertainty. To overcome these drawbacks, we propose a quantitative fuzzy valued 9 intersection matrix to obtain a fuzzy relationship between uncertain geographical objects. Then two new similarity computation techniques have been introduced to calculate the membership grade of similarity between the proposed matrix and the known crisp matrices. These similarity computations allow two spatial objects to have partial membership against the eight established topological relations. The quantitative calculations indicate the strength of the relationship. The superiority of the proposed model is established through various numerical examples. Further, certain linguistic variables are linked to the evaluated membership grades to generate an immediate association with the known crisp relations. An example is provided in support of this association.