A proposal for spatial relations between vague objects

Vagueness is often present in spatial phenomena. For a proper understanding and modeling of spatial phenomena is therefore important to represent and reason with vagueness in spatial information. An essential part of reasoning over space concerns the relations between objects. This paper provides spatial relations between vague objects: points, lines and regions. All vague object types are fuzzy sets in IR that have specific characteristics. Spatial relations between crisp objects are extended to relations between vague objects. Spatial relations we provide are defined in terms of degrees, taking values in the interval [0, 1]. For a relation R, a value v between the 0 and 1 means that objects are in relation R to the degree v. A value 0 for R means that objects are certainly not in relation R. A value 1 means that objects are certainly in relation R. Relations are such that if one of them is certain, all the others are impossible, meaning their value is 0.