Abstract
Fuzziness is found everywhere, in modeling spatial relations, fuzziness is found at object level as well as in relation semantics. Commonly, fuzzy topological relations are computed between fuzzy objects. Fuzziness in relation semantics is represented by fuzzy topological relations between crisp objects and these types of fuzzy topological relations are much less developed. In this paper, we propose a method for combining fuzzy topological and directional relations. We also propose an algorithm for defuzzification of relations which provides us a binary topological and directional relation between a 2D object pair. These relations are represented in a neighborhood graph. For validation and assessment, a number of experiments have been performed on artificial data.
Highlights
The space can be studied through objects as well as spatial relationship between them
Spatial relations are based on a connection relation C(x, y). This calculus is extended to fuzzy theory and fuzzy topological relations are developed between fuzzy objects [10,11,12] and a set of 46 topological configurations are considered
Method of combined fuzzy topological and directional (CTD) relations has twofold impacts, Allen relations are combined in such a way that whole space can be analyzed by using the directions [0, π] and this method answers well the question that where a topological relation exists in space
Summary
The space can be studied through objects as well as spatial relationship between them. Spatial relations are based on a connection relation C(x, y) This calculus is extended to fuzzy theory and fuzzy topological relations are developed between fuzzy objects [10,11,12] and a set of 46 topological configurations are considered. This theory is extended to deal fuzziness at relation semantics and fuzzy connection relation based on nearness is defined [13]. In projection-based methods, two-dimensional projections are taken on both axis Allen relations are used and nine directional relations are defined out of 169 possibilities Both methods provide similar results and MBR of the reference object is called neutral or direction-less region.
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