Fuzzy region connection calculus in finite discrete space domains

Abstract

Abstract Many practical applications involving spatial aspects work with finite discrete space domains, e.g. map grids, railways track layouts and road networks. Such space domains are computationally tractable and often include specialised forms of spatial reasoning. Moreover, in such applications, the spatial information naturally includes various forms of approximation, uncertainty or inexactness. Fuzzy representations are then appropriate. In this paper, we reformulate the region connection calculus (RCC) framework for finite, discrete space domains in simple set-theoretical terms. We generalise RCC framework and develop several fuzzy spatial concepts like fuzzy regions, fuzzy directions, fuzzy named distances. We propose a fuzzification of standard spatial relations in RCC. For this purpose, we enhance the fuzzy set theory to include fuzzy definitions for membership, subset and set equality crisp binary relations between sets (fuzzy or crisp). We illustrate the approach using a discrete finite two-dimensional map grid as the space domain.