A Combinatorial Fuzzy Set-Theoretic Approach to the Mapping Between Quantitative and Qualitative Data

The concept of space underlying geographic information systems is basically Euclidean and most attempts to deal with imprecise or uncertain geographic information try to accommodate for this imperfection rather than to change the conceptual view. In this paper, we describe a way of incorporating imprecise qualitative spatial reasoning with quantitative reasoning in geographic information systems (GIS). In particular, we show how the common models of geometry can be extended to allow for qualitative spatial reasoning. The idea is to use fuzzy sets to model qualitative spatial relations among objects, such as The downtown shopping mall is close to the harbour. The membership function of such a fuzzy set, in this instance, defines a fuzzy distance operator.

We illustrate a way of incorporating imprecise qualitative spatial reasoning with quantitative reasoning in GIS. For this, we develop a data model to support qualitative spatial reasoning based on constraints, and we provide an example to illustrate our model. We propose a set of locations, each consisting of a vector of base values. We then associate fuzzy membership functions with the locations to describe qualitative spatial information, from which spatial relations and queries can be computed, regardless of the crispness/fuzzyness of the base data.