Fuzzy Bayesian inference for mapping vague and place-based regions: a case study of sectarian territory

The problem of mapping regions with socially-derived boundaries has been a topic of discussion in the GIS literature for many years. Fuzzy approaches have frequently been suggested as solutions, but none have been adopted. This is likely due to difficulties associated with determining suitable membership functions, which are often as arbitrary as the crisp boundaries that they seek to replace. This paper presents a novel approach to fuzzy geographical modelling that replaces the membership function with a possibility distribution that is estimated using Bayesian inference. In this method, data from multiple sources are combined to estimate the degree to which a given location is a member of a given set and the level of uncertainty associated with that estimate. The Fuzzy Bayesian Inference approach is demonstrated through a case study in which census data are combined with perceptual and behavioural evidence to model the territory of two segregated groups (Catholics and Protestants) in Belfast, Northern Ireland, UK. This novel method provides a robust empirical basis for the use of fuzzy models in GIS, and therefore has applications for mapping a range of socially-derived and otherwise vague boundaries.