Modelling and analysing vague geographical places using fuzzy set theory

Vagueness is an essential part of how humans perceive and understand the geographical world they occupy. It has now become of increasing important to acknowledge this situation in geographical databases and analyses in the field of Geographical Information Science (GIScience). This research has tackled the wholly original topic of modelling vague geographical places (objects) based on fuzzy set theory with a view to assessing the implications of routing problem around those vague places. The research has focused on the modelling of vague places, for a number of villages and rural settlements, working with national address databases which have numerous ambiguous characteristics which add challenge to the work. It has demonstrated the way in which fuzzy set theory can be used to derive approximate boundaries for vague spatial extents (fuzzy footprint) form sets of precise addresses, reporting rural settlements, recorded in different databases. It has further explored the implications of applying the Travelling Salesman Problem (TSP) in traditional hard village extents versus the modelled fuzzy extents. The introduced methods evaluate the usefulness of fuzzy set theory in modelling and analysing such vague regions. The results imply that the fuzzy model is more efficient than the traditional hard, crisp model of approximating the spatial extent of rural areas. However, the TSP results showed that longer tours were mostly found in the fuzzy model than the traditional crisp model. This is mainly affected by the scale factor of rural areas, considering the relatively small distances between villages. One challenge for the approach outlined here is to incorporate this method applied in other novel analyses of geographical information based on fuzzy representation of geographical phenomena.