Fuzzy spatial network Voronoï diagram: a spatial decision support for transportation planning

The spatial network constitutes an essential support for the spatial organisation of the territory, where accessibility plays a key role in transportation dynamics. In fact, it is dependent on the transportation network quality and place structure; it influences our daily moving and our mobility decisions. In this paper we adopt the fuzzy spatial network Voronoi diagram (fuzzy-SNVD), an approach based on fuzzy arithmetic and graph theory, in order to evaluate the fuzzy Voronoi geographical accessibility to its generators (station, public facility, equipment, etc.). This evaluation and its cartographic representation occupy a key position among the necessary tools which can give decision makers effective assistance support in the transport planning process. Indeed, we propose within this framework two algorithms which allow calculating the fuzzy-SNVD and which consist in assigning each Voronoi generator to its closer nodes of the graph modelling a real spatial network. This assignment of the nodes is based on the comparison of the weights of the shortest traversed paths, which are considered fuzzy numbers representing, in a way more faithful to reality, the travel times, speeds or all values describing moving on the transport network.