A GIS-based framework using fuzzy relation equation system solutions in urban planning

Several fuzzy decision models are proposed in literature to solve urban planning problems. In this research we present a novel GIS-based framework to solve decision problems in urban planning based on a System of Fuzzy Relation Equations in which the unknowns represent characteristics affecting observable facts constituting the input variables. Aim of this research is to partition the urban study area into subzones, each of which identifies a sub-area of the study area within which the set of analyzed characteristics are homogeneous. The study area is initially decomposed in atomic urban areas called microzones; for each microzone are calculated the greatest and lowest solutions of a System of Fuzzy Relation Equations by using the Universal solution Algorithm and are calculated and fuzzified the values of the output variables. Spatially adjoining microzones with same output variables are dissolved forming homogeneous urban areas with reference to the problem analyzed, called Urban Contexts. For each output variable a thematic map is constructed; in addition, a thematic map of its reliability is created. This framework is tested on a study area given by the district of Ponticelli in the municipality of Naples (Italy); comparison tests performed with respect to a previous GIS-based framework based on a System of Fuzzy Relation Equations show that our method provides a more detailed knowledge of the characteristics of the urban study area with reference to the problem dealt with.