Abstract
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.
Highlights
A System of Fuzzy Relation Equation is given by the following system: ⎧ ⎪ a11 a∧ x1 ∨ ⋯ ∨ a1n ∧x ∨ ∨ a ∧ xn ∧x = = b1 b ⎨ 21 1 ⋯ 2n n (1)⎪⎩ am1 ∧ x1 ∨ ⋯ ∨⋯ amn ∧ xn = bmThe coefficient aij, with 0 ≤ aij ≤ 1, can be seen as the weight with which the jth cause affects the ith symptom
In this work we propose a GISbased framework in which we apply a method proposed in Cardone and Di Martino (2018) to partition an urban study area in homogeneous areas with respect to the characteristics analyzed; in Cardone and Di Martino (2018) the study area is initially partitioned in atomic homogeneous subzones, called microzones, made up of the census areas for which characteristics relating to the resident population and the urban fabric are measured; based on a fuzzy rule set prepared by the pool of experts, a Mamdani fuzzy system is applied to classify each microzone; adjoint microzones belonging to the same class are dissolved to form urban homogeneous areas called Urban Contexts
The application of a dynamic model that allows to obtain the best partitioning of the urban study area into UCs, homogeneous subzones with respect to all the characteristics of the study area taken into consideration; initially the SFRE method is applied to each of the microzones making up the study of area; subsequently adjacent microzones with the same values assigned to the output variables are dissolved, forming an UC; 1 3
Summary
A System of Fuzzy Relation Equation (for short, SFRE) is given by the following system:. Di Martino and Sessa (2011a) implement the Universal Algorithm in a GIS-based framework to solve urban planning problems They apply the Universal Algorithm on a study area; the SFRE (1) is constructed deriving the symptoms from a set of known r measurable facts (the input variables i1,..., ir). The application of a dynamic model that allows to obtain the best partitioning of the urban study area into UCs, homogeneous subzones with respect to all the characteristics of the study area taken into consideration; initially the SFRE method is applied to each of the microzones making up the study of area; subsequently adjacent microzones with the same values assigned to the output variables are dissolved, forming an UC;. The construction, for each output variable, of a reliability map of each UC, which allows to evaluate the spatial distribution of the reliability of the value assigned to the output variable
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