Incluindo uma política de construção de objetos espaciais fuzzy no pacote FSR

Abstract

Currently, geoscientists have shown interest in modeling spatial phenomena with types of imprecise data, thus, fuzzy set theory has been used as a framework to model these types of imprecise data, through fuzzy spatial objects. In this context, there are models to formally define fuzzy spatial objects, as well as formal algebras, such as the Spatial Algebra Plateau, that implement the formal concepts of fuzzy spatial objects. To build such objects, there is a methodology composed of two phases, where the first phase with fuzzification policies, and the second phase with construction policies based on Voronoi diagrams, Delaunay triangulations, and convex hulls. The fsr package, for the R programming language, implements the fuzzy saptial data types based on the Spatial Plateau Algebra. In the fsr package architecture, two construction policies were implemented, the Voronoi Diagram policy and the Delaunay Triangulation policy, and so far, the Convex Hull policy has not been developed. In this sense, the objective of this work is to implement the construction policy based on the convex hull build in the for package, and present a case study to validate the implementation performed. As a result, this work presents the implemented algorithm for the convex hull policy, describing how it works and how it was coupled in the for package. To validate the implementation, we simulated a spatial database and four classes of the fuzzy temperature phenomenon. This work also presents a case study that includes the three construction policies, Voronoi Diagram, Dalaunay Triangulation, and Convex hul, to analyze them. We conclude that the developed algorithm met the concepts of Spatial Plateau Algebra and applied the convex hull construction policy rules.