Generalizações do conceito de distância, i-distâncias, distâncias intervalares e topologia

In this dissertation we present some generalizations for the concept of distance by using more general value spaces, such as: fuzzy metrics, probabilistic metrics and generalized metrics. We show how such generalizations may be useful due to the possibility that the distance between two objects could carry more information about the objects than in the case where the distance is represented just by a real number. Also in this thesis we propose another generalization of distance which encompasses the notion of interval metric and generates a topology in a natural way. Several properties of this generalization are investigated, and its links with other existing generalizations