Métricas y normas en ambientes probabilísticos

Abstract

In this PhD thesis, sorne of the different concepts introduced until now about "fuzzy metric spaces" are studied. The properties underlying all of them are discussed and a unified vision of them through a new fuzzy metric valued on the fuzzy numbers is proposed. Todo this, the necessary algebraic preliminaries that allow us to understand the above concepts are introduced, and they are interpreted from a probabilistic point of view. Moreover, sorne of these constructions are used to present fuzzy fixed point theorems in both L-fuzzy metric spaces and fuzzy normed spaces (in particular, the existence of coupled fixed points is guaranteed). Finally, a new fuzzy regression methodology with crisp inputs and triangular fuzzy outputs is described.