arXiv subjects
Publications and source records attributed to Manuel Sanchis.
We extend Cardaliaguet-Euvrard neural network operators to the context of fuzzy number valued continuous functions and study their behaviour. We focus on level continuous, sendograph continuous and endograph continuous functions and obtain Jackson-type results in all these cases.
The authors introduced in a previous paper the notion of fuzzy Gromov-Hausdorff distance between non-Archimedean compact fuzzy metric spaces, presenting a fuzzy version of the Gromov's completeness theorem. In this paper we present a fuzzy version of the Gromov's precompactness theorem which allows to deduce the classical theorem for compact metric spaces by means of the standard fuzzy metric associated to a metric space. This completes the previous work.
Given a uniform space $(X, \mathcal{U})$, we denote by $\mathcal{F}(X)$ to the family of all normal upper semicontinuous fuzzy sets $u \colon X \to [0,1]$ with compact support. In this paper, we study transitivity on some uniformities on $\mathcal{F}(X)$: the level-wise uniformity $\mathcal{U}_{\infty}$, the Skorokhod uniformity $\mathcal{U}_{0}$, and the sendograph uniformity $\mathcal{U}_S$. If $f \colon (X, \mathcal{U}) \to (X, \mathcal{U})$ is a continuous function, we mainly characterize when the induced dynamical systems $\widehat{f} \colon (\mathcal{F}(X), \mathcal{U}_{\infty}) \to (\mathcal{F}(X), \mathcal{U}_{\infty})$, $\widehat{f} \colon (\mathcal{F}(X), \mathcal{U}_{0}) \to (\mathcal{F}(X), \mathcal{U}_{0})$ and $\widehat{f} \colon (\mathcal{F}(X), \mathcal{U}_{S}) \to (\mathcal{F}(X), \mathcal{U}_{S})$ are transitive, where $\widehat{f}$ is the Zadeh's extension of $f$.