J. J. Font, S. Macario, M. Sanchis
In this paper we provide a general setting to deal with level continuous fuzzy-valued functions. Namely, we embed such functions into a product of spaces of real-valued functions of two variables satisfying certain types of left-continuity, right-continuity and monotonicity.
J. J. Font, S. Macario, M. Sanchis
This paper contains 7 sections, 8 theorems, 60 equations.
Theorem 2.1
Let $u\in\mathbb{E}\sp{1}$ and $[u]\sp{\lambda}=[u^-(\lambda),u^+(\lambda)]$, $\lambda\in [0,1]$. Then the pair of functions $u\sp{-}(\lambda)$ and $u\sp{+}(\lambda)$ has the following properties: Conversely, if a pair of functions $\alpha (\lambda)$ and $\beta(\lambda)$ satisfy the above conditions (i)-(iv), then there exists a unique $u\in\mathbb{E}\sp{1}$ such that $[u]\sp{\lambda}=\mathopen[\
