Rough L-fuzzy sets: Their representation and related structures.

The combination of fuzzy set theory and rough set theory has been discussed in a lot of research papers over the years. In this paper, we examine one such combination, namely the notion of rough L -fuzzy sets. We provide a representation theorem that determines when a pair of L -fuzzy sets is a rough L -fuzzy set, and we establish a connection between the lattice of rough fuzzy sets and the lattice of rough relations. Furthermore, we investigate the properties of the lattice of rough L -fuzzy sets and characterize the case when a three-valued Łukasiewicz-algebra can be defined on it. [ABSTRACT FROM AUTHOR]