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In 2004 Anna Maria Radzikowska et al \cite{RK2004} investigated the fuzzyrough sets where the set of truth values is an arbitrary residuated lattice. Inthis paper, we extend their work by considering a residuated multilattice $M$as the set of truth values. $M$-fuzzy rough sets are defined using theresiduation operators provided by residuated multilattice $M$. Depending onclasses of binary fuzzy relations, we define several classes of $M$-fuzzy roughsets and investigate some properties of these classes.

Residuated Multilattice as set of Truth Values for Fuzzy Rough Sets