Rough sets and gradual decision rules

We propose a new fuzzy rough set approach which, differently from all known fuzzy set extensions of rough set theory, does not use any fuzzy logical connectives (t-norm, t-conorm, fuzzy implication). As there is no rationale for a particular choice of these connectives, avoiding this choice permits to reduce the part of arbitrary in the fuzzy rough approximation. Another advantage of the new approach is that it is based on the ordinal property of fuzzy membership degrees only. The concepts of fuzzy lower and upper approximations are thus proposed, creating a base for induction of fuzzy decision rules having syntax and semantics of gradual rules.