A New Proposal for Fuzzy Rough Approximations and Gradual Decision Rule Representation

Abstract

We propose a new fuzzy rough set approach which, differently from most of 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 uses only the ordinal property of fuzzy membership degrees. 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. The decision rules are induced from lower and upper approximations defined for positive and negative relationships between credibility of premise and conclusion; for this reason, there are four types of decision rules. In addition to decision rule representation, a new scheme of inference with a generalized fuzzy rough modus ponens is proposed.