Fuzzy rough sets and multiple-premise gradual decision rules

  • Authors:

  • Salvatore Greco;Masahiro Inuiguchi;Roman Slowinski

  • Affiliations:

  • Faculty of Economics, University of Catania, Corso Italia, 55, 95129 Catania, Italy;Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, Toyonaka, Osaka 560-8531, Japan;Institute of Computing Science, Poznan University of Technology, 60-965 Poznan, Poland and Institute for Systems Research, Polish Academy of Sciences, 01-447 Warsaw, Poland

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2006

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Abstract

We propose a new fuzzy rough set approach which, differently from most 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 properties 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. The proposed approach to rule induction is also interesting from the viewpoint of philosophy supporting data mining and knowledge discovery, because it is concordant with the method of concomitant variations by John Stuart Mill. The decision rules are induced from lower and upper approximations defined for positive and negative relationships between credibility degrees of multiple premises, on one hand, and conclusion, on the other hand.