Equivalence of Fuzzy-rough Modus Ponens and Fuzzy-rough Modus Tollens

Authors:
Masahiro Inuiguchi;Salvatore Greco;Roman Słowiński
Affiliations:
Graduate School of Engineering Science, Osaka University, Japan;Faculty of Economics, University of Catania, Italy;Institute of Computing Science, Poznań University of Technology, Poland and Institute for Systems Research, Polish Academy of Sciences, Poland
Venue:
Proceedings of the 2005 conference on Advances in Logic Based Intelligent Systems: Selected Papers of LAPTEC 2005
Year:
2005

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Abstract

We have proposed a fuzzy rough set approach to induce gradual decision rules from decision tables without using any fuzzy logical connective. In this paper, we discuss the equivalence between fuzzy-rough modus ponens and fuzzy-rough modus tollens obtained from the induced gradual decision rules. We show the necessary and sufficient conditions for fuzzy-rough modus ponens and fuzzy-rough modus tollens to be equivalent.