Modus ponens versus modus tollens associated with rough gradual decision rules induced from a decision table

Authors:
Masahiro Inuiguchi;Salvatore Greco;Roman Słowiński
Affiliations:
Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan (Corresponding author. E-mail: inuiguti@sys.es.osaka-u.ac.jp);Faculty of Economics, University of Catania, Corso Italia, 55, 95129 Catania, Italy;Institute of Computing Science, Poznań University of Technology, 60-965 Poznań, Poland and Institute for Systems Research, Polish Academy of Sciences, 01-447 Warsaw, Poland
Venue:
International Journal of Hybrid Intelligent Systems - Hybrid Intelligence using rough sets
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 connectives. In this paper, we discuss the use of these gradual decision rules within modus ponens and modus tollens inference patterns. We show differences and similarities between modus ponens and modus tollens through representation theorems of modifier functions characterizing the inference patterns. Moreover, we prove that modus ponens and modus tollens are equivalent under suitable monotonicity conditions. Finally, we conclude this paper with a comparison between the linear regression analysis and the proposed approach.