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

Issue title: Hybrid Intelligence using rough sets

Article type: Research Article

Authors: Inuiguchi, Masahiro^{a; *} | Greco, Salvatore^b | Słowiński, Roman^{c; d}

Affiliations: [a] Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan | [b] Faculty of Economics, University of Catania, Corso Italia, 55, 95129 Catania, Italy | [c] Institute of Computing Science, Poznań University of Technology, 60-965 Poznań, Poland | [d] Institute for Systems Research, Polish Academy of Sciences, 01-447 Warsaw, Poland

Correspondence: [*] Corresponding author. E-mail: [email protected]

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.

Keywords: fuzzy rough sets, gradual decision rules, modus ponens, modus tollens, approximate reasoning, modifier functions, linear regression

DOI: 10.3233/HIS-2005-2203

Journal: International Journal of Hybrid Intelligent Systems, vol. 2, no. 2, pp. 109-131, 2005