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Fuzzy-Rough Modus Ponens and Modus Tollens as a Basis for Approximate Reasoning

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Rough Sets and Current Trends in Computing (RSCTC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3066))

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Abstract

We have proposed a fuzzy rough set approach without using any fuzzy logical connectives to extract gradual decision rules from decision tables. In this paper, we discuss the use of these gradual decision rules within modus ponens and modus tollens inference patterns. We discuss the difference and similarity between modus ponens and modus tollens and, moreover, we generalize them to formalize approximate reasoning based on the extracted gradual decision rules. We demonstrate that approximate reasoning can be performed by manipulation of modifier functions associated with the gradual decision rules.

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Author information

Authors and Affiliations

  1. Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka, 560-8531, Japan

    Masahiro Inuiguchi

  2. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco

  3. Institute of Computing Science, Poznań University of Technology, 60-965, Poznańn, Poland

    Roman Słowiński

  4. Institute for Systems Research, Polish Academy of Sciences, 01-447, Warsaw, Poland

    Roman Słowiński

Authors
  1. Masahiro Inuiguchi
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  2. Salvatore Greco
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  3. Roman Słowiński
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Editor information

Editors and Affiliations

  1. Shimane University, 89-1 Enya-cho Izumo, 6938501, Shimane, Japan

    Shusaku Tsumoto

  2. Systems Research Institute, Polish Academy of Sciences, 01-447, Warsaw, Poland

    Roman Słowiński

  3. The Linnaeus Centre for Bioinformatics, Uppsala University, Uppsala, Sweden

    Jan Komorowski

  4. Institute of Computer Science, Polish Academy of Sciences, 01–237, Warsaw, Poland

    Jerzy W. Grzymała-Busse

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© 2004 Springer-Verlag Berlin Heidelberg

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Inuiguchi, M., Greco, S., Słowiński, R. (2004). Fuzzy-Rough Modus Ponens and Modus Tollens as a Basis for Approximate Reasoning. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds) Rough Sets and Current Trends in Computing. RSCTC 2004. Lecture Notes in Computer Science(), vol 3066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25929-9_9

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  • DOI: https://doi.org/10.1007/978-3-540-25929-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22117-3

  • Online ISBN: 978-3-540-25929-9

  • eBook Packages: Springer Book Archive

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