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On the Ordering Property and Law of Importation in Fuzzy Logic

On the Ordering Property and Law of Importation in Fuzzy Logic

Huiwen Deng, Huan Jiang
Copyright: © 2010 |Volume: 1 |Issue: 3 |Pages: 14
ISSN: 1947-3087|EISSN: 1947-3079|EISBN13: 9781609609535|DOI: 10.4018/jalr.2010070102
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MLA

Deng, Huiwen, and Huan Jiang. "On the Ordering Property and Law of Importation in Fuzzy Logic." IJALR vol.1, no.3 2010: pp.17-30. http://doi.org/10.4018/jalr.2010070102

APA

Deng, H. & Jiang, H. (2010). On the Ordering Property and Law of Importation in Fuzzy Logic. International Journal of Artificial Life Research (IJALR), 1(3), 17-30. http://doi.org/10.4018/jalr.2010070102

Chicago

Deng, Huiwen, and Huan Jiang. "On the Ordering Property and Law of Importation in Fuzzy Logic," International Journal of Artificial Life Research (IJALR) 1, no.3: 17-30. http://doi.org/10.4018/jalr.2010070102

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Abstract

In this paper, the authors investigate the ordering property (OP), , together with the general form of the law of importation(LI), i.e., , whereis a t-norm andis a fuzzy implication for the four main classes of fuzzy implications. The authors give necessary and sufficient conditions under which both (OP) and (LI) holds for S-, R-implications and some specific families of QL-, D-implications. Following this, the paper proposes the sufficient condition under which the equivalence between CRI and triple I method for FMP can be established. Moreover, this conclusion can be viewed as a unified triple I method, a generalized form of the known results proposed by Wang and Pei.

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