A Normative Approach to Fuzzy Logic Reasoning Using Residual Implications

Yahachiro Tsukamoto

doi:10.20965/jaciii.2009.p0262

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JACIII Vol.13 No.3 pp. 262-267

doi: 10.20965/jaciii.2009.p0262

(2009)

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A Normative Approach to Fuzzy Logic Reasoning Using Residual Implications

Yahachiro Tsukamoto

Department of Information Engineering, Faculty of Science and Technology, Meijo University, Shiogamaguchi, Tempaku-ku, Nagoya 468-8502, Japan

Received:

November 29, 2008

Accepted:

February 18, 2009

Published:

May 20, 2009

Keywords:

compositional rule of inference, residual implication, generalized modus ponens, normative rules

Abstract

Logical problems with fuzzy implications have been investigated minutely (Baczynski and Jayaram [1]). Considering some of the normative criteria to be met by generalized modus ponens, we have formulated a method of fuzzy reasoning based on residual implication. Among these criteria, the specificity possessed by the conclusion deduced by generalized modus ponens should not be stronger than that of the consequent in the fuzzy implication.

Cite this article as:

Y. Tsukamoto, “A Normative Approach to Fuzzy Logic Reasoning Using Residual Implications,” J. Adv. Comput. Intell. Intell. Inform., Vol.13 No.3, pp. 262-267, 2009.

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References

[1] M. Baczynski and B. Jayaram, “Fuzzy Implications,” Studies in Fuzziness and Soft Computing, Springer, 2008.
[2] L. A. Zadeh, “The concept of linguistic variable and its application to approximate reasoning Part 1,2,3,” Information Sciences, Vol.8,9, 1975, 1976.
[3] M. Mizumoto and H. J. Zimmermann, “Comparison of fuzzy reasoning methods,” Fuzzy Sets and Systems, Vol.8, pp. 253-283, 1982.
[4] Y. Tsukamoto, “Fuzzy information theory,” Daigaku Kyoiku Pub., 2004 (in Japanese).
[5] N. Rescher, “Many valued logic,” McGRAW-HILL, 1969.
[6] J. F. Baldwin, “A new approach to approximate reasoning using a fuzzy logic,” Fuzzy Sets and Systems, Vol.2, 1979.
[7] D. Dubois and H. Prade, “Fuzzy Sets and Systems: Theory and Applications,” Academic Press, 1980.
[8] E.P. Klement, “Some mathematical aspects of fuzzy sets: Triangular norms, fuzzy logics, and generalized measures,” Fuzzy Sets and Systems, Vol.90, No.2, 1997.
[9] I. Perfilieva, “Analytical theory fuzzy If-Then rules with compositional rule of inference,” in Fuzzy Logic, P.P. Wang, et al. (Eds.), Springer, 2007.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] M. Baczynski and B. Jayaram, “Fuzzy Implications,” Studies in Fuzziness and Soft Computing, Springer, 2008.

[2] [2] L. A. Zadeh, “The concept of linguistic variable and its application to approximate reasoning Part 1,2,3,” Information Sciences, Vol.8,9, 1975, 1976.

[3] [3] M. Mizumoto and H. J. Zimmermann, “Comparison of fuzzy reasoning methods,” Fuzzy Sets and Systems, Vol.8, pp. 253-283, 1982.

[4] [4] Y. Tsukamoto, “Fuzzy information theory,” Daigaku Kyoiku Pub., 2004 (in Japanese).

[5] [5] N. Rescher, “Many valued logic,” McGRAW-HILL, 1969.

[6] [6] J. F. Baldwin, “A new approach to approximate reasoning using a fuzzy logic,” Fuzzy Sets and Systems, Vol.2, 1979.

[7] [7] D. Dubois and H. Prade, “Fuzzy Sets and Systems: Theory and Applications,” Academic Press, 1980.

[8] [8] E.P. Klement, “Some mathematical aspects of fuzzy sets: Triangular norms, fuzzy logics, and generalized measures,” Fuzzy Sets and Systems, Vol.90, No.2, 1997.

[9] [9] I. Perfilieva, “Analytical theory fuzzy If-Then rules with compositional rule of inference,” in Fuzzy Logic, P.P. Wang, et al. (Eds.), Springer, 2007.