R-implications and the exchange principle: A complete characterization

Jayaram, Balasubramaniam and Baczynski, M and Mesiar, R (2011) R-implications and the exchange principle: A complete characterization. In: Joint 7th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2011 and 17th French Days on Fuzzy Logic and Applications, 18th July, 2011, Aix-les-Bains; France.

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It is well-known that the residual IT of a leftcontinuous t-norm T satisfies the exchange principle (EP), viz., IT (x, IT (y, z)) = IT (y, IT (x, z)) for all x, y, z [0, 1]. However, the left-continuity of T is only sufficient and not necessary, as many examples in the literature illustrate. In this work we study the necessary conditions on a t-norm T for its residual to satisfy (EP). The work presents a complete characterization of the class of t-norms whose residuals satisfy (EP).

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IITH Creators:
IITH CreatorsORCiD
Jayaram, Balasubramaniamhttp://orcid.org/0000-0001-7370-3821
Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: Exchange principle; Fuzzy implication; R-implication; T-norm
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: Team Library
Date Deposited: 29 Oct 2014 06:35
Last Modified: 20 Sep 2017 08:55
URI: http://raiith.iith.ac.in/id/eprint/503
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