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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Abstract
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).
[error in script]
| IITH Creators: |
| IITH Creators | ORCiD |
|---|
| Jayaram, Balasubramaniam | http://orcid.org/0000-0001-7370-3821 |
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| Item Type: |
Conference or Workshop Item
(Paper)
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| Uncontrolled Keywords: |
Exchange principle; Fuzzy implication; R-implication; T-norm |
| Subjects: |
Mathematics |
| Divisions: |
Department of Mathematics |
| Depositing User: |
Team Library
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| Date Deposited: |
29 Oct 2014 06:35 |
| Last Modified: |
20 Sep 2017 08:55 |
| URI: |
http://raiithold.iith.ac.in/id/eprint/503 |
| Publisher URL: |
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| Related URLs: |
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