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A generalization of the Mulholland inequality for continuous Archimedean t-norms |
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| Authors: | Susanne Saminger-Platz Bernard De Baets |
| Affiliation: | a Department of Knowledge-Based Mathematical Systems, Johannes Kepler University Linz, Altenbergerstrasse 69, A-4040 Linz, Austria b Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B-9000 Gent, Belgium c Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9, B-9000 Gent, Belgium |
| Abstract: | It is well known that dominance between strict t-norms is closely related to the Mulholland inequality, which can be seen as a generalization of the Minkowski inequality. However, strict t-norms constitute only one part of the class of continuous Archimedean t-norms, the basic elements from which all continuous t-norms are composed. In this paper, dominance between continuous Archimedean t-norms is shown to be related to a generalization of the Mulholland inequality. We provide sufficient and necessary conditions for its fulfillment. |
| Keywords: | Mulholland inequality Minkowski inequality Triangular norm (t-norm) Dominance relation |
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