Publication details
On functions that solve Mulholland inequality and on compositions of such functions
| Authors | |
|---|---|
| Year of publication | 2013 |
| Type | Article in Proceedings |
| Conference | Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology, EUSFLAT-2013 |
| Citation | |
| Doi | http://dx.doi.org/10.2991/eusflat.2013.76 |
| Keywords | Mulholland inequality Minkowski inequality strict triangular norm dominance relation |
| Description | Two results related to Mulholland inequality are presented. First, there are functions that are not geo-convex but solve Mulholland inequality; thus Mulholland's condition is not necessary. Second, the set of functions that solve Mulholland inequality is not closed with respect to compositions. As a corollary, the dominance relation on the set of strict triangular norms is not transitive. The proofs of both the results are of geometric nature and benefit from the level set plots of the pseudo-additions generated by the functions in question. |
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