On functions that solve Mulholland inequality and on compositions of such functions
Available Online August 2013.
- 10.2991/eusflat.2013.76How to use a DOI?
- Mulholland inequality Minkowski inequality strict triangular norm dominance relation
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.
- © 2013, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - CONF AU - Milan Petrík PY - 2013/08 DA - 2013/08 TI - On functions that solve Mulholland inequality and on compositions of such functions BT - Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13) PB - Atlantis Press SP - 543 EP - 548 SN - 1951-6851 UR - https://doi.org/10.2991/eusflat.2013.76 DO - 10.2991/eusflat.2013.76 ID - Petrík2013/08 ER -