On functions that solve Mulholland inequality and on compositions of such functions

DOI

10.2991/eusflat.2013.76How to use a DOI?

Keywords

Mulholland inequality Minkowski inequality strict triangular norm dominance relation

Abstract

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.

Copyright

© 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/).

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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  -