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

0395819 - ÚI 2014 RIV NL eng C - Conference Paper (international conference)
Petrík, Milan
On functions that solve Mulholland inequality and on compositions of such functions.
Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology EUSFLAT 2013. Paris: Atlantis Press, 2013 - (Pasi, G.; Montero, J.; Ciucci, D.), s. 543-548. Advances in Intelligent Systems Research. ISBN 978-1-62993-219-4.
[EUSFLAT 2013. Milan (IT), 11.09.2013-13.09.2013]
R&D Projects: GA ČR GPP201/12/P055
Grant - others:GA MŠk(CZ) EE2.3.20.0051
Institutional support: RVO:67985807
Keywords : Mulholland inequality * Minkowski inequality * strict triangular norm * dominance relation
Subject RIV: BA - General Mathematics

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.
Permanent Link: http://hdl.handle.net/11104/0223731