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

Authors: Milan Petrík
Publication year: 2013
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology EUSFLAT 2013
Projects: Geometry of associative structures
Bibliographic citation: PETRÍK, Milan. On functions that solve Mulholland inequality and on compositions of such functions. In: PASI, G., MONTERO, J., CIUCCI, D, eds. Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology EUSFLAT 2013. Paris: Atlantis Press, 2013, S. 543-548. Advances in Intelligent Systems Research. ISBN 978-1-62993-219-4
Dostupné z: doi:10.2991/eusflat.2013.76
DOI: 10.2991/eusflat.2013.76
ID: 395819

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.