{"paper":{"title":"On the existence of aggregation functions with given super-additive and sub-additive transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexandra \\v{S}ipo\\v{s}ov\\'a, Jozef \\v{S}ir\\'a\\v{n}, Ladislav \\v{S}ipeky","submitted_at":"2016-07-11T11:34:44Z","abstract_excerpt":"In this note we study restrictions on the recently introduced super-additive and sub-additive transformations, $A\\mapsto A^*$ and $A\\mapsto A_*$, of an aggregation function $A$. We prove that if $A^*$ has a slightly stronger property of being strictly directionally convex, then $A=A^*$ and $A_*$ is linear; dually, if $A_*$ is strictly directionally concave, then $A=A_*$ and $A^*$ is linear. This implies, for example, the existence of pairs of functions $f\\le g$ sub-additive and super-additive on $[0,\\infty[^n$, respectively, with zero value at the origin and satisfying relatively mild extra co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03862","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}