{"paper":{"title":"Generators of aggregation functions and fuzzy connectives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jozef P\\'ocs, Radko Mesiar, Radom\\'ir Hala\\v{s}","submitted_at":"2018-10-09T07:52:37Z","abstract_excerpt":"We show that the class of all aggregation functions on $[0,1]$ can be generated as a composition of infinitary sup-operation $\\bigvee$ acting on sets with cardinality not exceeding $\\mathfrak{c}$, $b$-medians $\\mathsf{Med}_b$, $b\\in[0,1[$, and unary aggregation functions $1_{]0,1]}$ and $1_{[a,1]}$, $a\\in ]0,1]$. Moreover, we show that we cannot relax the cardinality of argument sets for suprema to be countable, thus showing a kind of minimality of the introduced generating set. As a by product, generating sets for fuzzy connectives, such as fuzzy unions, fuzzy intersections and fuzzy implicat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06406","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"}