{"paper":{"title":"Probabilistic-valued decomposable set functions with respect to triangle functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.PR","authors_text":"Jana Moln\\'arov\\'a, Lenka Hal\\v{c}inov\\'a, Ondrej Hutn\\'ik","submitted_at":"2013-09-22T18:33:17Z","abstract_excerpt":"In the framework of the generalized measure theory the decomposable probabilistic-valued set functions are introduced with triangle functions $\\tau$ in an appropriate probabilistic metric space as natural candidates for the \"addition\", leading to the concept of $\\tau$-decomposable measures. Several set functions, among them the classical (sub)measures, previously defined $\\tau_T$-submeasures, $\\tau_{L,A}$-submeasures as well as recently introduced Shen's (sub)measures are described and investigated in a unified way. Basic properties and characterizations of $\\tau$-decomposable (sub)measures ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5628","kind":"arxiv","version":2},"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"}