{
  "annotation_id": "f8439ab0-0614-400b-bf81-5916f70709dc",
  "date_created": "2026-02-17T05:53:12.592000Z",
  "date_modified": "2026-02-17T05:53:12.592000Z",
  "file_hash": "dfd0409ed23a90a97438b906c159312093007940cde4111d00eec138738ca16d",
  "private": false,
  "record": {
    "abstract": "This article focuses on the construction of left-continuous t-norms on complete lattices. The concepts of $\\mathfrak{f}$-mappings and weak $\\mathfrak{f}$-mappings on complete lattices are first introduced, respectively. They are then applied to establish the following key results: weak $\\mathfrak{f}$-mappings are used to induce left-continuous t-subnorms; $\\mathfrak{f}$-mappings are used to generate left-continuous t-norms whenever the top element $1$ of the complete lattice is a completely join-irreducible element. Finally, some necessary and sufficient conditions are provided for an operator constructed by the ordinal sum of a series of annihilating binary operators being a left-continuous t-norm on a complete lattice.",
    "arxiv_id": "2601.07146",
    "authors": [
      "Peng He",
      "Xue-ping Wang"
    ],
    "categories": [
      "math.GM"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "title": "Constructing left-continuous triangular norms on complete lattices",
    "url": "https://arxiv.org/abs/2601.07146",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "afdf20db-3d44-4b4e-9eb5-bce4a3b85797",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}