{
  "abstract": "In this article, we mainly investigate when the binary operation $T^{[n]}:[0, 1]^2\\rightarrow [0, 1]$ satisfies the associative law and thus becomes a triangular norm where \\begin{equation*} T^{[n]}(x,y)=\\left\\{\\begin{array}{ll} f_{n}(T(f_{n}(x),f_{n}(y))), &\\text{if}\\,\\, (x,y)\\in{[0,1)^{2}}, \\\\ \\min\\{x,y\\}, &\\text{otherwise,} \\end{array}\\right. \\end{equation*} $f_{n}:[0,1]\\rightarrow\\left\\{0, \\frac{1}{n}, \\frac{2}{n}, \\dots, \\frac{n-1}{n}, 1\\right\\}$ given by $f_{n}(x)=\\frac{1}{n}{\\lfloor nx \\rfloor}$ with $n$ a positive integer and $T:[0, 1]^2\\rightarrow [0, 1]$ is a triangular norm. We present some sufficient conditions for $T^{[n]}$ to be triangular norms, and for $T^{[n]}$ to be never associative when $T$ is strictly monotonic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14072",
  "author_total": 2,
  "authors": [
    {
      "name": "Di Zhang"
    },
    {
      "name": "Xue-ping Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9rw7ntmtq48w7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14072",
  "fulltext_url": null,
  "id": "9rw7ntmtq48w7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14072",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GM"
    ],
    [
      "openalex",
      "1703|Advanced Algebra and Logic"
    ]
  ],
  "openalex": "W7221748142",
  "pdf_url": "https://arxiv.org/pdf/2610.14072",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9rw7ntmtq48w7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14072",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14072"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GM",
      "subfield": "general"
    }
  ],
  "title": "Associativity of discretized triangular norms",
  "title_text": "Associativity of discretized triangular norms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/9rw7ntmtq48w7",
  "venue": "arXiv",
  "versions": []
}