{
  "abstract": "This paper studies continuous selections in the framework of intuitionistic fuzzy sets. To each intuitionistic fuzzy set $A=(μ,ν)$ on a topological space $X$ we associate the interval-valued map $F_{A}(x)=[μ(x),1-ν(x)]$, whose width is the hesitation degree. Hence, in this setting, a selection of $F_{A}$ is an ordinary fuzzy membership function compatible with the intuitionistic information, and every selection is the membership function of Atanassov's operator $D_{\\vartheta}$ for a suitable pointwise parameter $\\vartheta$. When $X$ is normal and $μ$, $ν$ are upper semi-continuous, a continuous selection exists by the Katětov--Tong insertion theorem. We show that upper semi-continuity arises naturally in a voting model, in which a panel of experts divides a metric universe into closed regions of acceptance and rejection, and for this model we construct an explicit continuous selection, the consensus selection, illustrated by a non-compact example in the plane. On metric spaces we characterise the intuitionistic fuzzy sets that admit an $L$-Lipschitz selection through a non-local version of the condition $μ+ν\\leq 1$, and we give the largest and the smallest such selections in closed form. Finally, we prove that the set of continuous selections depends in a $1$-Lipschitz way on the intuitionistic fuzzy set, with respect to the Hausdorff-type distance of Grzegorzewski. We also characterise the intuitionistic fuzzy sets admitting locally Lipschitz selections.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00857",
  "author_total": 3,
  "authors": [
    {
      "name": "Giuseppe Failla"
    },
    {
      "name": "Gianmarco La Rosa"
    },
    {
      "name": "Marco Elio Tabacchi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fpsdq356qen26.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00857",
  "fulltext_url": null,
  "id": "fpsdq356qen26",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00857",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.GN"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00857",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fpsdq356qen26.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00857",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00857"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Continuous, locally Lipschitz and Lipschitz selections for intuitionistic fuzzy sets, with applications to expert voting",
  "title_text": "Continuous, locally Lipschitz and Lipschitz selections for intuitionistic fuzzy sets, with applications to expert voting",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/fpsdq356qen26",
  "venue": "arXiv",
  "versions": []
}