Ordinal sums and idempotents of copulas View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2010-03

AUTHORS

Radko Mesiar, Carlo Sempi

ABSTRACT

We prove that the ordinal sum of n-copulas is always an n-copula and show that every copula may be represented as an ordinal sum, once the set of its idempotents is known. In particular, it will be shown that every copula can be expressed as the ordinal sum of copulas having only trivial idempotents. As a by-product, we also characterize all associative copulas whose n-ary forms are n-copulas for all n. More... »

PAGES

39-52

References to SciGraph publications

  • 2000. Triangular Norms in NONE
  • 1974-06. A probabilistic interpretation of complete monotonicity in AEQUATIONES MATHEMATICAE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00010-010-0013-6

    DOI

    http://dx.doi.org/10.1007/s00010-010-0013-6

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1037639518


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Institute of the Theory of Information and Automation, Czech Academy of Sciences, Prague, Czech Republic", 
              "id": "http://www.grid.ac/institutes/grid.418095.1", 
              "name": [
                "Department of Mathematics and Descriptive Geometry, SvF, Slovak University of Technology, Radlinsk\u00e9ho 11, 813 68, Bratislava, Slovakia", 
                "Institute of the Theory of Information and Automation, Czech Academy of Sciences, Prague, Czech Republic"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Mesiar", 
            "givenName": "Radko", 
            "id": "sg:person.013374353164.75", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013374353164.75"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Dipartimento di Matematica \u201cEnnio De Giorgi\u201d, Universit\u00e0 del Salento, 73100, Lecce, Italy", 
              "id": "http://www.grid.ac/institutes/grid.9906.6", 
              "name": [
                "Dipartimento di Matematica \u201cEnnio De Giorgi\u201d, Universit\u00e0 del Salento, 73100, Lecce, Italy"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Sempi", 
            "givenName": "Carlo", 
            "id": "sg:person.07603035605.17", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07603035605.17"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf01832852", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001875633", 
              "https://doi.org/10.1007/bf01832852"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-94-015-9540-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025931387", 
              "https://doi.org/10.1007/978-94-015-9540-7"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2010-03", 
        "datePublishedReg": "2010-03-01", 
        "description": "We prove that the ordinal sum of n-copulas is always an n-copula and show that every copula may be represented as an ordinal sum, once the set of its idempotents is known. In particular, it will be shown that every copula can be expressed as the ordinal sum of copulas having only trivial idempotents. As a by-product, we also characterize all associative copulas whose n-ary forms are n-copulas for all n.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/s00010-010-0013-6", 
        "inLanguage": "en", 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136868", 
            "issn": [
              "0001-9054", 
              "1420-8903"
            ], 
            "name": "Aequationes mathematicae", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1-2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "79"
          }
        ], 
        "keywords": [
          "form", 
          "sum", 
          "products", 
          "show", 
          "set", 
          "copula", 
          "idempotents", 
          "ordinal sum", 
          "only trivial idempotents", 
          "trivial idempotents", 
          "associative copulas", 
          "ary forms", 
          "idempotents of copulas"
        ], 
        "name": "Ordinal sums and idempotents of copulas", 
        "pagination": "39-52", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1037639518"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00010-010-0013-6"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00010-010-0013-6", 
          "https://app.dimensions.ai/details/publication/pub.1037639518"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2021-11-01T18:14", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20211101/entities/gbq_results/article/article_508.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/s00010-010-0013-6"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00010-010-0013-6'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00010-010-0013-6'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00010-010-0013-6'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00010-010-0013-6'


     

    This table displays all metadata directly associated to this object as RDF triples.

    90 TRIPLES      22 PREDICATES      41 URIs      31 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00010-010-0013-6 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N5f992c0787f24aac80fe8784f5d1b377
    4 schema:citation sg:pub.10.1007/978-94-015-9540-7
    5 sg:pub.10.1007/bf01832852
    6 schema:datePublished 2010-03
    7 schema:datePublishedReg 2010-03-01
    8 schema:description We prove that the ordinal sum of n-copulas is always an n-copula and show that every copula may be represented as an ordinal sum, once the set of its idempotents is known. In particular, it will be shown that every copula can be expressed as the ordinal sum of copulas having only trivial idempotents. As a by-product, we also characterize all associative copulas whose n-ary forms are n-copulas for all n.
    9 schema:genre article
    10 schema:inLanguage en
    11 schema:isAccessibleForFree false
    12 schema:isPartOf Na3a72d066d5c4d6f9546f3af45d07c3b
    13 Nf9184e8829144926bcab881bfa2ee180
    14 sg:journal.1136868
    15 schema:keywords ary forms
    16 associative copulas
    17 copula
    18 form
    19 idempotents
    20 idempotents of copulas
    21 only trivial idempotents
    22 ordinal sum
    23 products
    24 set
    25 show
    26 sum
    27 trivial idempotents
    28 schema:name Ordinal sums and idempotents of copulas
    29 schema:pagination 39-52
    30 schema:productId N79688fe805f9495c9aa4b0d0fe2c2fc4
    31 Nf005d6e684c44dfeb493565d808cb0d9
    32 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037639518
    33 https://doi.org/10.1007/s00010-010-0013-6
    34 schema:sdDatePublished 2021-11-01T18:14
    35 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    36 schema:sdPublisher Na2c72dc7e8704e69b97fa67b3014c225
    37 schema:url https://doi.org/10.1007/s00010-010-0013-6
    38 sgo:license sg:explorer/license/
    39 sgo:sdDataset articles
    40 rdf:type schema:ScholarlyArticle
    41 N5f992c0787f24aac80fe8784f5d1b377 rdf:first sg:person.013374353164.75
    42 rdf:rest Na41a01c34b644332832ac3794e018b25
    43 N79688fe805f9495c9aa4b0d0fe2c2fc4 schema:name dimensions_id
    44 schema:value pub.1037639518
    45 rdf:type schema:PropertyValue
    46 Na2c72dc7e8704e69b97fa67b3014c225 schema:name Springer Nature - SN SciGraph project
    47 rdf:type schema:Organization
    48 Na3a72d066d5c4d6f9546f3af45d07c3b schema:volumeNumber 79
    49 rdf:type schema:PublicationVolume
    50 Na41a01c34b644332832ac3794e018b25 rdf:first sg:person.07603035605.17
    51 rdf:rest rdf:nil
    52 Nf005d6e684c44dfeb493565d808cb0d9 schema:name doi
    53 schema:value 10.1007/s00010-010-0013-6
    54 rdf:type schema:PropertyValue
    55 Nf9184e8829144926bcab881bfa2ee180 schema:issueNumber 1-2
    56 rdf:type schema:PublicationIssue
    57 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    58 schema:name Mathematical Sciences
    59 rdf:type schema:DefinedTerm
    60 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    61 schema:name Pure Mathematics
    62 rdf:type schema:DefinedTerm
    63 sg:journal.1136868 schema:issn 0001-9054
    64 1420-8903
    65 schema:name Aequationes mathematicae
    66 schema:publisher Springer Nature
    67 rdf:type schema:Periodical
    68 sg:person.013374353164.75 schema:affiliation grid-institutes:grid.418095.1
    69 schema:familyName Mesiar
    70 schema:givenName Radko
    71 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013374353164.75
    72 rdf:type schema:Person
    73 sg:person.07603035605.17 schema:affiliation grid-institutes:grid.9906.6
    74 schema:familyName Sempi
    75 schema:givenName Carlo
    76 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07603035605.17
    77 rdf:type schema:Person
    78 sg:pub.10.1007/978-94-015-9540-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025931387
    79 https://doi.org/10.1007/978-94-015-9540-7
    80 rdf:type schema:CreativeWork
    81 sg:pub.10.1007/bf01832852 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001875633
    82 https://doi.org/10.1007/bf01832852
    83 rdf:type schema:CreativeWork
    84 grid-institutes:grid.418095.1 schema:alternateName Institute of the Theory of Information and Automation, Czech Academy of Sciences, Prague, Czech Republic
    85 schema:name Department of Mathematics and Descriptive Geometry, SvF, Slovak University of Technology, Radlinského 11, 813 68, Bratislava, Slovakia
    86 Institute of the Theory of Information and Automation, Czech Academy of Sciences, Prague, Czech Republic
    87 rdf:type schema:Organization
    88 grid-institutes:grid.9906.6 schema:alternateName Dipartimento di Matematica “Ennio De Giorgi”, Università del Salento, 73100, Lecce, Italy
    89 schema:name Dipartimento di Matematica “Ennio De Giorgi”, Università del Salento, 73100, Lecce, Italy
    90 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...