Monotonicity in the Construction of Ordinal Sums of Fuzzy Implications View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2018

AUTHORS

Michał Baczyński , Paweł Drygaś , Radko Mesiar

ABSTRACT

In this contribution we discus the problem of monotonicity of intervals in the ordinal sums of fuzzy implication constructions. As a result, new ways of constructing of ordinal sums of fuzzy implications are obtained. These methods allow to adapt the value of fuzzy implication to specific requirements. For our new methods of construction, several sufficient properties for obtaining a fuzzy implication as a result are presented. Moreover, preservation of some properties of the ordinal sums are examined. Among others neutrality property, identity property, and ordering property are considered. More... »

PAGES

189-199

References to SciGraph publications

  • 2017-09-27. Two Constructions of Ordinal Sums of Fuzzy Implications in UNCERTAINTY AND IMPRECISION IN DECISION MAKING AND DECISION SUPPORT: CROSS-FERTILIZATION, NEW MODELS AND APPLICATIONS
  • 2007-10. Conjunctors and their Residual Implicators: Characterizations and Construction Methods in MEDITERRANEAN JOURNAL OF MATHEMATICS
  • 2016. Various Kinds of Ordinal Sums of Fuzzy Implications in NOVEL DEVELOPMENTS IN UNCERTAINTY REPRESENTATION AND PROCESSING
  • 1994. Fuzzy Preference Modelling and Multicriteria Decision Support in NONE
  • 2000. Triangular Norms in NONE
  • Book

    TITLE

    Aggregation Functions in Theory and in Practice

    ISBN

    978-3-319-59305-0
    978-3-319-59306-7

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-59306-7_20

    DOI

    http://dx.doi.org/10.1007/978-3-319-59306-7_20

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1085440702


    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/2008/0103", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Numerical and Computational Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "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"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "University of Silesia", 
              "id": "https://www.grid.ac/institutes/grid.11866.38", 
              "name": [
                "University of Silesia in Katowice"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Baczy\u0144ski", 
            "givenName": "Micha\u0142", 
            "id": "sg:person.016161210032.28", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016161210032.28"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Rzesz\u00f3w University", 
              "id": "https://www.grid.ac/institutes/grid.13856.39", 
              "name": [
                "University of Rzesz\u00f3w"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Dryga\u015b", 
            "givenName": "Pawe\u0142", 
            "id": "sg:person.014445135367.34", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014445135367.34"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "name": [
                "Slovak University of Technology"
              ], 
              "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"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1016/j.fss.2003.06.008", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004547494"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0165-0114(01)00040-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013950305"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1023562048", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-94-017-1648-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023562048", 
              "https://doi.org/10.1007/978-94-017-1648-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-94-017-1648-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023562048", 
              "https://doi.org/10.1007/978-94-017-1648-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1025931387", 
            "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"
          }, 
          {
            "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"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ins.2014.09.021", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029390065"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-319-26211-6_4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036227333", 
              "https://doi.org/10.1007/978-3-319-26211-6_4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00009-007-0122-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047385904", 
              "https://doi.org/10.1007/s00009-007-0122-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ins.2015.03.049", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052395207"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ins.2014.04.021", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052614947"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1515/tmmp-2016-0018", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1074230829"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-319-65545-1_10", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1092033288", 
              "https://doi.org/10.1007/978-3-319-65545-1_10"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-319-65545-1_10", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1092033288", 
              "https://doi.org/10.1007/978-3-319-65545-1_10"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2991/eusflat.2013.113", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1099214556"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2991/eusflat.2013.113", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1099214556"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2018", 
        "datePublishedReg": "2018-01-01", 
        "description": "In this contribution we discus the problem of monotonicity of intervals in the ordinal sums of fuzzy implication constructions. As a result, new ways of constructing of ordinal sums of fuzzy implications are obtained. These methods allow to adapt the value of fuzzy implication to specific requirements. For our new methods of construction, several sufficient properties for obtaining a fuzzy implication as a result are presented. Moreover, preservation of some properties of the ordinal sums are examined. Among others neutrality property, identity property, and ordering property are considered.", 
        "editor": [
          {
            "familyName": "Torra", 
            "givenName": "Vicen\u00e7", 
            "type": "Person"
          }, 
          {
            "familyName": "Mesiar", 
            "givenName": "Radko", 
            "type": "Person"
          }, 
          {
            "familyName": "Baets", 
            "givenName": "Bernard De", 
            "type": "Person"
          }
        ], 
        "genre": "chapter", 
        "id": "sg:pub.10.1007/978-3-319-59306-7_20", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isFundedItemOf": [
          {
            "id": "sg:grant.7400816", 
            "type": "MonetaryGrant"
          }, 
          {
            "id": "sg:grant.4361101", 
            "type": "MonetaryGrant"
          }
        ], 
        "isPartOf": {
          "isbn": [
            "978-3-319-59305-0", 
            "978-3-319-59306-7"
          ], 
          "name": "Aggregation Functions in Theory and in Practice", 
          "type": "Book"
        }, 
        "name": "Monotonicity in the Construction of Ordinal Sums of Fuzzy Implications", 
        "pagination": "189-199", 
        "productId": [
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/978-3-319-59306-7_20"
            ]
          }, 
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "815fe7d4bd0f104fad2b8ff958a36d82d0b607f35042f3d79a752bc4dcdfc53c"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1085440702"
            ]
          }
        ], 
        "publisher": {
          "location": "Cham", 
          "name": "Springer International Publishing", 
          "type": "Organisation"
        }, 
        "sameAs": [
          "https://doi.org/10.1007/978-3-319-59306-7_20", 
          "https://app.dimensions.ai/details/publication/pub.1085440702"
        ], 
        "sdDataset": "chapters", 
        "sdDatePublished": "2019-04-15T19:13", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8684_00000279.jsonl", 
        "type": "Chapter", 
        "url": "http://link.springer.com/10.1007/978-3-319-59306-7_20"
      }
    ]
     

    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.10.1007/978-3-319-59306-7_20'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-59306-7_20'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-59306-7_20'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-59306-7_20'


     

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

    143 TRIPLES      23 PREDICATES      41 URIs      20 LITERALS      8 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/978-3-319-59306-7_20 schema:about anzsrc-for:01
    2 anzsrc-for:0103
    3 schema:author N0a93ffcc95a04060874b0925e8e8e7d5
    4 schema:citation sg:pub.10.1007/978-3-319-26211-6_4
    5 sg:pub.10.1007/978-3-319-65545-1_10
    6 sg:pub.10.1007/978-94-015-9540-7
    7 sg:pub.10.1007/978-94-017-1648-2
    8 sg:pub.10.1007/s00009-007-0122-1
    9 https://app.dimensions.ai/details/publication/pub.1023562048
    10 https://app.dimensions.ai/details/publication/pub.1025931387
    11 https://doi.org/10.1016/j.fss.2003.06.008
    12 https://doi.org/10.1016/j.ins.2014.04.021
    13 https://doi.org/10.1016/j.ins.2014.09.021
    14 https://doi.org/10.1016/j.ins.2015.03.049
    15 https://doi.org/10.1016/s0165-0114(01)00040-9
    16 https://doi.org/10.1515/tmmp-2016-0018
    17 https://doi.org/10.2991/eusflat.2013.113
    18 schema:datePublished 2018
    19 schema:datePublishedReg 2018-01-01
    20 schema:description In this contribution we discus the problem of monotonicity of intervals in the ordinal sums of fuzzy implication constructions. As a result, new ways of constructing of ordinal sums of fuzzy implications are obtained. These methods allow to adapt the value of fuzzy implication to specific requirements. For our new methods of construction, several sufficient properties for obtaining a fuzzy implication as a result are presented. Moreover, preservation of some properties of the ordinal sums are examined. Among others neutrality property, identity property, and ordering property are considered.
    21 schema:editor N003e80f36b3c475bbaa98484cd7039fd
    22 schema:genre chapter
    23 schema:inLanguage en
    24 schema:isAccessibleForFree false
    25 schema:isPartOf Na6cab538f23246f88621e8757772da67
    26 schema:name Monotonicity in the Construction of Ordinal Sums of Fuzzy Implications
    27 schema:pagination 189-199
    28 schema:productId N555ee9588abd4c9ea184b7fe333f7be0
    29 N92f941c7e74e4e45b367b118fa803599
    30 Nff2bc3cd36fd4ff4b90338e3a664947d
    31 schema:publisher N670b3e2037cd4ca4a681f17bc8c37c55
    32 schema:sameAs https://app.dimensions.ai/details/publication/pub.1085440702
    33 https://doi.org/10.1007/978-3-319-59306-7_20
    34 schema:sdDatePublished 2019-04-15T19:13
    35 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    36 schema:sdPublisher Ndffbd3bf758d4c55aecaae6200cd2925
    37 schema:url http://link.springer.com/10.1007/978-3-319-59306-7_20
    38 sgo:license sg:explorer/license/
    39 sgo:sdDataset chapters
    40 rdf:type schema:Chapter
    41 N003e80f36b3c475bbaa98484cd7039fd rdf:first Ndc7485ec0e364f7eb5733edadc01f299
    42 rdf:rest N8eac779e7380466590e84c7cea10341e
    43 N09f5b613610440069a6d67ae55173d59 rdf:first sg:person.014445135367.34
    44 rdf:rest N4c5d79cf33434d9386d6f0831198ea60
    45 N0a93ffcc95a04060874b0925e8e8e7d5 rdf:first sg:person.016161210032.28
    46 rdf:rest N09f5b613610440069a6d67ae55173d59
    47 N0f6cac09393c4b3dbd70723f2bbb7572 schema:name Slovak University of Technology
    48 rdf:type schema:Organization
    49 N23f508520860436793dbf84304dc281a rdf:first N3bb52bedc6154438982588b85df0d0c6
    50 rdf:rest rdf:nil
    51 N3bb52bedc6154438982588b85df0d0c6 schema:familyName Baets
    52 schema:givenName Bernard De
    53 rdf:type schema:Person
    54 N4c5d79cf33434d9386d6f0831198ea60 rdf:first sg:person.013374353164.75
    55 rdf:rest rdf:nil
    56 N555ee9588abd4c9ea184b7fe333f7be0 schema:name dimensions_id
    57 schema:value pub.1085440702
    58 rdf:type schema:PropertyValue
    59 N670b3e2037cd4ca4a681f17bc8c37c55 schema:location Cham
    60 schema:name Springer International Publishing
    61 rdf:type schema:Organisation
    62 N8eac779e7380466590e84c7cea10341e rdf:first Nc08cc0e7c91040e0acf08a51f26fa2dc
    63 rdf:rest N23f508520860436793dbf84304dc281a
    64 N92f941c7e74e4e45b367b118fa803599 schema:name doi
    65 schema:value 10.1007/978-3-319-59306-7_20
    66 rdf:type schema:PropertyValue
    67 Na6cab538f23246f88621e8757772da67 schema:isbn 978-3-319-59305-0
    68 978-3-319-59306-7
    69 schema:name Aggregation Functions in Theory and in Practice
    70 rdf:type schema:Book
    71 Nc08cc0e7c91040e0acf08a51f26fa2dc schema:familyName Mesiar
    72 schema:givenName Radko
    73 rdf:type schema:Person
    74 Ndc7485ec0e364f7eb5733edadc01f299 schema:familyName Torra
    75 schema:givenName Vicenç
    76 rdf:type schema:Person
    77 Ndffbd3bf758d4c55aecaae6200cd2925 schema:name Springer Nature - SN SciGraph project
    78 rdf:type schema:Organization
    79 Nff2bc3cd36fd4ff4b90338e3a664947d schema:name readcube_id
    80 schema:value 815fe7d4bd0f104fad2b8ff958a36d82d0b607f35042f3d79a752bc4dcdfc53c
    81 rdf:type schema:PropertyValue
    82 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    83 schema:name Mathematical Sciences
    84 rdf:type schema:DefinedTerm
    85 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
    86 schema:name Numerical and Computational Mathematics
    87 rdf:type schema:DefinedTerm
    88 sg:grant.4361101 http://pending.schema.org/fundedItem sg:pub.10.1007/978-3-319-59306-7_20
    89 rdf:type schema:MonetaryGrant
    90 sg:grant.7400816 http://pending.schema.org/fundedItem sg:pub.10.1007/978-3-319-59306-7_20
    91 rdf:type schema:MonetaryGrant
    92 sg:person.013374353164.75 schema:affiliation N0f6cac09393c4b3dbd70723f2bbb7572
    93 schema:familyName Mesiar
    94 schema:givenName Radko
    95 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013374353164.75
    96 rdf:type schema:Person
    97 sg:person.014445135367.34 schema:affiliation https://www.grid.ac/institutes/grid.13856.39
    98 schema:familyName Drygaś
    99 schema:givenName Paweł
    100 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014445135367.34
    101 rdf:type schema:Person
    102 sg:person.016161210032.28 schema:affiliation https://www.grid.ac/institutes/grid.11866.38
    103 schema:familyName Baczyński
    104 schema:givenName Michał
    105 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016161210032.28
    106 rdf:type schema:Person
    107 sg:pub.10.1007/978-3-319-26211-6_4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036227333
    108 https://doi.org/10.1007/978-3-319-26211-6_4
    109 rdf:type schema:CreativeWork
    110 sg:pub.10.1007/978-3-319-65545-1_10 schema:sameAs https://app.dimensions.ai/details/publication/pub.1092033288
    111 https://doi.org/10.1007/978-3-319-65545-1_10
    112 rdf:type schema:CreativeWork
    113 sg:pub.10.1007/978-94-015-9540-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025931387
    114 https://doi.org/10.1007/978-94-015-9540-7
    115 rdf:type schema:CreativeWork
    116 sg:pub.10.1007/978-94-017-1648-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023562048
    117 https://doi.org/10.1007/978-94-017-1648-2
    118 rdf:type schema:CreativeWork
    119 sg:pub.10.1007/s00009-007-0122-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047385904
    120 https://doi.org/10.1007/s00009-007-0122-1
    121 rdf:type schema:CreativeWork
    122 https://app.dimensions.ai/details/publication/pub.1023562048 schema:CreativeWork
    123 https://app.dimensions.ai/details/publication/pub.1025931387 schema:CreativeWork
    124 https://doi.org/10.1016/j.fss.2003.06.008 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004547494
    125 rdf:type schema:CreativeWork
    126 https://doi.org/10.1016/j.ins.2014.04.021 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052614947
    127 rdf:type schema:CreativeWork
    128 https://doi.org/10.1016/j.ins.2014.09.021 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029390065
    129 rdf:type schema:CreativeWork
    130 https://doi.org/10.1016/j.ins.2015.03.049 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052395207
    131 rdf:type schema:CreativeWork
    132 https://doi.org/10.1016/s0165-0114(01)00040-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013950305
    133 rdf:type schema:CreativeWork
    134 https://doi.org/10.1515/tmmp-2016-0018 schema:sameAs https://app.dimensions.ai/details/publication/pub.1074230829
    135 rdf:type schema:CreativeWork
    136 https://doi.org/10.2991/eusflat.2013.113 schema:sameAs https://app.dimensions.ai/details/publication/pub.1099214556
    137 rdf:type schema:CreativeWork
    138 https://www.grid.ac/institutes/grid.11866.38 schema:alternateName University of Silesia
    139 schema:name University of Silesia in Katowice
    140 rdf:type schema:Organization
    141 https://www.grid.ac/institutes/grid.13856.39 schema:alternateName Rzeszów University
    142 schema:name University of Rzeszów
    143 rdf:type schema:Organization
     




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


    ...