Linear Regression With Random Fuzzy Numbers View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1998

AUTHORS

Bilal M. Ayyub , Madan M. Gupta , Wolfgang. Näther , Ralf. Körner

ABSTRACT

This chapter deals with problems which arise if for well justified statistical models like linear regression only fuzzy data are available. Three approaches are discussed: The first one is an application of Zadeh’s extension principle to optimal classical estimators, but unfortunately they lose their optimality. The second one is the attempt to develop some kind of best linear estimates, but unfortunately fuzzy sets do not constitute a linear space. Therefore, in the third approach, the least squares approximation principle for fuzzy data is considered, which leads to most acceptable results. More... »

PAGES

193-212

References to SciGraph publications

  • 1998. Fuzzy Regression Analysis in FUZZY SETS IN DECISION ANALYSIS, OPERATIONS RESEARCH AND STATISTICS
  • 1987. Statistics with Vague Data in NONE
  • Book

    TITLE

    Uncertainty Analysis in Engineering and Sciences: Fuzzy Logic, Statistics, and Neural Network Approach

    ISBN

    978-1-4613-7500-5
    978-1-4615-5473-8

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-1-4615-5473-8_13

    DOI

    http://dx.doi.org/10.1007/978-1-4615-5473-8_13

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1049980572


    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/2008/0104", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Statistics", 
            "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": [
          {
            "familyName": "Ayyub", 
            "givenName": "Bilal M.", 
            "type": "Person"
          }, 
          {
            "familyName": "Gupta", 
            "givenName": "Madan M.", 
            "type": "Person"
          }, 
          {
            "familyName": "N\u00e4ther", 
            "givenName": "Wolfgang.", 
            "id": "sg:person.014367310401.44", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014367310401.44"
            ], 
            "type": "Person"
          }, 
          {
            "familyName": "K\u00f6rner", 
            "givenName": "Ralf.", 
            "id": "sg:person.015617360634.01", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015617360634.01"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1016/0020-0255(78)90019-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000052059"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0020-0255(78)90019-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000052059"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4615-5645-9_11", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004204608", 
              "https://doi.org/10.1007/978-1-4615-5645-9_11"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4615-5645-9_11", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004204608", 
              "https://doi.org/10.1007/978-1-4615-5645-9_11"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1006047231", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-94-009-3943-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006047231", 
              "https://doi.org/10.1007/978-94-009-3943-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-94-009-3943-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006047231", 
              "https://doi.org/10.1007/978-94-009-3943-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0898-1221(97)00063-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018118194"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0165-0114(96)00169-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018900260"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0165-0114(91)90218-f", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019955006"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0165-0114(91)90218-f", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019955006"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0165-0114(88)90054-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023197634"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0165-0114(88)90054-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023197634"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0898-1221(94)00127-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033269776"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0020-0255(88)90047-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035565224"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0020-0255(88)90047-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035565224"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0022-247x(86)90093-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043810381"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0165-0114(87)90070-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044058669"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0165-0114(87)90070-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044058669"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0165-0114(87)90033-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046385757"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0165-0114(87)90033-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046385757"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1998", 
        "datePublishedReg": "1998-01-01", 
        "description": "This chapter deals with problems which arise if for well justified statistical models like linear regression only fuzzy data are available. Three approaches are discussed: The first one is an application of Zadeh\u2019s extension principle to optimal classical estimators, but unfortunately they lose their optimality. The second one is the attempt to develop some kind of best linear estimates, but unfortunately fuzzy sets do not constitute a linear space. Therefore, in the third approach, the least squares approximation principle for fuzzy data is considered, which leads to most acceptable results.", 
        "genre": "chapter", 
        "id": "sg:pub.10.1007/978-1-4615-5473-8_13", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": {
          "isbn": [
            "978-1-4613-7500-5", 
            "978-1-4615-5473-8"
          ], 
          "name": "Uncertainty Analysis in Engineering and Sciences: Fuzzy Logic, Statistics, and Neural Network Approach", 
          "type": "Book"
        }, 
        "name": "Linear Regression With Random Fuzzy Numbers", 
        "pagination": "193-212", 
        "productId": [
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/978-1-4615-5473-8_13"
            ]
          }, 
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "ee1742afad099008ce4aff30d1a6512be5383adef2a9937dd751fa2f3d0c0c1c"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1049980572"
            ]
          }
        ], 
        "publisher": {
          "location": "Boston, MA", 
          "name": "Springer US", 
          "type": "Organisation"
        }, 
        "sameAs": [
          "https://doi.org/10.1007/978-1-4615-5473-8_13", 
          "https://app.dimensions.ai/details/publication/pub.1049980572"
        ], 
        "sdDataset": "chapters", 
        "sdDatePublished": "2019-04-15T15:24", 
        "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_8672_00000274.jsonl", 
        "type": "Chapter", 
        "url": "http://link.springer.com/10.1007/978-1-4615-5473-8_13"
      }
    ]
     

    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.10.1007/978-1-4615-5473-8_13'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-1-4615-5473-8_13'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-1-4615-5473-8_13'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-1-4615-5473-8_13'


     

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

    111 TRIPLES      22 PREDICATES      39 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/978-1-4615-5473-8_13 schema:about anzsrc-for:01
    2 anzsrc-for:0104
    3 schema:author Nee633c321f0b4e0c8fe8589c1c76b180
    4 schema:citation sg:pub.10.1007/978-1-4615-5645-9_11
    5 sg:pub.10.1007/978-94-009-3943-1
    6 https://app.dimensions.ai/details/publication/pub.1006047231
    7 https://doi.org/10.1016/0020-0255(78)90019-1
    8 https://doi.org/10.1016/0020-0255(88)90047-3
    9 https://doi.org/10.1016/0022-247x(86)90093-4
    10 https://doi.org/10.1016/0165-0114(87)90033-9
    11 https://doi.org/10.1016/0165-0114(87)90070-4
    12 https://doi.org/10.1016/0165-0114(88)90054-1
    13 https://doi.org/10.1016/0165-0114(91)90218-f
    14 https://doi.org/10.1016/0898-1221(94)00127-8
    15 https://doi.org/10.1016/s0165-0114(96)00169-8
    16 https://doi.org/10.1016/s0898-1221(97)00063-1
    17 schema:datePublished 1998
    18 schema:datePublishedReg 1998-01-01
    19 schema:description This chapter deals with problems which arise if for well justified statistical models like linear regression only fuzzy data are available. Three approaches are discussed: The first one is an application of Zadeh’s extension principle to optimal classical estimators, but unfortunately they lose their optimality. The second one is the attempt to develop some kind of best linear estimates, but unfortunately fuzzy sets do not constitute a linear space. Therefore, in the third approach, the least squares approximation principle for fuzzy data is considered, which leads to most acceptable results.
    20 schema:genre chapter
    21 schema:inLanguage en
    22 schema:isAccessibleForFree false
    23 schema:isPartOf N3a28ba42a8e7439699565d4b89627c10
    24 schema:name Linear Regression With Random Fuzzy Numbers
    25 schema:pagination 193-212
    26 schema:productId N88b6ee9896b743ac96b800d73d4c0d7b
    27 N8ad37bd40ce8456b938ca9a70650a92b
    28 N92dd393ea897424d80035477bf474106
    29 schema:publisher N0fb4326593844b1b82c4c1156663dbc5
    30 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049980572
    31 https://doi.org/10.1007/978-1-4615-5473-8_13
    32 schema:sdDatePublished 2019-04-15T15:24
    33 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    34 schema:sdPublisher Na4e71d3828b3429d89b000b655de898a
    35 schema:url http://link.springer.com/10.1007/978-1-4615-5473-8_13
    36 sgo:license sg:explorer/license/
    37 sgo:sdDataset chapters
    38 rdf:type schema:Chapter
    39 N0fb4326593844b1b82c4c1156663dbc5 schema:location Boston, MA
    40 schema:name Springer US
    41 rdf:type schema:Organisation
    42 N3a28ba42a8e7439699565d4b89627c10 schema:isbn 978-1-4613-7500-5
    43 978-1-4615-5473-8
    44 schema:name Uncertainty Analysis in Engineering and Sciences: Fuzzy Logic, Statistics, and Neural Network Approach
    45 rdf:type schema:Book
    46 N75f4602bcc3f4e71b85211ec4bd644c3 rdf:first Ndf813bf8ee80400da6eaf604893b04a6
    47 rdf:rest Nf58c287bcc3a4fdb86346d81769ff457
    48 N88b6ee9896b743ac96b800d73d4c0d7b schema:name dimensions_id
    49 schema:value pub.1049980572
    50 rdf:type schema:PropertyValue
    51 N8ad37bd40ce8456b938ca9a70650a92b schema:name readcube_id
    52 schema:value ee1742afad099008ce4aff30d1a6512be5383adef2a9937dd751fa2f3d0c0c1c
    53 rdf:type schema:PropertyValue
    54 N92dd393ea897424d80035477bf474106 schema:name doi
    55 schema:value 10.1007/978-1-4615-5473-8_13
    56 rdf:type schema:PropertyValue
    57 Na4e71d3828b3429d89b000b655de898a schema:name Springer Nature - SN SciGraph project
    58 rdf:type schema:Organization
    59 Nafb847672daf470e98d55e287bff01c1 rdf:first sg:person.015617360634.01
    60 rdf:rest rdf:nil
    61 Ndf813bf8ee80400da6eaf604893b04a6 schema:familyName Gupta
    62 schema:givenName Madan M.
    63 rdf:type schema:Person
    64 Ne8813685cb72441b8692183df9bbee8e schema:familyName Ayyub
    65 schema:givenName Bilal M.
    66 rdf:type schema:Person
    67 Nee633c321f0b4e0c8fe8589c1c76b180 rdf:first Ne8813685cb72441b8692183df9bbee8e
    68 rdf:rest N75f4602bcc3f4e71b85211ec4bd644c3
    69 Nf58c287bcc3a4fdb86346d81769ff457 rdf:first sg:person.014367310401.44
    70 rdf:rest Nafb847672daf470e98d55e287bff01c1
    71 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    72 schema:name Mathematical Sciences
    73 rdf:type schema:DefinedTerm
    74 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
    75 schema:name Statistics
    76 rdf:type schema:DefinedTerm
    77 sg:person.014367310401.44 schema:familyName Näther
    78 schema:givenName Wolfgang.
    79 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014367310401.44
    80 rdf:type schema:Person
    81 sg:person.015617360634.01 schema:familyName Körner
    82 schema:givenName Ralf.
    83 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015617360634.01
    84 rdf:type schema:Person
    85 sg:pub.10.1007/978-1-4615-5645-9_11 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004204608
    86 https://doi.org/10.1007/978-1-4615-5645-9_11
    87 rdf:type schema:CreativeWork
    88 sg:pub.10.1007/978-94-009-3943-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006047231
    89 https://doi.org/10.1007/978-94-009-3943-1
    90 rdf:type schema:CreativeWork
    91 https://app.dimensions.ai/details/publication/pub.1006047231 schema:CreativeWork
    92 https://doi.org/10.1016/0020-0255(78)90019-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000052059
    93 rdf:type schema:CreativeWork
    94 https://doi.org/10.1016/0020-0255(88)90047-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035565224
    95 rdf:type schema:CreativeWork
    96 https://doi.org/10.1016/0022-247x(86)90093-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043810381
    97 rdf:type schema:CreativeWork
    98 https://doi.org/10.1016/0165-0114(87)90033-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046385757
    99 rdf:type schema:CreativeWork
    100 https://doi.org/10.1016/0165-0114(87)90070-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044058669
    101 rdf:type schema:CreativeWork
    102 https://doi.org/10.1016/0165-0114(88)90054-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023197634
    103 rdf:type schema:CreativeWork
    104 https://doi.org/10.1016/0165-0114(91)90218-f schema:sameAs https://app.dimensions.ai/details/publication/pub.1019955006
    105 rdf:type schema:CreativeWork
    106 https://doi.org/10.1016/0898-1221(94)00127-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033269776
    107 rdf:type schema:CreativeWork
    108 https://doi.org/10.1016/s0165-0114(96)00169-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018900260
    109 rdf:type schema:CreativeWork
    110 https://doi.org/10.1016/s0898-1221(97)00063-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018118194
    111 rdf:type schema:CreativeWork
     




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


    ...