On Patchwork Techniques for 2-Increasing Aggregation Functions and Copulas View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2008-01-01

AUTHORS

Fabrizio Durante , Susanne Saminger-Platz , Peter Sarkoci

ABSTRACT

In recent years, there has been a raise of interest in the determination of copulas with given values at some fixed points, or with given horizontal, vertical, affine, diagonal, or sub-diagonal sections and combinations thereof. Closely related to these investigations are the determination and characterization of increasing and 2-increasing functions with given margins whose domain is a subset of the unit square as well as necessary and sufficient conditions providing that the combination (patchwork) of such functions on sub-domains yields a (new) 2-increasing aggregation function on [0,1]2, in particular a copula. In the present contribution we provide a full characterization of increasing, 2-increasing functions with prescribed margins acting on a sub-rectangle of the unit square. The characterization allows to determine easily the greatest and smallest such functions and to look at the results on copulas with given horizontal and/or vertical sections and its boundaries from a more general and unified viewpoint. We further discuss necessary and sufficient conditions for a patchwork based on triangular sub-domains. More... »

PAGES

349-356

Book

TITLE

Soft Methods for Handling Variability and Imprecision

ISBN

978-3-540-85026-7
978-3-540-85027-4

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-540-85027-4_42

DOI

http://dx.doi.org/10.1007/978-3-540-85027-4_42

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1035902672


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/2008/06", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Biological Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0601", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Biochemistry and Cell Biology", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Knowledge-Based Mathematical Systems, Johannes Kepler University Linz, Linz, Austria", 
          "id": "http://www.grid.ac/institutes/grid.9970.7", 
          "name": [
            "Department of Knowledge-Based Mathematical Systems, Johannes Kepler University Linz, Linz, Austria"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Durante", 
        "givenName": "Fabrizio", 
        "id": "sg:person.013475607471.22", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013475607471.22"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Knowledge-Based Mathematical Systems, Johannes Kepler University Linz, Linz, Austria", 
          "id": "http://www.grid.ac/institutes/grid.9970.7", 
          "name": [
            "Department of Knowledge-Based Mathematical Systems, Johannes Kepler University Linz, Linz, Austria"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Saminger-Platz", 
        "givenName": "Susanne", 
        "id": "sg:person.011012612513.67", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011012612513.67"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Knowledge-Based Mathematical Systems, Johannes Kepler University Linz, Linz, Austria", 
          "id": "http://www.grid.ac/institutes/grid.9970.7", 
          "name": [
            "Department of Knowledge-Based Mathematical Systems, Johannes Kepler University Linz, Linz, Austria"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Sarkoci", 
        "givenName": "Peter", 
        "id": "sg:person.016517420341.77", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016517420341.77"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2008-01-01", 
    "datePublishedReg": "2008-01-01", 
    "description": "In recent years, there has been a raise of interest in the determination of copulas with given values at some fixed points, or with given horizontal, vertical, affine, diagonal, or sub-diagonal sections and combinations thereof. Closely related to these investigations are the determination and characterization of increasing and 2-increasing functions with given margins whose domain is a subset of the unit square as well as necessary and sufficient conditions providing that the combination (patchwork) of such functions on sub-domains yields a (new) 2-increasing aggregation function on [0,1]2, in particular a copula. In the present contribution we provide a full characterization of increasing, 2-increasing functions with prescribed margins acting on a sub-rectangle of the unit square. The characterization allows to determine easily the greatest and smallest such functions and to look at the results on copulas with given horizontal and/or vertical sections and its boundaries from a more general and unified viewpoint. We further discuss necessary and sufficient conditions for a patchwork based on triangular sub-domains.", 
    "editor": [
      {
        "familyName": "Dubois", 
        "givenName": "Didier", 
        "type": "Person"
      }, 
      {
        "familyName": "Lubiano", 
        "givenName": "M. Asunci\u00f3n", 
        "type": "Person"
      }, 
      {
        "familyName": "Prade", 
        "givenName": "Henri", 
        "type": "Person"
      }, 
      {
        "familyName": "Gil", 
        "givenName": "Mar\u00eda \u00c1ngeles", 
        "type": "Person"
      }, 
      {
        "familyName": "Grzegorzewski", 
        "givenName": "Przemys\u0142aw", 
        "type": "Person"
      }, 
      {
        "familyName": "Hryniewicz", 
        "givenName": "Olgierd", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-540-85027-4_42", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-540-85026-7", 
        "978-3-540-85027-4"
      ], 
      "name": "Soft Methods for Handling Variability and Imprecision", 
      "type": "Book"
    }, 
    "keywords": [
      "characterization", 
      "function", 
      "such functions", 
      "domain", 
      "patchwork technique", 
      "patchwork", 
      "full characterization", 
      "yield", 
      "combination", 
      "recent years", 
      "subset", 
      "conditions", 
      "determination", 
      "present contribution", 
      "contribution", 
      "prescribed margins", 
      "results", 
      "interest", 
      "investigation", 
      "margin", 
      "sections", 
      "years", 
      "boundaries", 
      "aggregation functions", 
      "raise", 
      "point", 
      "copula", 
      "technique", 
      "values", 
      "affine", 
      "vertical sections", 
      "viewpoint", 
      "squares", 
      "unified viewpoint", 
      "sufficient conditions", 
      "unit square"
    ], 
    "name": "On Patchwork Techniques for 2-Increasing Aggregation Functions and Copulas", 
    "pagination": "349-356", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1035902672"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-540-85027-4_42"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-540-85027-4_42", 
      "https://app.dimensions.ai/details/publication/pub.1035902672"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2022-05-20T07:44", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220519/entities/gbq_results/chapter/chapter_249.jsonl", 
    "type": "Chapter", 
    "url": "https://doi.org/10.1007/978-3-540-85027-4_42"
  }
]
 

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.10.1007/978-3-540-85027-4_42'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-540-85027-4_42'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-540-85027-4_42'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-540-85027-4_42'


 

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

135 TRIPLES      23 PREDICATES      61 URIs      54 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-540-85027-4_42 schema:about anzsrc-for:06
2 anzsrc-for:0601
3 schema:author N36ffb9954f394010877c09d0738d42e3
4 schema:datePublished 2008-01-01
5 schema:datePublishedReg 2008-01-01
6 schema:description In recent years, there has been a raise of interest in the determination of copulas with given values at some fixed points, or with given horizontal, vertical, affine, diagonal, or sub-diagonal sections and combinations thereof. Closely related to these investigations are the determination and characterization of increasing and 2-increasing functions with given margins whose domain is a subset of the unit square as well as necessary and sufficient conditions providing that the combination (patchwork) of such functions on sub-domains yields a (new) 2-increasing aggregation function on [0,1]2, in particular a copula. In the present contribution we provide a full characterization of increasing, 2-increasing functions with prescribed margins acting on a sub-rectangle of the unit square. The characterization allows to determine easily the greatest and smallest such functions and to look at the results on copulas with given horizontal and/or vertical sections and its boundaries from a more general and unified viewpoint. We further discuss necessary and sufficient conditions for a patchwork based on triangular sub-domains.
7 schema:editor N02f6612b0ec0498ba51fd75fac7dc507
8 schema:genre chapter
9 schema:inLanguage en
10 schema:isAccessibleForFree false
11 schema:isPartOf Nc8c5f23ebb1e4d8baba7cce28bfe1d64
12 schema:keywords affine
13 aggregation functions
14 boundaries
15 characterization
16 combination
17 conditions
18 contribution
19 copula
20 determination
21 domain
22 full characterization
23 function
24 interest
25 investigation
26 margin
27 patchwork
28 patchwork technique
29 point
30 prescribed margins
31 present contribution
32 raise
33 recent years
34 results
35 sections
36 squares
37 subset
38 such functions
39 sufficient conditions
40 technique
41 unified viewpoint
42 unit square
43 values
44 vertical sections
45 viewpoint
46 years
47 yield
48 schema:name On Patchwork Techniques for 2-Increasing Aggregation Functions and Copulas
49 schema:pagination 349-356
50 schema:productId N99bc761dcac041b7abbea1785328543c
51 Nb30f89195bd14ed19f9e4695273db716
52 schema:publisher Na10e9ed1133a4ffa910b14eb3406de0a
53 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035902672
54 https://doi.org/10.1007/978-3-540-85027-4_42
55 schema:sdDatePublished 2022-05-20T07:44
56 schema:sdLicense https://scigraph.springernature.com/explorer/license/
57 schema:sdPublisher N40bc59e63c0041288c9ec89a1641eafa
58 schema:url https://doi.org/10.1007/978-3-540-85027-4_42
59 sgo:license sg:explorer/license/
60 sgo:sdDataset chapters
61 rdf:type schema:Chapter
62 N02f6612b0ec0498ba51fd75fac7dc507 rdf:first N0d93be013af44bf99da7e986102b599e
63 rdf:rest N632b1f6fb8ac4e4fab769843b5238b01
64 N0d93be013af44bf99da7e986102b599e schema:familyName Dubois
65 schema:givenName Didier
66 rdf:type schema:Person
67 N115e539878564a9aba60a2c6794971b8 schema:familyName Lubiano
68 schema:givenName M. Asunción
69 rdf:type schema:Person
70 N194b154a916140e1a1beabb826a17ab3 schema:familyName Grzegorzewski
71 schema:givenName Przemysław
72 rdf:type schema:Person
73 N32339275aaed407a8199b4f258860365 rdf:first Neec3ed2e33c94869a69f8ba77aa7efae
74 rdf:rest rdf:nil
75 N34b413ebe0144a6a847a9c3410645f54 rdf:first N194b154a916140e1a1beabb826a17ab3
76 rdf:rest N32339275aaed407a8199b4f258860365
77 N365898060fa949d88b790cddd4d609dc rdf:first sg:person.016517420341.77
78 rdf:rest rdf:nil
79 N36ffb9954f394010877c09d0738d42e3 rdf:first sg:person.013475607471.22
80 rdf:rest Nc1bcc3b61f9c40c5a7fe0dba9b98200b
81 N40bc59e63c0041288c9ec89a1641eafa schema:name Springer Nature - SN SciGraph project
82 rdf:type schema:Organization
83 N43da095f94a242329910e148df336448 rdf:first N59bfb0155d1a4e589dab4f9ed254a7c3
84 rdf:rest Nd51e22345fe84feba2f4f5fd72505114
85 N59bfb0155d1a4e589dab4f9ed254a7c3 schema:familyName Prade
86 schema:givenName Henri
87 rdf:type schema:Person
88 N632b1f6fb8ac4e4fab769843b5238b01 rdf:first N115e539878564a9aba60a2c6794971b8
89 rdf:rest N43da095f94a242329910e148df336448
90 N99bc761dcac041b7abbea1785328543c schema:name doi
91 schema:value 10.1007/978-3-540-85027-4_42
92 rdf:type schema:PropertyValue
93 Na10e9ed1133a4ffa910b14eb3406de0a schema:name Springer Nature
94 rdf:type schema:Organisation
95 Nb30f89195bd14ed19f9e4695273db716 schema:name dimensions_id
96 schema:value pub.1035902672
97 rdf:type schema:PropertyValue
98 Nc1bcc3b61f9c40c5a7fe0dba9b98200b rdf:first sg:person.011012612513.67
99 rdf:rest N365898060fa949d88b790cddd4d609dc
100 Nc2e89c1a853441c4b895d2835e6bd558 schema:familyName Gil
101 schema:givenName María Ángeles
102 rdf:type schema:Person
103 Nc8c5f23ebb1e4d8baba7cce28bfe1d64 schema:isbn 978-3-540-85026-7
104 978-3-540-85027-4
105 schema:name Soft Methods for Handling Variability and Imprecision
106 rdf:type schema:Book
107 Nd51e22345fe84feba2f4f5fd72505114 rdf:first Nc2e89c1a853441c4b895d2835e6bd558
108 rdf:rest N34b413ebe0144a6a847a9c3410645f54
109 Neec3ed2e33c94869a69f8ba77aa7efae schema:familyName Hryniewicz
110 schema:givenName Olgierd
111 rdf:type schema:Person
112 anzsrc-for:06 schema:inDefinedTermSet anzsrc-for:
113 schema:name Biological Sciences
114 rdf:type schema:DefinedTerm
115 anzsrc-for:0601 schema:inDefinedTermSet anzsrc-for:
116 schema:name Biochemistry and Cell Biology
117 rdf:type schema:DefinedTerm
118 sg:person.011012612513.67 schema:affiliation grid-institutes:grid.9970.7
119 schema:familyName Saminger-Platz
120 schema:givenName Susanne
121 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011012612513.67
122 rdf:type schema:Person
123 sg:person.013475607471.22 schema:affiliation grid-institutes:grid.9970.7
124 schema:familyName Durante
125 schema:givenName Fabrizio
126 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013475607471.22
127 rdf:type schema:Person
128 sg:person.016517420341.77 schema:affiliation grid-institutes:grid.9970.7
129 schema:familyName Sarkoci
130 schema:givenName Peter
131 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016517420341.77
132 rdf:type schema:Person
133 grid-institutes:grid.9970.7 schema:alternateName Department of Knowledge-Based Mathematical Systems, Johannes Kepler University Linz, Linz, Austria
134 schema:name Department of Knowledge-Based Mathematical Systems, Johannes Kepler University Linz, Linz, Austria
135 rdf:type schema:Organization
 




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


...