# Decomposition Integral Based Generalizations of OWA Operators

Ontology type: schema:Chapter

### Chapter Info

DATE

2016-06-11

AUTHORS ABSTRACT

Based on the representation of OWA operators as Choquet integrals with respect to symmetric capacities, a new kind of OWA generalizations based on decomposition integrals is proposed and discussed. The symmetry of the underlying capacity is not sufficient to guarantee the symmetry of the resulting operator, and thus we deal with symmetric saturated decomposition systems only. All possible generalized OWA operators on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X = \{1,2\}$$\end{document} are introduced. Similarly, when considering the maximal decomposition system on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X = \{1,2,3\},$$\end{document} all generalized OWA operators are shown, based on the ordinal structure of the normed weighting vector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf w} = (w_1,w_2,w_3).$$\end{document} More... »

PAGES

3-10

### Book

TITLE

Information Processing and Management of Uncertainty in Knowledge-Based Systems

ISBN

978-3-319-40595-7
978-3-319-40596-4

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-40596-4_1

DOI

http://dx.doi.org/10.1007/978-3-319-40596-4_1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1018271435

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:

[
{
"@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json",
{
"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": "Faculty of Civil Engineering, Slovak University of Technology, Radlinsk\u00e9ho 11, 81005, Bratislava, Slovak Republic",
"id": "http://www.grid.ac/institutes/grid.440789.6",
"name": [
"Faculty of Civil Engineering, Slovak University of Technology, Radlinsk\u00e9ho 11, 81005, Bratislava, Slovak Republic"
],
"type": "Organization"
},
"familyName": "Mesiar",
"id": "sg:person.013374353164.75",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013374353164.75"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Faculty of Civil Engineering, Slovak University of Technology, Radlinsk\u00e9ho 11, 81005, Bratislava, Slovak Republic",
"id": "http://www.grid.ac/institutes/grid.440789.6",
"name": [
"Faculty of Civil Engineering, Slovak University of Technology, Radlinsk\u00e9ho 11, 81005, Bratislava, Slovak Republic"
],
"type": "Organization"
},
"familyName": "Stup\u0148anov\u00e1",
"givenName": "Andrea",
"id": "sg:person.014024440251.00",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014024440251.00"
],
"type": "Person"
}
],
"datePublished": "2016-06-11",
"datePublishedReg": "2016-06-11",
"description": "Based on the representation of OWA operators as Choquet integrals with respect to symmetric capacities, a new kind of OWA generalizations based on decomposition integrals is proposed and discussed. The symmetry of the underlying capacity is not sufficient to guarantee the symmetry of the resulting operator, and thus we deal with symmetric saturated decomposition systems only. All possible generalized OWA operators on \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$X = \\{1,2\\}$$\\end{document} are introduced. Similarly, when considering the maximal decomposition system on \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$X = \\{1,2,3\\},$$\\end{document} all generalized OWA operators are shown, based on the ordinal structure of the normed weighting vector \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathbf w} = (w_1,w_2,w_3).$$\\end{document}",
"editor": [
{
"familyName": "Carvalho",
"givenName": "Joao Paulo",
"type": "Person"
},
{
"familyName": "Lesot",
"givenName": "Marie-Jeanne",
"type": "Person"
},
{
"familyName": "Kaymak",
"givenName": "Uzay",
"type": "Person"
},
{
"familyName": "Vieira",
"givenName": "Susana",
"type": "Person"
},
{
"familyName": "Bouchon-Meunier",
"type": "Person"
},
{
"familyName": "Yager",
"givenName": "Ronald R.",
"type": "Person"
}
],
"genre": "chapter",
"id": "sg:pub.10.1007/978-3-319-40596-4_1",
"inLanguage": "en",
"isAccessibleForFree": false,
"isPartOf": {
"isbn": [
"978-3-319-40595-7",
"978-3-319-40596-4"
],
"name": "Information Processing and Management of Uncertainty in Knowledge-Based Systems",
"type": "Book"
},
"keywords": [
"OWA operator",
"operators",
"ordinal structure",
"decomposition integrals",
"decomposition system",
"Choquet integral",
"integrals",
"generalization",
"symmetry",
"symmetric capacity",
"new kind",
"system",
"representation",
"underlying capacity",
"vector",
"respect",
"kind",
"structure",
"capacity",
"OWA generalizations",
"maximal decomposition system",
"Decomposition Integral Based Generalizations",
"Integral Based Generalizations",
"Based Generalizations"
],
"name": "Decomposition Integral Based Generalizations of OWA Operators",
"pagination": "3-10",
"productId": [
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1018271435"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/978-3-319-40596-4_1"
]
}
],
"publisher": {
"name": "Springer Nature",
"type": "Organisation"
},
"sameAs": [
"https://doi.org/10.1007/978-3-319-40596-4_1",
"https://app.dimensions.ai/details/publication/pub.1018271435"
],
"sdDataset": "chapters",
"sdDatePublished": "2021-12-01T20:06",
"sdPublisher": {
"name": "Springer Nature - SN SciGraph project",
"type": "Organization"
},
"sdSource": "s3://com-springernature-scigraph/baseset/20211201/entities/gbq_results/chapter/chapter_358.jsonl",
"type": "Chapter",
"url": "https://doi.org/10.1007/978-3-319-40596-4_1"
}
]

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.10.1007/978-3-319-40596-4_1'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-40596-4_1'

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-40596-4_1'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-40596-4_1'

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

116 TRIPLES      23 PREDICATES      49 URIs      42 LITERALS      7 BLANK NODES

Subject Predicate Object
2 anzsrc-for:0101
3 schema:author N9a61a2ebb09949e480f927c7f5f97d50
4 schema:datePublished 2016-06-11
5 schema:datePublishedReg 2016-06-11
6 schema:description Based on the representation of OWA operators as Choquet integrals with respect to symmetric capacities, a new kind of OWA generalizations based on decomposition integrals is proposed and discussed. The symmetry of the underlying capacity is not sufficient to guarantee the symmetry of the resulting operator, and thus we deal with symmetric saturated decomposition systems only. All possible generalized OWA operators on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X = \{1,2\}$$\end{document} are introduced. Similarly, when considering the maximal decomposition system on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X = \{1,2,3\},$$\end{document} all generalized OWA operators are shown, based on the ordinal structure of the normed weighting vector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf w} = (w_1,w_2,w_3).$$\end{document}
7 schema:editor N44d589bcfd3e4688b0352ebf09fa6163
8 schema:genre chapter
9 schema:inLanguage en
10 schema:isAccessibleForFree false
11 schema:isPartOf Nb58752df00434c0f82390c29ab7c5719
12 schema:keywords Based Generalizations
13 Choquet integral
14 Decomposition Integral Based Generalizations
15 Integral Based Generalizations
16 OWA generalizations
17 OWA operator
18 capacity
19 decomposition integrals
20 decomposition system
21 generalization
22 integrals
23 kind
24 maximal decomposition system
25 new kind
26 operators
27 ordinal structure
28 representation
29 respect
30 structure
31 symmetric capacity
32 symmetry
33 system
34 underlying capacity
35 vector
36 schema:name Decomposition Integral Based Generalizations of OWA Operators
37 schema:pagination 3-10
38 schema:productId N4fececca84514e50bbafc4383e2dbeac
39 N94f7659bda01450eab20d921811379a4
40 schema:publisher N8f270ce708a6440d895ef2034e5973b3
41 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018271435
42 https://doi.org/10.1007/978-3-319-40596-4_1
43 schema:sdDatePublished 2021-12-01T20:06
45 schema:sdPublisher N1f20ed4014f240ec82b361594dfe9b8d
46 schema:url https://doi.org/10.1007/978-3-319-40596-4_1
48 sgo:sdDataset chapters
49 rdf:type schema:Chapter
50 N19f908eddea94953919f30906d44d4c5 rdf:first sg:person.014024440251.00
51 rdf:rest rdf:nil
52 N1f20ed4014f240ec82b361594dfe9b8d schema:name Springer Nature - SN SciGraph project
53 rdf:type schema:Organization
54 N2e2c3367766d4c00980b566e28ee6d7a schema:familyName Yager
55 schema:givenName Ronald R.
56 rdf:type schema:Person
57 N424b7b7bbd1f40f1afd91a4bc5417946 schema:familyName Vieira
58 schema:givenName Susana
59 rdf:type schema:Person
60 N44d589bcfd3e4688b0352ebf09fa6163 rdf:first N96b6d8164eac48639be18f65b6dcb9f3
61 rdf:rest Nd1f159910cb34b8098ace580a949f8de
62 N4fececca84514e50bbafc4383e2dbeac schema:name doi
63 schema:value 10.1007/978-3-319-40596-4_1
64 rdf:type schema:PropertyValue
65 N6f413ea4d8284e15bb7efb8c23d1c45b schema:familyName Kaymak
66 schema:givenName Uzay
67 rdf:type schema:Person
68 N8221a7c2df414bf18c79d37b9ba2a954 rdf:first Nf2060ca414974a449585ff428782c910
69 rdf:rest Nfab9cd6d6bd7445ab8a7597a7ab0fe9b
70 N8f270ce708a6440d895ef2034e5973b3 schema:name Springer Nature
71 rdf:type schema:Organisation
72 N94f7659bda01450eab20d921811379a4 schema:name dimensions_id
73 schema:value pub.1018271435
74 rdf:type schema:PropertyValue
75 N96b6d8164eac48639be18f65b6dcb9f3 schema:familyName Carvalho
76 schema:givenName Joao Paulo
77 rdf:type schema:Person
78 N9a61a2ebb09949e480f927c7f5f97d50 rdf:first sg:person.013374353164.75
79 rdf:rest N19f908eddea94953919f30906d44d4c5
80 Naaeb43e3b5b341e29d61892dfe6544dc schema:familyName Lesot
81 schema:givenName Marie-Jeanne
82 rdf:type schema:Person
83 Nb58752df00434c0f82390c29ab7c5719 schema:isbn 978-3-319-40595-7
84 978-3-319-40596-4
85 schema:name Information Processing and Management of Uncertainty in Knowledge-Based Systems
86 rdf:type schema:Book
87 Nc8e46b3137ae48e699bf7d7a18ed64b2 rdf:first N424b7b7bbd1f40f1afd91a4bc5417946
88 rdf:rest N8221a7c2df414bf18c79d37b9ba2a954
89 Nd1f159910cb34b8098ace580a949f8de rdf:first Naaeb43e3b5b341e29d61892dfe6544dc
90 rdf:rest Nf6c5f6a0bf0947b98c4b0b1d07344ed9
91 Nf2060ca414974a449585ff428782c910 schema:familyName Bouchon-Meunier
93 rdf:type schema:Person
94 Nf6c5f6a0bf0947b98c4b0b1d07344ed9 rdf:first N6f413ea4d8284e15bb7efb8c23d1c45b
95 rdf:rest Nc8e46b3137ae48e699bf7d7a18ed64b2
96 Nfab9cd6d6bd7445ab8a7597a7ab0fe9b rdf:first N2e2c3367766d4c00980b566e28ee6d7a
97 rdf:rest rdf:nil
98 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
99 schema:name Mathematical Sciences
100 rdf:type schema:DefinedTerm
101 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
102 schema:name Pure Mathematics
103 rdf:type schema:DefinedTerm
104 sg:person.013374353164.75 schema:affiliation grid-institutes:grid.440789.6
105 schema:familyName Mesiar
107 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013374353164.75
108 rdf:type schema:Person
109 sg:person.014024440251.00 schema:affiliation grid-institutes:grid.440789.6
110 schema:familyName Stupňanová
111 schema:givenName Andrea
112 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014024440251.00
113 rdf:type schema:Person
114 grid-institutes:grid.440789.6 schema:alternateName Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 81005, Bratislava, Slovak Republic
115 schema:name Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 81005, Bratislava, Slovak Republic
116 rdf:type schema:Organization