On stability of maximal entropy OWA operator weights

The maximal entropy OWA operator (MEOWA) weights can be obtained by solving a nonlinear programming problem with a linear constraint for the level of orness. Since the exact MEOWA weights are not known for the general case we can only find approximate solutions. We will prove that the nonlinear prog...

Full description

Saved in:
Bibliographic Details
Published in:Fuzzy sets and systems Vol. 448; pp. 145 - 156
Main Authors: Harmati, István Á., Fullér, Robert, Felde, Imre
Format: Journal Article
Language:English
Published: Elsevier B.V 05.11.2022
Subjects:
Implicit function theorem
Maximal entropy OWA operator weights
Stability
Maximal entropy OWA operator weights
Implicit function theorem
Stability
ISSN:0165-0114, 1872-6801
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract The maximal entropy OWA operator (MEOWA) weights can be obtained by solving a nonlinear programming problem with a linear constraint for the level of orness. Since the exact MEOWA weights are not known for the general case we can only find approximate solutions. We will prove that the nonlinear programming problem for obtaining MEOWA weights is well-posed: it has a unique solution and each MEOWA weight changes continuously with the initial level of orness. Using the implicit function theorem we will show that MEOWA weights are Lipschitz-continuous functions of the orness level. The stability property of the MEOWA weights under small changes of the orness level guarantees that small rounding errors of digital computation and small errors of measurement of the orness level can cause only a small deviation in MEOWA weights, i.e. every successive approximation method can be applied to the computation of the approximation of the exact MEOWA weights.
AbstractList The maximal entropy OWA operator (MEOWA) weights can be obtained by solving a nonlinear programming problem with a linear constraint for the level of orness. Since the exact MEOWA weights are not known for the general case we can only find approximate solutions. We will prove that the nonlinear programming problem for obtaining MEOWA weights is well-posed: it has a unique solution and each MEOWA weight changes continuously with the initial level of orness. Using the implicit function theorem we will show that MEOWA weights are Lipschitz-continuous functions of the orness level. The stability property of the MEOWA weights under small changes of the orness level guarantees that small rounding errors of digital computation and small errors of measurement of the orness level can cause only a small deviation in MEOWA weights, i.e. every successive approximation method can be applied to the computation of the approximation of the exact MEOWA weights.
Author Harmati, István Á.
Fullér, Robert
Felde, Imre
Author_xml – sequence: 1
  givenname: István Á.
  orcidid: 0000-0002-0915-9718
  surname: Harmati
  fullname: Harmati, István Á.
  email: harmati@sze.hu
  organization: Department of Mathematics and Computational Sciences, Széchenyi István University, Egyetem tér 1, Győr 9026, Hungary
– sequence: 2
  givenname: Robert
  surname: Fullér
  fullname: Fullér, Robert
  email: rfuller@sze.hu
  organization: Department of Informatics, Széchenyi István University, Egyetem tér 1, Győr 9026, Hungary
– sequence: 3
  givenname: Imre
  surname: Felde
  fullname: Felde, Imre
  email: felde@uni-obuda.hu
  organization: John von Neumann Faculty of Informatics, Óbuda University, Bécsi út 96b, Budapest 1034, Hungary
BookMark eNp9z71OwzAQwHELFYm28ABseYGEOydxUjFVFV9SpS4gRst2LuAqjSvbAvr2uCoTQyff4P_pfjM2Gd1IjN0iFAgo7rZFH0LBgfMCsAAoL9gU24bnogWcsGn6U-eAWF2xWQhbgDQLmLJqM2YhKm0HGw-Z67Od-rE7NWQ0Ru_2h2zzvszcnryKzmffZD8-Y7hml70aAt38vXP29vjwunrO15unl9VynZuygphThw1o3gihdVeXra64aXDBNakSuFataFVbGyLsTGMUllpVuhLCgFn0WKtyzprTXuNdCJ56aWxU0bp0m7KDRJBHvNzKhJdHvASUCZ9K_FfufWL5w9nm_tRQIn1Z8jIYS6OhznoyUXbOnql_AZIedG8
CitedBy_id crossref_primary_10_1007_s41066_022_00316_3
crossref_primary_10_1016_j_fss_2024_109039
crossref_primary_10_1016_j_eswa_2023_121979
crossref_primary_10_3390_electronics12153269
crossref_primary_10_1007_s10479_024_05926_5
crossref_primary_10_1016_j_asoc_2023_111205
crossref_primary_10_1016_j_fss_2024_108998
crossref_primary_10_1007_s10462_025_11205_x
crossref_primary_10_3233_JIFS_222241
crossref_primary_10_1016_j_fss_2024_108859
crossref_primary_10_1007_s00500_025_10559_2
crossref_primary_10_1111_acfi_13282
Cites_doi 10.1016/j.cie.2007.11.012
10.1109/TSMCB.2007.912745
10.1109/21.87068
10.1016/S0165-0114(02)00267-1
10.1016/S0165-0114(01)00007-0
ContentType Journal Article
Copyright 2022
Copyright_xml – notice: 2022
DBID 6I.
AAFTH
AAYXX
CITATION
DOI 10.1016/j.fss.2022.01.003
DatabaseName ScienceDirect Open Access Titles
Elsevier:ScienceDirect:Open Access
CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1872-6801
EndPage 156
ExternalDocumentID 10_1016_j_fss_2022_01_003
S0165011422000045
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
1B1
1OL
1RT
1~.
1~5
29H
4.4
457
4G.
5VS
6I.
7-5
71M
8P~
9JN
9JO
AAAKF
AAAKG
AABNK
AACTN
AAEDT
AAEDW
AAFTH
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AARIN
AAXUO
AAYFN
ABAOU
ABBOA
ABEFU
ABFNM
ABJNI
ABMAC
ABUCO
ABXDB
ABYKQ
ACAZW
ACDAQ
ACGFS
ACNCT
ACNNM
ACRLP
ACZNC
ADBBV
ADEZE
ADGUI
ADJOM
ADMUD
ADTZH
AEBSH
AECPX
AEKER
AENEX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHJVU
AHZHX
AI.
AIALX
AIEXJ
AIGVJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
AOUOD
APLSM
ARUGR
ASPBG
AVWKF
AXJTR
AZFZN
BJAXD
BKOJK
BLXMC
CS3
DU5
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
F0J
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-Q
GBLVA
GBOLZ
HAMUX
HLZ
HVGLF
HZ~
IHE
J1W
JJJVA
K-O
KOM
LG9
LY1
M41
MHUIS
MO0
N9A
O-L
O9-
OAUVE
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
ROL
RPZ
SBC
SDF
SDG
SDP
SDS
SES
SEW
SPC
SPCBC
SSB
SSD
SST
SSV
SSW
SSZ
T5K
TN5
VH1
WH7
WUQ
XPP
ZMT
~02
~G-
9DU
AATTM
AAXKI
AAYWO
AAYXX
ABWVN
ACLOT
ACRPL
ACVFH
ADCNI
ADNMO
AEIPS
AEUPX
AFJKZ
AFPUW
AGQPQ
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
CITATION
EFKBS
~HD
ID FETCH-LOGICAL-c340t-ed170b2766bbd538b42c7192bea302ba868a85cee1dc7ca13ba4b466c0c9f15a3
ISICitedReferencesCount 13
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000862759400010&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0165-0114
IngestDate Sat Nov 29 07:25:17 EST 2025
Tue Nov 18 21:09:56 EST 2025
Fri Feb 23 02:40:55 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Keywords Maximal entropy OWA operator weights
Implicit function theorem
Stability
Language English
License This is an open access article under the CC BY-NC-ND license.
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c340t-ed170b2766bbd538b42c7192bea302ba868a85cee1dc7ca13ba4b466c0c9f15a3
ORCID 0000-0002-0915-9718
OpenAccessLink https://dx.doi.org/10.1016/j.fss.2022.01.003
PageCount 12
ParticipantIDs crossref_citationtrail_10_1016_j_fss_2022_01_003
crossref_primary_10_1016_j_fss_2022_01_003
elsevier_sciencedirect_doi_10_1016_j_fss_2022_01_003
PublicationCentury 2000
PublicationDate 2022-11-05
PublicationDateYYYYMMDD 2022-11-05
PublicationDate_xml – month: 11
  year: 2022
  text: 2022-11-05
  day: 05
PublicationDecade 2020
PublicationTitle Fuzzy sets and systems
PublicationYear 2022
Publisher Elsevier B.V
Publisher_xml – name: Elsevier B.V
References Zarghami, Szidarovszky (br0040) 2008; 54
Hong, Kim (br0090) 2006; 17
Torra (br0010) 2001
Yager (br0050) 1988; 18
Carbonell, Mas, Mayor (br0070) 1997
Fullér, Majlender (br0110) 2003; 136
O'Hagan (br0060) 1988
Fullér, Majlender (br0080) 2001; 124
Zarghami, Szidarovszky, Ardakanian (br0030) 2008; 38
Zarghaami, Ardakanian, Szidarovszky (br0020) 2007
Sohrab (br0100) 2014
Zarghami (10.1016/j.fss.2022.01.003_br0040) 2008; 54
Fullér (10.1016/j.fss.2022.01.003_br0080) 2001; 124
Yager (10.1016/j.fss.2022.01.003_br0050) 1988; 18
Zarghaami (10.1016/j.fss.2022.01.003_br0020) 2007
Torra (10.1016/j.fss.2022.01.003_br0010) 2001
O'Hagan (10.1016/j.fss.2022.01.003_br0060) 1988
Carbonell (10.1016/j.fss.2022.01.003_br0070) 1997
Fullér (10.1016/j.fss.2022.01.003_br0110) 2003; 136
Zarghami (10.1016/j.fss.2022.01.003_br0030) 2008; 38
Hong (10.1016/j.fss.2022.01.003_br0090) 2006; 17
Sohrab (10.1016/j.fss.2022.01.003_br0100) 2014
References_xml – start-page: 134
  year: 2001
  end-page: 137
  ident: br0010
  article-title: Sensitivity analysis for WOWA, OWA and WM operators
  publication-title: ISIE 2001. 2001 IEEE International Symposium on Industrial Electronics Proceedings, Vol. 1
– volume: 54
  start-page: 1006
  year: 2008
  end-page: 1018
  ident: br0040
  article-title: Fuzzy quantifiers in sensitivity analysis of OWA operator
  publication-title: Comput. Ind. Eng.
– volume: 136
  start-page: 203
  year: 2003
  end-page: 215
  ident: br0110
  article-title: On obtaining minimal variability OWA operator weights
  publication-title: Fuzzy Sets Syst.
– start-page: 1695
  year: 1997
  end-page: 1700
  ident: br0070
  article-title: On a class of monotonic extended OWA operators
  publication-title: Proceedings of 6th International Fuzzy Systems Conference, Vol. 3
– start-page: 280
  year: 2007
  end-page: 287
  ident: br0020
  article-title: Obtaining robust decisions under uncertainty by sensitivity analysis on OWA operator
  publication-title: 2007 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making
– start-page: 681
  year: 1988
  end-page: 689
  ident: br0060
  article-title: Aggregating template or rule antecedents in real-time expert systems with fuzzy set logic
  publication-title: Twenty-Second Asilomar Conference on Signals, Systems and Computers, Vol. 2
– volume: 38
  start-page: 547
  year: 2008
  end-page: 552
  ident: br0030
  article-title: Sensitivity analysis of the OWA operator
  publication-title: IEEE Trans. Syst. Man Cybern., Part B, Cybern.
– volume: 124
  start-page: 53
  year: 2001
  end-page: 57
  ident: br0080
  article-title: An analytic approach for obtaining maximal entropy OWA operator weights
  publication-title: Fuzzy Sets Syst.
– volume: 17
  start-page: 537
  year: 2006
  end-page: 541
  ident: br0090
  article-title: A note on maximal entropy OWA operator weights
  publication-title: J. Korean Data Inf. Sci. Soc.
– year: 2014
  ident: br0100
  article-title: Basic Real Analysis
– volume: 18
  start-page: 183
  year: 1988
  end-page: 190
  ident: br0050
  article-title: On ordered weighted averaging aggregation operators in multicriteria decisionmaking
  publication-title: IEEE Trans. Syst. Man Cybern.
– start-page: 280
  year: 2007
  ident: 10.1016/j.fss.2022.01.003_br0020
  article-title: Obtaining robust decisions under uncertainty by sensitivity analysis on OWA operator
– volume: 54
  start-page: 1006
  issue: 4
  year: 2008
  ident: 10.1016/j.fss.2022.01.003_br0040
  article-title: Fuzzy quantifiers in sensitivity analysis of OWA operator
  publication-title: Comput. Ind. Eng.
  doi: 10.1016/j.cie.2007.11.012
– start-page: 134
  year: 2001
  ident: 10.1016/j.fss.2022.01.003_br0010
  article-title: Sensitivity analysis for WOWA, OWA and WM operators
– volume: 38
  start-page: 547
  issue: 2
  year: 2008
  ident: 10.1016/j.fss.2022.01.003_br0030
  article-title: Sensitivity analysis of the OWA operator
  publication-title: IEEE Trans. Syst. Man Cybern., Part B, Cybern.
  doi: 10.1109/TSMCB.2007.912745
– year: 2014
  ident: 10.1016/j.fss.2022.01.003_br0100
– volume: 18
  start-page: 183
  issue: 1
  year: 1988
  ident: 10.1016/j.fss.2022.01.003_br0050
  article-title: On ordered weighted averaging aggregation operators in multicriteria decisionmaking
  publication-title: IEEE Trans. Syst. Man Cybern.
  doi: 10.1109/21.87068
– volume: 136
  start-page: 203
  issue: 2
  year: 2003
  ident: 10.1016/j.fss.2022.01.003_br0110
  article-title: On obtaining minimal variability OWA operator weights
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/S0165-0114(02)00267-1
– start-page: 681
  year: 1988
  ident: 10.1016/j.fss.2022.01.003_br0060
  article-title: Aggregating template or rule antecedents in real-time expert systems with fuzzy set logic
– start-page: 1695
  year: 1997
  ident: 10.1016/j.fss.2022.01.003_br0070
  article-title: On a class of monotonic extended OWA operators
– volume: 17
  start-page: 537
  issue: 2
  year: 2006
  ident: 10.1016/j.fss.2022.01.003_br0090
  article-title: A note on maximal entropy OWA operator weights
  publication-title: J. Korean Data Inf. Sci. Soc.
– volume: 124
  start-page: 53
  issue: 1
  year: 2001
  ident: 10.1016/j.fss.2022.01.003_br0080
  article-title: An analytic approach for obtaining maximal entropy OWA operator weights
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/S0165-0114(01)00007-0
SSID ssj0001160
Score 2.4684522
Snippet The maximal entropy OWA operator (MEOWA) weights can be obtained by solving a nonlinear programming problem with a linear constraint for the level of orness....
SourceID crossref
elsevier
SourceType Enrichment Source
Index Database
Publisher
StartPage 145
SubjectTerms Implicit function theorem
Maximal entropy OWA operator weights
Stability
Title On stability of maximal entropy OWA operator weights
URI https://dx.doi.org/10.1016/j.fss.2022.01.003
Volume 448
WOSCitedRecordID wos000862759400010&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVESC
  databaseName: Elsevier SD Freedom Collection Journals 2021
  customDbUrl:
  eissn: 1872-6801
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0001160
  issn: 0165-0114
  databaseCode: AIEXJ
  dateStart: 19950113
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1bb9MwGLWg4wEeJq5iDFAeeKJKZceJ7TxWaBNDsCIxoG-Rb5E2bWm1ZKPbr-fzJWnFAAESL2llxWnr89U-_i7HCL2yNSOGMZxyWF_TvHb_OWxoanNhSCa1Ln244Mt7fngo5vPyYzz4r_XHCfCmEatVufyvUEMbgO1KZ_8C7uGh0ADvAXS4Auxw_SPgZ43zD_ic1xA9l6vjMwDCuXEXy6vx7Ot0vFhaH14ff_Oe0XaTou5fXF9fjVvbBfXmdkPS3M9UnuP6qaXtLn2cnYABwasgk8EaYGMbQvAb6dtr1nkatH4PzmLmbfQ6wIbVeVKLtSvsRjlM8E4ylwkYqkInNsyogmcpE8FjcWO-Dq6Dk0ndOun0LPMSqpiuF6chZfCTe3io_PX7muI22sp4UYoR2poe7M3fDesvIb42fPgyfSzbZ_X98EE_ZyMbDOPoPtqOW4NkGiB9gG7Z5iG692HQ1W0foXzWJAO4yaJOIrhJBDcBcJMe3CSC-xh93t87evM2jedepJrmuEutIRyrjDOmlIEFSeWZ5sDElZUUZ0oKJqQogN0Qo7mWhCqZq5wxjXVZk0LSJ2jULBr7FCWZVNDEa8NonVtaKiNr6iQb4WajqNxBuP_9lY6i8O5sktOqz_47qWDIKjdkFSZOSXYHvR66LIMiyu9uzvtBrSKlC1StAgv4dbdn_9ZtF91d2-pzNOrOL-wLdEdfdsft-ctoJ98BIKVq7A
linkProvider Elsevier
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+stability+of+maximal+entropy+OWA+operator+weights&rft.jtitle=Fuzzy+sets+and+systems&rft.au=Harmati%2C+Istv%C3%A1n+%C3%81.&rft.au=Full%C3%A9r%2C+Robert&rft.au=Felde%2C+Imre&rft.date=2022-11-05&rft.pub=Elsevier+B.V&rft.issn=0165-0114&rft.eissn=1872-6801&rft_id=info:doi/10.1016%2Fj.fss.2022.01.003&rft.externalDocID=S0165011422000045
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0165-0114&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0165-0114&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0165-0114&client=summon