Solving fuzzy relation equations with a linear objective function

An optimization model with a linear objective function subject to a system of fuzzy relation equations is presented. Due to the non-convexity of its feasible domain defined by fuzzy relation equations, designing an efficient solution procedure for solving such problems is not a trivial job. In this...

Full description

Saved in:

Bibliographic Details
Published in:	Fuzzy sets and systems Vol. 103; no. 1; pp. 107 - 113
Main Authors:	Fang, Shu-Cherng, Li, Guangzhi
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01.04.1999 Elsevier
Subjects:	Applied sciences Artificial intelligence Branch-and-bound method Computer science; control theory; systems Exact sciences and technology Fuzzy relation equations Integer programming Mathematical programming Operational research and scientific management Operational research. Management science Problem solving, game playing Fuzzy relation equations Integer programming Branch-and-bound method Branch and bound method Optimization method Fuzzy relation Convexity Objective function Algorithm
ISSN:	0165-0114, 1872-6801
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	An optimization model with a linear objective function subject to a system of fuzzy relation equations is presented. Due to the non-convexity of its feasible domain defined by fuzzy relation equations, designing an efficient solution procedure for solving such problems is not a trivial job. In this paper, we first characterize the feasible domain and then convert the problem to an equivalent problem involving 0–1 integer programming with a branch-and-bound solution technique. After presenting our solution procedure, a concrete example is included for illustration purpose.
AbstractList	An optimization model with a linear objective function subject to a system of fuzzy relation equations is presented. Due to the non-convexity of its feasible domain defined by fuzzy relation equations, designing an efficient solution procedure for solving such problems is not a trivial job. In this paper, we first characterize the feasible domain and then convert the problem to an equivalent problem involving 0–1 integer programming with a branch-and-bound solution technique. After presenting our solution procedure, a concrete example is included for illustration purpose.
Author	Fang, Shu-Cherng Li, Guangzhi
Author_xml	– sequence: 1 givenname: Shu-Cherng surname: Fang fullname: Fang, Shu-Cherng – sequence: 2 givenname: Guangzhi surname: Li fullname: Li, Guangzhi
BackLink	http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=1786968$$DView record in Pascal Francis
BookMark	eNqFkD1PAjEAhhuDiYD-BJMbHHQ4be96_YiDIcSvhMQBBram1w8tOXvYHhD49R6HYXBhaTs8z5v0GYCer70B4BrBewQReZi2R5FChPAtp3cQIobT-RnoI0azlDCIeqB_RC7AIMYFbClEYB-MpnW1dv4zsavdbpsEU8nG1T4xP6vuEZONa74SmVTOGxmSulwY1bi1aQWv9sQlOLeyiubq7x6C2cvzbPyWTj5e38ejSarynDRphq0ssNVZgWyWS0Up1wxllCuKDC4NRZqXnFidM4U1yTjOuSIl1jpXTJf5ENwcZpcyKlnZIL1yUSyD-5ZhKxBlhBPWYo8HTIU6xmCsUK7pftIE6SqBoNg3E10zsQ8iOBVdMzFv7eKffdw_4T0dPNMGWDsTRFTOeGW0C20uoWt3YuEXVW6G9w
CODEN	FSSYD8
CitedBy_id	crossref_primary_10_1109_TFUZZ_2012_2232932 crossref_primary_10_1007_s40314_024_02945_7 crossref_primary_10_1016_j_fss_2007_07_017 crossref_primary_10_1016_j_fss_2024_108946 crossref_primary_10_1016_j_fss_2024_108944 crossref_primary_10_1016_j_jfranklin_2019_02_007 crossref_primary_10_1155_2019_8179763 crossref_primary_10_1016_j_ins_2008_04_004 crossref_primary_10_1109_ACCESS_2019_2912217 crossref_primary_10_1016_j_asoc_2009_02_004 crossref_primary_10_1007_s12597_011_0039_0 crossref_primary_10_1007_s10700_019_09305_9 crossref_primary_10_1007_s10898_017_0499_8 crossref_primary_10_1016_j_fss_2004_09_010 crossref_primary_10_1016_j_asoc_2009_12_014 crossref_primary_10_26599_FIE_2024_9270047 crossref_primary_10_1016_j_camwa_2011_01_023 crossref_primary_10_1155_2018_1610349 crossref_primary_10_1109_TFUZZ_2002_800657 crossref_primary_10_1007_s11518_014_5261_x crossref_primary_10_1016_j_asoc_2018_04_029 crossref_primary_10_1016_j_ins_2007_10_010 crossref_primary_10_1007_s13042_016_0527_x crossref_primary_10_1016_j_fss_2025_109363 crossref_primary_10_1007_s11424_009_9146_x crossref_primary_10_1016_j_fss_2009_03_007 crossref_primary_10_1016_j_fss_2017_08_001 crossref_primary_10_1109_TFUZZ_2022_3201982 crossref_primary_10_1155_2019_4960638 crossref_primary_10_1016_j_amc_2005_12_006 crossref_primary_10_1016_j_ins_2023_119497 crossref_primary_10_1088_1742_6596_2158_1_012032 crossref_primary_10_1109_ACCESS_2022_3197611 crossref_primary_10_1109_TFUZZ_2020_2991304 crossref_primary_10_1016_j_cie_2008_08_015 crossref_primary_10_1080_10170660809509095 crossref_primary_10_1023_B_FODM_0000036862_45420_ea crossref_primary_10_1016_j_amc_2007_07_061 crossref_primary_10_1080_10170669_2010_514124 crossref_primary_10_3233_IFS_151546 crossref_primary_10_1016_j_ins_2014_02_110 crossref_primary_10_1109_91_784204 crossref_primary_10_1016_S0165_0114_01_00052_5 crossref_primary_10_1016_j_proeng_2012_06_400 crossref_primary_10_1016_j_ins_2016_04_041 crossref_primary_10_1109_ACCESS_2021_3092745 crossref_primary_10_1016_j_egyr_2022_01_183 crossref_primary_10_1023_A_1022800330844 crossref_primary_10_1007_s10700_022_09390_3 crossref_primary_10_1109_ACCESS_2020_2984095 crossref_primary_10_1016_j_ins_2011_06_009 crossref_primary_10_1016_j_fss_2025_109344 crossref_primary_10_1016_j_cie_2020_106537 crossref_primary_10_1016_j_mcm_2010_07_018 crossref_primary_10_1016_j_ins_2011_09_030 crossref_primary_10_1109_ACCESS_2018_2878748 crossref_primary_10_1007_s40995_016_0108_6 crossref_primary_10_1016_j_fss_2008_04_007 crossref_primary_10_3390_math9090937 crossref_primary_10_1016_j_fss_2008_02_017 crossref_primary_10_1016_j_cam_2009_09_042 crossref_primary_10_1186_s13660_016_1056_6 crossref_primary_10_1016_j_mcm_2008_10_018 crossref_primary_10_1109_TFUZZ_2021_3078529 crossref_primary_10_1109_TFUZZ_2009_2031561 crossref_primary_10_1007_BF03398834 crossref_primary_10_1016_j_ins_2007_07_022 crossref_primary_10_1109_TFUZZ_2016_2598367 crossref_primary_10_1016_j_fss_2021_07_014 crossref_primary_10_1016_S0165_0114_98_00417_5 crossref_primary_10_1007_s00500_018_3236_4 crossref_primary_10_1016_j_fiae_2017_12_002 crossref_primary_10_1016_j_cie_2018_03_038 crossref_primary_10_1109_TFUZZ_2017_2771406 crossref_primary_10_1007_s10700_011_9099_0 crossref_primary_10_1007_s40815_018_0530_3 crossref_primary_10_1016_j_amc_2005_11_069 crossref_primary_10_1016_j_ins_2020_03_047 crossref_primary_10_1016_j_ins_2007_02_037 crossref_primary_10_1109_TFUZZ_2023_3305641 crossref_primary_10_1109_TFUZZ_2017_2648864 crossref_primary_10_1016_j_amc_2005_04_021 crossref_primary_10_1007_s10898_017_0602_1 crossref_primary_10_1016_j_ins_2023_119696 crossref_primary_10_1016_j_mcm_2007_04_010 crossref_primary_10_1016_j_ins_2015_07_058 crossref_primary_10_1007_s10700_005_4914_0 crossref_primary_10_1016_j_fss_2025_109561 crossref_primary_10_3233_JIFS_151820 crossref_primary_10_1016_j_fss_2014_04_007 crossref_primary_10_1016_j_fss_2012_04_009 crossref_primary_10_1142_S0217595908001717 crossref_primary_10_1109_ACCESS_2024_3467191 crossref_primary_10_1007_s00500_014_1464_9 crossref_primary_10_1016_j_mcm_2010_01_006 crossref_primary_10_1016_j_fss_2022_03_017 crossref_primary_10_1016_j_fss_2024_109011 crossref_primary_10_1007_s10700_007_9017_7 crossref_primary_10_1109_TFUZZ_2016_2593496 crossref_primary_10_1109_ACCESS_2018_2834231 crossref_primary_10_1109_TFUZZ_2019_2920806 crossref_primary_10_1016_j_eswa_2022_116663 crossref_primary_10_1016_j_ins_2019_06_058 crossref_primary_10_1007_s10700_012_9129_6 crossref_primary_10_1007_s10700_019_09306_8 crossref_primary_10_1016_j_fss_2019_08_012 crossref_primary_10_1007_s10700_021_09368_7 crossref_primary_10_1016_j_phpro_2012_05_276 crossref_primary_10_1016_j_amc_2007_02_001 crossref_primary_10_1016_j_ins_2011_04_042 crossref_primary_10_1016_j_fss_2021_08_007 crossref_primary_10_1007_s10700_008_9029_y crossref_primary_10_1007_s10700_009_9054_5 crossref_primary_10_1016_j_cie_2007_11_011 crossref_primary_10_1016_j_ins_2017_07_032 crossref_primary_10_1016_j_asoc_2012_03_002 crossref_primary_10_1016_j_fss_2021_12_005 crossref_primary_10_1109_TFUZZ_2025_3568468 crossref_primary_10_1023_A_1022848114005 crossref_primary_10_1109_TFUZZ_2020_3021726 crossref_primary_10_1016_j_amc_2005_12_027 crossref_primary_10_1023_A_1020955112523 crossref_primary_10_1016_j_eswa_2009_03_037 crossref_primary_10_1016_j_ins_2022_01_023 crossref_primary_10_1016_j_cie_2011_09_012 crossref_primary_10_1016_j_cie_2014_03_024 crossref_primary_10_1007_s12190_025_02559_0 crossref_primary_10_1007_s10700_011_9115_4 crossref_primary_10_1016_j_fss_2017_04_002
Cites_doi	10.1016/0165-0114(93)90292-P 10.1016/0165-0114(81)90059-2 10.1016/0165-0114(82)90043-4 10.1016/0165-0114(84)90026-5 10.1016/0165-0114(88)90008-5 10.1016/S0019-9958(76)90446-0 10.1109/TSMC.1986.4308946
ContentType	Journal Article
Copyright	1999 1999 INIST-CNRS
Copyright_xml	– notice: 1999 – notice: 1999 INIST-CNRS
DBID	AAYXX CITATION IQODW
DOI	10.1016/S0165-0114(97)00184-X
DatabaseName	CrossRef Pascal-Francis
DatabaseTitle	CrossRef
DatabaseTitleList
DeliveryMethod	fulltext_linktorsrc
Discipline	Mathematics Applied Sciences
EISSN	1872-6801
EndPage	113
ExternalDocumentID	1786968 10_1016_S0165_0114_97_00184_X S016501149700184X
GroupedDBID	--K --M -~X .DC .~1 0R~ 1B1 1OL 1RT 1~. 1~5 29H 4.4 457 4G. 5VS 7-5 71M 8P~ 9JN 9JO AAAKF AAAKG AABNK AACTN AAEDT AAEDW 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 AFXIZ AGCQF AGRNS BNPGV IQODW SSH
ID	FETCH-LOGICAL-c336t-24fa54fd251f23ac779d81279c71e4be71d9b96fd38c4d629439c6b4dd3c8db3
ISICitedReferencesCount	185
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000078726700008&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	Mon Jul 21 09:11:02 EDT 2025 Sat Nov 29 01:59:54 EST 2025 Tue Nov 18 22:32:53 EST 2025 Fri Feb 23 02:27:24 EST 2024
IsPeerReviewed	true
IsScholarly	true
Issue	1
Keywords	Fuzzy relation equations Integer programming Branch-and-bound method Branch and bound method Optimization method Fuzzy relation Convexity Objective function Algorithm
Language	English
License	https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0
LinkModel	OpenURL
MergedId	FETCHMERGED-LOGICAL-c336t-24fa54fd251f23ac779d81279c71e4be71d9b96fd38c4d629439c6b4dd3c8db3
PageCount	7
ParticipantIDs	pascalfrancis_primary_1786968 crossref_citationtrail_10_1016_S0165_0114_97_00184_X crossref_primary_10_1016_S0165_0114_97_00184_X elsevier_sciencedirect_doi_10_1016_S0165_0114_97_00184_X
PublicationCentury	1900
PublicationDate	1999-04-01
PublicationDateYYYYMMDD	1999-04-01
PublicationDate_xml	– month: 04 year: 1999 text: 1999-04-01 day: 01
PublicationDecade	1990
PublicationPlace	Amsterdam
PublicationPlace_xml	– name: Amsterdam
PublicationTitle	Fuzzy sets and systems
PublicationYear	1999
Publisher	Elsevier B.V Elsevier
Publisher_xml	– name: Elsevier B.V – name: Elsevier
References	Wang (BIB11) 1988 Adlassnig (BIB2) 1986; 16 Di Nola (BIB4) 1985; 107 Wang, Sessa, Di Nola, Pedrycz (BIB12) 1984; 18 Winston (BIB13) 1995 Adamopoulos, Pappis (BIB1) 1993; 60 Czogala, Drewniak, Pedrycz (BIB3) 1982; 7 Guo, Wang, Di Nola, Sessa (BIB6) 1988; 26 Zimmermann (BIB14) 1991 Higashi, Klir (BIB7) 1984; 13 Fang, Puthenpura (BIB5) 1993 Sanchez (BIB10) 1976; 30 Li, Fang (BIB8) May 1996 Prevot (BIB9) 1985; 5 Adamopoulos (10.1016/S0165-0114(97)00184-X_BIB1) 1993; 60 Li (10.1016/S0165-0114(97)00184-X_BIB8) 1996 Winston (10.1016/S0165-0114(97)00184-X_BIB13) 1995 Zimmermann (10.1016/S0165-0114(97)00184-X_BIB14) 1991 Di Nola (10.1016/S0165-0114(97)00184-X_BIB4) 1985; 107 Higashi (10.1016/S0165-0114(97)00184-X_BIB7) 1984; 13 Czogala (10.1016/S0165-0114(97)00184-X_BIB3) 1982; 7 Adlassnig (10.1016/S0165-0114(97)00184-X_BIB2) 1986; 16 Sanchez (10.1016/S0165-0114(97)00184-X_BIB10) 1976; 30 Guo (10.1016/S0165-0114(97)00184-X_BIB6) 1988; 26 Wang (10.1016/S0165-0114(97)00184-X_BIB12) 1984; 18 Wang (10.1016/S0165-0114(97)00184-X_BIB11) 1988 Fang (10.1016/S0165-0114(97)00184-X_BIB5) 1993 Prevot (10.1016/S0165-0114(97)00184-X_BIB9) 1985; 5
References_xml	– volume: 16 start-page: 260 year: 1986 end-page: 265 ident: BIB2 article-title: Fuzzy set theory in medical diagnosis publication-title: IEEE Trans. Systems Man Cybernet. – year: 1993 ident: BIB5 article-title: Linear Optimization and Extensions: Theory and Algorithm – volume: 60 start-page: 83 year: 1993 end-page: 88 ident: BIB1 article-title: Some results on the resolution of fuzzy relation equations publication-title: Fuzzy Sets and Systems – volume: 26 start-page: 93 year: 1988 end-page: 104 ident: BIB6 article-title: Further contributions to the study of finite fuzzy relation equations publication-title: Fuzzy Sets and Systems – start-page: 242 year: 1988 end-page: 249 ident: BIB11 article-title: An algorithm for solving iterated composite relation equations publication-title: Proc. NAFIPS – volume: 13 start-page: 65 year: 1984 end-page: 82 ident: BIB7 article-title: Resolution of finite fuzzy relation equations publication-title: Fuzzy Sets and Systems – year: 1991 ident: BIB14 article-title: Fuzzy Set Theory and Its Applications – volume: 18 start-page: 67 year: 1984 end-page: 74 ident: BIB12 article-title: How many lower solutions does a fuzzy relation equation have? publication-title: Bull. pour. Sous. Ens. Flous. Appl. (BUSEFAL) – year: 1995 ident: BIB13 article-title: Introduction to Mathematical Programming: Application and Algorithms – volume: 107 start-page: 148 year: 1985 end-page: 155 ident: BIB4 article-title: Relational equations in totally ordered lattices and their complete resolution publication-title: J. Math. Appl. – volume: 7 start-page: 89 year: 1982 end-page: 101 ident: BIB3 article-title: Fuzzy relation equations on a finite set publication-title: Fuzzy Sets and Systems – volume: 30 start-page: 38 year: 1976 end-page: 48 ident: BIB10 article-title: Resolution of composite fuzzy relation equations publication-title: Inform. and Control – volume: 5 start-page: 319 year: 1985 end-page: 322 ident: BIB9 article-title: Algorithm for the solution of fuzzy relations equations publication-title: Fuzzy Sets and Systems – year: May 1996 ident: BIB8 article-title: On the Resolution of Finite Fuzzy Relation Equations publication-title: OR Report No. 322 – volume: 107 start-page: 148 year: 1985 ident: 10.1016/S0165-0114(97)00184-X_BIB4 article-title: Relational equations in totally ordered lattices and their complete resolution publication-title: J. Math. Appl. – year: 1993 ident: 10.1016/S0165-0114(97)00184-X_BIB5 – year: 1991 ident: 10.1016/S0165-0114(97)00184-X_BIB14 – volume: 60 start-page: 83 year: 1993 ident: 10.1016/S0165-0114(97)00184-X_BIB1 article-title: Some results on the resolution of fuzzy relation equations publication-title: Fuzzy Sets and Systems doi: 10.1016/0165-0114(93)90292-P – volume: 5 start-page: 319 year: 1985 ident: 10.1016/S0165-0114(97)00184-X_BIB9 article-title: Algorithm for the solution of fuzzy relations equations publication-title: Fuzzy Sets and Systems doi: 10.1016/0165-0114(81)90059-2 – volume: 7 start-page: 89 year: 1982 ident: 10.1016/S0165-0114(97)00184-X_BIB3 article-title: Fuzzy relation equations on a finite set publication-title: Fuzzy Sets and Systems doi: 10.1016/0165-0114(82)90043-4 – volume: 13 start-page: 65 year: 1984 ident: 10.1016/S0165-0114(97)00184-X_BIB7 article-title: Resolution of finite fuzzy relation equations publication-title: Fuzzy Sets and Systems doi: 10.1016/0165-0114(84)90026-5 – year: 1995 ident: 10.1016/S0165-0114(97)00184-X_BIB13 – volume: 26 start-page: 93 year: 1988 ident: 10.1016/S0165-0114(97)00184-X_BIB6 article-title: Further contributions to the study of finite fuzzy relation equations publication-title: Fuzzy Sets and Systems doi: 10.1016/0165-0114(88)90008-5 – start-page: 242 year: 1988 ident: 10.1016/S0165-0114(97)00184-X_BIB11 article-title: An algorithm for solving iterated composite relation equations – volume: 30 start-page: 38 year: 1976 ident: 10.1016/S0165-0114(97)00184-X_BIB10 article-title: Resolution of composite fuzzy relation equations publication-title: Inform. and Control doi: 10.1016/S0019-9958(76)90446-0 – volume: 16 start-page: 260 year: 1986 ident: 10.1016/S0165-0114(97)00184-X_BIB2 article-title: Fuzzy set theory in medical diagnosis publication-title: IEEE Trans. Systems Man Cybernet. doi: 10.1109/TSMC.1986.4308946 – year: 1996 ident: 10.1016/S0165-0114(97)00184-X_BIB8 article-title: On the Resolution of Finite Fuzzy Relation Equations – volume: 18 start-page: 67 year: 1984 ident: 10.1016/S0165-0114(97)00184-X_BIB12 article-title: How many lower solutions does a fuzzy relation equation have? publication-title: Bull. pour. Sous. Ens. Flous. Appl. (BUSEFAL)
SSID	ssj0001160
Score	2.0432
Snippet	An optimization model with a linear objective function subject to a system of fuzzy relation equations is presented. Due to the non-convexity of its feasible...
SourceID	pascalfrancis crossref elsevier
SourceType	Index Database Enrichment Source Publisher
StartPage	107
SubjectTerms	Applied sciences Artificial intelligence Branch-and-bound method Computer science; control theory; systems Exact sciences and technology Fuzzy relation equations Integer programming Mathematical programming Operational research and scientific management Operational research. Management science Problem solving, game playing
Title	Solving fuzzy relation equations with a linear objective function
URI	https://dx.doi.org/10.1016/S0165-0114(97)00184-X
Volume	103
WOSCitedRecordID	wos000078726700008&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/eLvHCXMwtV1Lb9QwELZgy4EKIZ5qgSIfOIBWgcbO2vGxqooAiQqpe8gt8iu0VZVdNruo7K9n_IizUEHpgUsURfLEyvfFMx7PA6FXuYQ9gGIqk0Ir2KBImSmiVKYFkzo3jPJS-2YT_Pi4rCrxJfZs7Xw7Ad625eWlmP9XqOEZgO1SZ28AdxIKD-AeQIcrwA7XfwL-ZHbhnQTNar3-EXNVAGL7bRWj3kI629jZl3IxnqnzsOaNnYpLMPWdO72Qzi5DKeduo765r-AYnc2nq-wQwI9a0MX3-CAB4F_7dX16NrgWQjmCFJESvY3MRfaFLM-0XO7TK7wIi1_sXxv1aB5yTK8s0cFbcJJkgyHtigEL1x6wyKpBL_Vn8b-pqxREuBGfxia1E1X7w3QQU1e30RbhE1GO0NbBx6PqU9LOee4zx9Prh6yud8OcXgv-Js7nT_bKvbns4C9qQvuTDZtk-gDdj5sJfBBI8BDdsu0jtP05VeLtHoPaDHTAng64pwNOdMCODljiQAec6IB7OjxB0_dH08MPWWybkWlK2TIjRSMnRWPAcm0IlZpzYcCM40Lz3BbK8twIJVhjaKkLw4gAm1QzVRhDdWkUfYpG7ay1OwiziSK20USTxhR0XwlCLFNUCrDxS2nILir6b1PrWFLedTa5qP-KzS56m4bNQ02V6waU_Yevo2EYDL4aSHXd0L1fgBpeyEtXF-rZTefyHN0dfpUXaLRcrOweuqO_L8-6xcvItp91FIpp
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=Solving+fuzzy+relation+equations+with+a+linear+objective+function&rft.jtitle=Fuzzy+sets+and+systems&rft.au=Fang%2C+Shu-Cherng&rft.au=Li%2C+Guangzhi&rft.date=1999-04-01&rft.issn=0165-0114&rft.volume=103&rft.issue=1&rft.spage=107&rft.epage=113&rft_id=info:doi/10.1016%2FS0165-0114%2897%2900184-X&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_S0165_0114_97_00184_X
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