Obtaining Efficient Solutions of Interval Multi-objective Linear Programming Problems
In this paper, we consider interval multi-objective linear programming (IMOLP) models which are used to deal with uncertainties of real-world problems. So far, a variety of approaches for obtaining efficient solutions (ESs) of these problems have been developed. In this paper, we propose a new and t...
Saved in:
| Published in: | International journal of fuzzy systems Vol. 22; no. 3; pp. 873 - 890 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.04.2020
Springer Nature B.V |
| Subjects: | |
| ISSN: | 1562-2479, 2199-3211 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | In this paper, we consider interval multi-objective linear programming (IMOLP) models which are used to deal with uncertainties of real-world problems. So far, a variety of approaches for obtaining efficient solutions (ESs) of these problems have been developed. In this paper, we propose a new and two generalized methods. In the new method, converting IMOLP into an interval linear programming (ILP) and then obtaining its optimal solutions (OSs), ESs of the IMOLP are determined. This method has several advantages: (i) This method is the only method which obtains a solution box for IMOLP models. (ii) The solving process is not time consuming. (iii) The number of ESs is higher than for other methods. (V) The method is applicable for large-scale problems. Also, we generalize the
ε
-constraint and lexicographic methods which are used for obtaining ESs of the multi-objective linear programming (MOLP) models which do not have any problems such as lengthy and time-consuming and are applicable for large-scale problems. Some examples were solved to show the efficiency of the proposed methods. Finally, by the proposed method, we solve the IMOLP model corresponding to the problem of the facilities and non-return funds in a bank. |
|---|---|
| AbstractList | In this paper, we consider interval multi-objective linear programming (IMOLP) models which are used to deal with uncertainties of real-world problems. So far, a variety of approaches for obtaining efficient solutions (ESs) of these problems have been developed. In this paper, we propose a new and two generalized methods. In the new method, converting IMOLP into an interval linear programming (ILP) and then obtaining its optimal solutions (OSs), ESs of the IMOLP are determined. This method has several advantages: (i) This method is the only method which obtains a solution box for IMOLP models. (ii) The solving process is not time consuming. (iii) The number of ESs is higher than for other methods. (V) The method is applicable for large-scale problems. Also, we generalize the ε-constraint and lexicographic methods which are used for obtaining ESs of the multi-objective linear programming (MOLP) models which do not have any problems such as lengthy and time-consuming and are applicable for large-scale problems. Some examples were solved to show the efficiency of the proposed methods. Finally, by the proposed method, we solve the IMOLP model corresponding to the problem of the facilities and non-return funds in a bank. In this paper, we consider interval multi-objective linear programming (IMOLP) models which are used to deal with uncertainties of real-world problems. So far, a variety of approaches for obtaining efficient solutions (ESs) of these problems have been developed. In this paper, we propose a new and two generalized methods. In the new method, converting IMOLP into an interval linear programming (ILP) and then obtaining its optimal solutions (OSs), ESs of the IMOLP are determined. This method has several advantages: (i) This method is the only method which obtains a solution box for IMOLP models. (ii) The solving process is not time consuming. (iii) The number of ESs is higher than for other methods. (V) The method is applicable for large-scale problems. Also, we generalize the ε -constraint and lexicographic methods which are used for obtaining ESs of the multi-objective linear programming (MOLP) models which do not have any problems such as lengthy and time-consuming and are applicable for large-scale problems. Some examples were solved to show the efficiency of the proposed methods. Finally, by the proposed method, we solve the IMOLP model corresponding to the problem of the facilities and non-return funds in a bank. |
| Author | Batamiz, Aida Allahdadi, Mehdi Hladík, Milan |
| Author_xml | – sequence: 1 givenname: Aida surname: Batamiz fullname: Batamiz, Aida organization: Mathematics Faculty, University of Sistan and Baluchestan – sequence: 2 givenname: Mehdi orcidid: 0000-0002-0574-0580 surname: Allahdadi fullname: Allahdadi, Mehdi email: m_allahdadi@math.usb.ac.ir organization: Mathematics Faculty, University of Sistan and Baluchestan – sequence: 3 givenname: Milan surname: Hladík fullname: Hladík, Milan organization: Department of Applied Mathematics, Charles University, Department of Econometrics, University of Economics |
| BookMark | eNp9kEtLAzEQgINUsNb-AU8LnqOTzWYfRylVC5UK2nNIsklJ2SY1SQv-e7euIHjoaQZmvnl812jkvNMI3RK4JwDVQyygJgxDDhigBsDsAo1z0jSY5oSM0JiwMsd5UTVXaBqjlUBJXlJW0jFar2QS1lm3yebGWGW1S9m77w7Jehczb7KFSzocRZe9HrpksZdbrZI96mxpnRYhewt-E8RudxrR57LTu3iDLo3oop7-xglaP80_Zi94uXpezB6XWNGySpjWUgoglEgjFZMETMGYqDUo3baibRQrW6lIqRWQ0piGKVPJggpGi75gSjpBd8PcffCfBx0T3_pDcP1Knjf09DHQuu_Khy4VfIxBG74PdifCFyfATwb5YJD3BvmPQc56qP4HKZvEyUoKwnbnUTqgsd_jNjr8XXWG-ga_JojX |
| CitedBy_id | crossref_primary_10_1007_s12597_021_00512_w crossref_primary_10_1007_s40815_022_01348_2 crossref_primary_10_1016_j_fss_2023_03_004 crossref_primary_10_1016_j_dajour_2021_100005 crossref_primary_10_3390_axioms14080569 crossref_primary_10_4018_IJDSST_286695 crossref_primary_10_3390_su14094943 crossref_primary_10_1080_16168658_2021_2002544 |
| Cites_doi | 10.1016/j.ejor.2018.08.020 10.1016/0377-2217(94)00093-R 10.1057/palgrave.jors.2600891 10.1002/zamm.200108115114 10.1137/S0895479896310743 10.1007/s11590-012-0530-4 10.2298/YJOR180117020A 10.1016/j.ejor.2005.12.042 10.1016/j.eswa.2017.10.020 10.1016/j.ins.2015.12.037 10.1007/s12351-018-0383-4 10.1007/s11590-011-0315-1 10.1057/palgrave.jors.2600322 10.1109/IFSA-NAFIPS.2013.6608401 10.1007/s10100-012-0252-9 10.1007/s40815-019-00655-5 10.1007/s10700-015-9226-4 10.1016/0377-2217(91)90169-V 10.1007/s40815-018-0541-0 10.1016/0377-2217(94)00092-Q 10.1080/00207729308949477 10.1016/0165-0114(95)00169-7 10.1108/03684921311323707 10.1007/s11590-012-0589-y 10.1016/0165-0114(94)90097-3 10.1007/s40815-019-00646-6 10.1016/j.ins.2019.02.012 10.1111/itor.12216 10.1016/j.ejor.2008.12.019 10.1016/j.laa.2013.02.012 10.1016/j.ins.2014.05.019 |
| ContentType | Journal Article |
| Copyright | Taiwan Fuzzy Systems Association 2020 Taiwan Fuzzy Systems Association 2020. |
| Copyright_xml | – notice: Taiwan Fuzzy Systems Association 2020 – notice: Taiwan Fuzzy Systems Association 2020. |
| DBID | AAYXX CITATION 8FE 8FG ABJCF AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ JQ2 K7- L6V M7S P5Z P62 PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PTHSS |
| DOI | 10.1007/s40815-020-00800-5 |
| DatabaseName | CrossRef ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central ProQuest Technology Collection ProQuest One ProQuest Central Korea ProQuest Central Student SciTech Collection (ProQuest) ProQuest Computer Science Collection Computer Science Database ProQuest Engineering Collection Engineering Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition Engineering Collection |
| DatabaseTitle | CrossRef Computer Science Database ProQuest Central Student Technology Collection ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection SciTech Premium Collection ProQuest One Community College ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Engineering Collection Advanced Technologies & Aerospace Collection Engineering Database ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Materials Science & Engineering Collection ProQuest One Academic ProQuest One Academic (New) |
| DatabaseTitleList | Computer Science Database |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 2199-3211 |
| EndPage | 890 |
| ExternalDocumentID | 10_1007_s40815_020_00800_5 |
| GroupedDBID | -EM .4S .DC 0R~ 188 203 2UF 4.4 406 5GY 9RA A8Z AACDK AAHNG AAIAL AAJBT AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO ABAKF ABDZT ABECU ABFTV ABJCF ABJNI ABJOX ABKCH ABMQK ABQBU ABTEG ABTKH ABTMW ABXPI ACAOD ACDTI ACGFS ACHSB ACIWK ACKNC ACMLO ACOKC ACPIV ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AESKC AEVLU AEXYK AFBBN AFKRA AFQWF AFZKB AGAYW AGDGC AGMZJ AGQEE AGQMX AGRTI AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AIAKS AIGIU AILAN AINHJ AITGF AJBLW AJRNO AJZVZ ALFXC ALMA_UNASSIGNED_HOLDINGS AMKLP AMXSW AMYLF AMYQR ARAPS ARCSS ATFKH AVXWI AXYYD BENPR BGLVJ BGNMA CCPQU CNMHZ CSCUP CVCKV DNIVK DPUIP EBLON EBS EDO EIOEI EJD ESBYG FERAY FIGPU FINBP FNLPD FRRFC FSGXE GGCAI GJIRD HCIFZ HG6 HRMNR I-F IKXTQ IWAJR IXD J-C J9A JBSCW JZLTJ K7- KOV LLZTM M4Y M7S NPVJJ NQJWS NU0 O9J OK1 P2P PT4 PTHSS RLLFE ROL RSV SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE TSG TUS TUXDW UG4 UOJIU UTJUX UZ4 UZXMN VFIZW Z88 ZMTXR AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADKFA AEZWR AFDZB AFFHD AFHIU AFOHR AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION ESTFP PHGZM PHGZT PQGLB 8FE 8FG AZQEC DWQXO GNUQQ JQ2 L6V P62 PKEHL PQEST PQQKQ PQUKI |
| ID | FETCH-LOGICAL-c367t-38bba0131bfbc5b10f455a8e0ceddad9c56dbc16ec016ff95cf7b43a5346dbf63 |
| IEDL.DBID | M7S |
| ISICitedReferencesCount | 9 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000516485700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1562-2479 |
| IngestDate | Wed Nov 05 08:08:06 EST 2025 Sat Nov 29 05:19:47 EST 2025 Tue Nov 18 21:14:27 EST 2025 Fri Feb 21 02:32:47 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Keywords | Interval multi-objective linear programming Uncertainty constraint Weighted sum Lexicographic Efficient solution |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c367t-38bba0131bfbc5b10f455a8e0ceddad9c56dbc16ec016ff95cf7b43a5346dbf63 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-0574-0580 |
| PQID | 2932479038 |
| PQPubID | 2043640 |
| PageCount | 18 |
| ParticipantIDs | proquest_journals_2932479038 crossref_primary_10_1007_s40815_020_00800_5 crossref_citationtrail_10_1007_s40815_020_00800_5 springer_journals_10_1007_s40815_020_00800_5 |
| PublicationCentury | 2000 |
| PublicationDate | 2020-04-01 |
| PublicationDateYYYYMMDD | 2020-04-01 |
| PublicationDate_xml | – month: 04 year: 2020 text: 2020-04-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Berlin/Heidelberg |
| PublicationPlace_xml | – name: Berlin/Heidelberg – name: Heidelberg |
| PublicationTitle | International journal of fuzzy systems |
| PublicationTitleAbbrev | Int. J. Fuzzy Syst |
| PublicationYear | 2020 |
| Publisher | Springer Berlin Heidelberg Springer Nature B.V |
| Publisher_xml | – name: Springer Berlin Heidelberg – name: Springer Nature B.V |
| References | EhrgottMMulticriteria Optimization2005BerlinSpringer1132.90001 HuangGHBaetzBWPatryGGGrey integer programming: an application to waste management planning under uncertaintyEur. J. Oper. Res.19958359462010.1016/0377-2217(94)00093-R HladíkMComplexity of necessary efficiency in interval linear programming and multiobjective linear programmingOptim. Lett.201265893899292562510.1007/s11590-011-0315-1 ZhouFHuangGHChenGGuoHEnhanced-interval linear programmingEur. J. Oper. Res.2009199323333253327810.1016/j.ejor.2008.12.019 Inuiguchi, M.: Necessary efficiency is partitioned into possible an necessary optimalities, IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), pp. 209–214. Edmonton, AB, Canada (2013) XuJFangHZengFChenYHGuoHRobust observer design and fuzzy optimization for uncertain dynamic systemsInt. J. Fuzzy Syst.201921515111523397769310.1007/s40815-019-00646-6 InuiguchiMSakawaMPossible and necessary efficiency in possibilistic multiobjective linear programming problems and possible efficiency testFuzzy Sets Syst.199678321341137938810.1016/0165-0114(95)00169-7 RohnJForty necessary and sufficient conditions for regularity of interval matrices: a surveyElectron J. Linear Algebra20091850051225386191189.65088 RivazSYaghoobiMAHladíkMUsing modified maximum regret for finding a necessarily efficient solution in an interval MOLP problemFuzzy Optim. Decis. Mak.2016153237253353596710.1007/s10700-015-9226-4 Dechao LiLLeungYWeizhiWMultiobjective interval linear programming in admissible-order vector spaceInf. Sci.201948611910.1016/j.ins.2019.02.012 HladíkMWeak and strong solvability of interval linear systems of equations and inequalitiesLinear Algebra Appl.20134381141564165303452210.1016/j.laa.2013.02.012 YangYZhaoJXiaJZhuangGZhangWMultiobjective optimization control for uncertain nonlinear stochastic system with state-delayInt. J. Fuzzy Syst.20182117283393359410.1007/s40815-018-0541-0 RexJRohnJSufficient conditions for regularity and singularity of interval matricesSIAM J. Matrix Anal. Appl.1998202437445165139610.1137/S0895479896310743 BotteaMSchöbelADominance for multi-objective robust optimization conceptsEur. J. Oper. Res.20192732430440390712010.1016/j.ejor.2018.08.020 DouradoADPLobatoFSAp CavaliniASteffenVFuzzy reliability-based optimization for engineering system designInt. J. Fuzzy Syst.20192151418142910.1007/s40815-019-00655-5 TongSCInterval number, fuzzy number linear programmingFuzzy Sets Syst.199466301306130028610.1016/0165-0114(94)90097-3 SteuerREMultiple criteria optimization: theory, computation and application1989New YorkWiley0742.90068 AllahdadiMDengCAn improved three-step method for solving the interval linear programming problemYugoslav J. Oper. Res.2018284435451388444910.2298/YJOR180117020A RivazSYaghoobiMAMinimax regret solution to linear programming problems with an interval objective functionEur. J. Oper. Res.2013213625649309285110.1007/s10100-012-0252-9 Hladík, M.: One necessarily efficient solutions in interval multi objective linear programming, Proceedings of the 25th Mini-EURO Conference Uncertainty and Robustness in Planning and Decision Making URPDM 2010, pp. 1–10. Coimbra, Portugal (2010) Razavi HajiaghaSHProgramming with interval multi-objective linear coefficients: a fuzzy set based approachKybernetes2013423482496308915510.1108/03684921311323707 AshayerinasabHANehiHMAllahdadiMSolving the interval linear programming problem: a new algorithm for a general caseExpert Syst. Appl.201893394910.1016/j.eswa.2017.10.020 AlefeldGHerzbergerJIntroduction to Interval Computations1983New YorkAcademic Press0552.65041 InuiguchiMSakawaMAn achievement rate approach to linear programming problems with an interval objective functionJ. Oper. Res. Soc.199748253310.1057/palgrave.jors.2600322 InuiguchiMSakawaMMinimax regret solution to multi objective linear programming problems with interval objective function coefficientsEur. J. Oper. Res.19958652653610.1016/0377-2217(94)00092-Q HuangGHMooreRDGrey linear programming, its solving approach, and its applicationInt. J. Syst. Sci.199324159172120212710.1080/00207729308949477 KoníčkováJSufficient condition of basis stability of an interval linear programming problemZAMM. Z. Angew. Math. Mech.200181367767810.1002/zamm.200108115114 AllahdadiMNehiHMThe optimal value bounds of the objective function in the interval linear programming problemChiang Mai. J. Sci.20154225015111349.90600 WangXHuangGViolation analysis on two-step method for interval linear programmingInf. Sci.20142818596323092210.1016/j.ins.2014.05.019 HladíkMMannZAInterval linear programming: a surveyLinear Programming, New Frontiers in Theory and Applications, Chapter 22012New YorkNova Science Publishers85120 RivazSYaghoobiMAWeighted sum of maximum regrets in an interval MOLP problemInt. Trans. Oper. Res.201525516591676380773410.1111/itor.12216 InuiguchiMKumeYGoal programming approach for solving IMOLP problemsEur. J. Oper. Res.19915234536010.1016/0377-2217(91)90169-V HladíkMHow to determine basis stability in interval linear programmingOptim. Lett.20148375389315292410.1007/s11590-012-0589-y AllahdadiMNehiHMThe optimal solutions set of the interval linear programming problemsOptim. Lett.201378931911305739710.1007/s11590-012-0530-4 ChinneckJWRamadanKLinear programming with interval coefficientsJ. Oper. Res. Soc.20005120922010.1057/palgrave.jors.2600891 Garajová, E., Hladík, M., Rada, M.: The effects of transformations on the optimal set in interval linear programming, In: Proceedings of the 14th international symposium on operational research, SOR’17, Bled, Slovenian Society Informatika, Ljubljana, Slovenia, pp. 487–492 (2017) RohnJCheap and tight bound: the recent result by E. Hansen can be made more efficientInterval Comput.19934132113058560830.65019 AllahdadiMNehiHMAshayerinasabHAJavanmardMImproving the modified interval linear programming method by new techniquesInf. Sci.201633922423610.1016/j.ins.2015.12.037 Mishmast NehiHAshayerinasabHAAllahdadiMSolving methods for interval linear programming problem: a review and an improved methodOper. Res.201810.1007/s12351-018-0383-4 OliveiraCAntunesCHMultiple objective linear programming models with interval coefficient-an illustrated overviewEur. J. Oper. Res.20071811434146310.1016/j.ejor.2005.12.042 ADP Dourado (800_CR10) 2019; 21 M Inuiguchi (800_CR23) 1995; 86 S Rivaz (800_CR31) 2015; 25 GH Huang (800_CR18) 1995; 83 C Oliveira (800_CR27) 2007; 181 GH Huang (800_CR19) 1993; 24 RE Steuer (800_CR35) 1989 J Rohn (800_CR34) 2009; 18 S Rivaz (800_CR30) 2013; 21 L Dechao Li (800_CR9) 2019; 486 M Allahdadi (800_CR2) 2018; 28 S Rivaz (800_CR32) 2016; 15 M Allahdadi (800_CR4) 2015; 42 800_CR16 H Mishmast Nehi (800_CR26) 2018 J Koníčková (800_CR25) 2001; 81 M Inuiguchi (800_CR24) 1996; 78 800_CR12 M Allahdadi (800_CR3) 2013; 7 J Xu (800_CR38) 2019; 21 G Alefeld (800_CR1) 1983 J Rex (800_CR29) 1998; 20 M Hladík (800_CR17) 2013; 438 M Hladík (800_CR14) 2014; 8 Y Yang (800_CR39) 2018; 21 M Inuiguchi (800_CR21) 1991; 52 X Wang (800_CR37) 2014; 281 HA Ashayerinasab (800_CR6) 2018; 93 M Allahdadi (800_CR5) 2016; 339 SH Razavi Hajiagha (800_CR28) 2013; 42 M Hladík (800_CR15) 2012 SC Tong (800_CR36) 1994; 66 J Rohn (800_CR33) 1993; 4 M Inuiguchi (800_CR22) 1997; 48 M Bottea (800_CR7) 2019; 273 JW Chinneck (800_CR8) 2000; 51 800_CR20 M Ehrgott (800_CR11) 2005 F Zhou (800_CR40) 2009; 199 M Hladík (800_CR13) 2012; 6 |
| References_xml | – reference: RivazSYaghoobiMAHladíkMUsing modified maximum regret for finding a necessarily efficient solution in an interval MOLP problemFuzzy Optim. Decis. Mak.2016153237253353596710.1007/s10700-015-9226-4 – reference: BotteaMSchöbelADominance for multi-objective robust optimization conceptsEur. J. Oper. Res.20192732430440390712010.1016/j.ejor.2018.08.020 – reference: HladíkMHow to determine basis stability in interval linear programmingOptim. Lett.20148375389315292410.1007/s11590-012-0589-y – reference: HladíkMWeak and strong solvability of interval linear systems of equations and inequalitiesLinear Algebra Appl.20134381141564165303452210.1016/j.laa.2013.02.012 – reference: InuiguchiMSakawaMMinimax regret solution to multi objective linear programming problems with interval objective function coefficientsEur. J. Oper. Res.19958652653610.1016/0377-2217(94)00092-Q – reference: DouradoADPLobatoFSAp CavaliniASteffenVFuzzy reliability-based optimization for engineering system designInt. J. Fuzzy Syst.20192151418142910.1007/s40815-019-00655-5 – reference: InuiguchiMKumeYGoal programming approach for solving IMOLP problemsEur. J. Oper. Res.19915234536010.1016/0377-2217(91)90169-V – reference: Mishmast NehiHAshayerinasabHAAllahdadiMSolving methods for interval linear programming problem: a review and an improved methodOper. Res.201810.1007/s12351-018-0383-4 – reference: Razavi HajiaghaSHProgramming with interval multi-objective linear coefficients: a fuzzy set based approachKybernetes2013423482496308915510.1108/03684921311323707 – reference: AllahdadiMNehiHMThe optimal solutions set of the interval linear programming problemsOptim. Lett.201378931911305739710.1007/s11590-012-0530-4 – reference: InuiguchiMSakawaMAn achievement rate approach to linear programming problems with an interval objective functionJ. Oper. Res. Soc.199748253310.1057/palgrave.jors.2600322 – reference: Dechao LiLLeungYWeizhiWMultiobjective interval linear programming in admissible-order vector spaceInf. Sci.201948611910.1016/j.ins.2019.02.012 – reference: HuangGHBaetzBWPatryGGGrey integer programming: an application to waste management planning under uncertaintyEur. J. Oper. Res.19958359462010.1016/0377-2217(94)00093-R – reference: Inuiguchi, M.: Necessary efficiency is partitioned into possible an necessary optimalities, IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), pp. 209–214. Edmonton, AB, Canada (2013) – reference: AlefeldGHerzbergerJIntroduction to Interval Computations1983New YorkAcademic Press0552.65041 – reference: AllahdadiMNehiHMAshayerinasabHAJavanmardMImproving the modified interval linear programming method by new techniquesInf. Sci.201633922423610.1016/j.ins.2015.12.037 – reference: AllahdadiMNehiHMThe optimal value bounds of the objective function in the interval linear programming problemChiang Mai. J. Sci.20154225015111349.90600 – reference: RexJRohnJSufficient conditions for regularity and singularity of interval matricesSIAM J. Matrix Anal. Appl.1998202437445165139610.1137/S0895479896310743 – reference: RivazSYaghoobiMAMinimax regret solution to linear programming problems with an interval objective functionEur. J. Oper. Res.2013213625649309285110.1007/s10100-012-0252-9 – reference: SteuerREMultiple criteria optimization: theory, computation and application1989New YorkWiley0742.90068 – reference: HuangGHMooreRDGrey linear programming, its solving approach, and its applicationInt. J. Syst. Sci.199324159172120212710.1080/00207729308949477 – reference: InuiguchiMSakawaMPossible and necessary efficiency in possibilistic multiobjective linear programming problems and possible efficiency testFuzzy Sets Syst.199678321341137938810.1016/0165-0114(95)00169-7 – reference: RivazSYaghoobiMAWeighted sum of maximum regrets in an interval MOLP problemInt. Trans. Oper. Res.201525516591676380773410.1111/itor.12216 – reference: AshayerinasabHANehiHMAllahdadiMSolving the interval linear programming problem: a new algorithm for a general caseExpert Syst. Appl.201893394910.1016/j.eswa.2017.10.020 – reference: ChinneckJWRamadanKLinear programming with interval coefficientsJ. Oper. Res. Soc.20005120922010.1057/palgrave.jors.2600891 – reference: HladíkMMannZAInterval linear programming: a surveyLinear Programming, New Frontiers in Theory and Applications, Chapter 22012New YorkNova Science Publishers85120 – reference: XuJFangHZengFChenYHGuoHRobust observer design and fuzzy optimization for uncertain dynamic systemsInt. J. Fuzzy Syst.201921515111523397769310.1007/s40815-019-00646-6 – reference: Garajová, E., Hladík, M., Rada, M.: The effects of transformations on the optimal set in interval linear programming, In: Proceedings of the 14th international symposium on operational research, SOR’17, Bled, Slovenian Society Informatika, Ljubljana, Slovenia, pp. 487–492 (2017) – reference: TongSCInterval number, fuzzy number linear programmingFuzzy Sets Syst.199466301306130028610.1016/0165-0114(94)90097-3 – reference: RohnJForty necessary and sufficient conditions for regularity of interval matrices: a surveyElectron J. Linear Algebra20091850051225386191189.65088 – reference: ZhouFHuangGHChenGGuoHEnhanced-interval linear programmingEur. J. Oper. Res.2009199323333253327810.1016/j.ejor.2008.12.019 – reference: RohnJCheap and tight bound: the recent result by E. Hansen can be made more efficientInterval Comput.19934132113058560830.65019 – reference: WangXHuangGViolation analysis on two-step method for interval linear programmingInf. Sci.20142818596323092210.1016/j.ins.2014.05.019 – reference: OliveiraCAntunesCHMultiple objective linear programming models with interval coefficient-an illustrated overviewEur. J. Oper. Res.20071811434146310.1016/j.ejor.2005.12.042 – reference: AllahdadiMDengCAn improved three-step method for solving the interval linear programming problemYugoslav J. Oper. Res.2018284435451388444910.2298/YJOR180117020A – reference: YangYZhaoJXiaJZhuangGZhangWMultiobjective optimization control for uncertain nonlinear stochastic system with state-delayInt. J. Fuzzy Syst.20182117283393359410.1007/s40815-018-0541-0 – reference: HladíkMComplexity of necessary efficiency in interval linear programming and multiobjective linear programmingOptim. Lett.201265893899292562510.1007/s11590-011-0315-1 – reference: EhrgottMMulticriteria Optimization2005BerlinSpringer1132.90001 – reference: KoníčkováJSufficient condition of basis stability of an interval linear programming problemZAMM. Z. Angew. Math. Mech.200181367767810.1002/zamm.200108115114 – reference: Hladík, M.: One necessarily efficient solutions in interval multi objective linear programming, Proceedings of the 25th Mini-EURO Conference Uncertainty and Robustness in Planning and Decision Making URPDM 2010, pp. 1–10. Coimbra, Portugal (2010) – volume: 273 start-page: 430 issue: 2 year: 2019 ident: 800_CR7 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2018.08.020 – volume: 83 start-page: 594 year: 1995 ident: 800_CR18 publication-title: Eur. J. Oper. Res. doi: 10.1016/0377-2217(94)00093-R – volume-title: Multiple criteria optimization: theory, computation and application year: 1989 ident: 800_CR35 – volume: 51 start-page: 209 year: 2000 ident: 800_CR8 publication-title: J. Oper. Res. Soc. doi: 10.1057/palgrave.jors.2600891 – volume: 81 start-page: 677 issue: 3 year: 2001 ident: 800_CR25 publication-title: ZAMM. Z. Angew. Math. Mech. doi: 10.1002/zamm.200108115114 – volume: 20 start-page: 437 issue: 2 year: 1998 ident: 800_CR29 publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479896310743 – volume: 7 start-page: 893 year: 2013 ident: 800_CR3 publication-title: Optim. Lett. doi: 10.1007/s11590-012-0530-4 – volume: 28 start-page: 435 issue: 4 year: 2018 ident: 800_CR2 publication-title: Yugoslav J. Oper. Res. doi: 10.2298/YJOR180117020A – volume: 181 start-page: 1434 year: 2007 ident: 800_CR27 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2005.12.042 – volume: 93 start-page: 39 year: 2018 ident: 800_CR6 publication-title: Expert Syst. Appl. doi: 10.1016/j.eswa.2017.10.020 – volume: 339 start-page: 224 year: 2016 ident: 800_CR5 publication-title: Inf. Sci. doi: 10.1016/j.ins.2015.12.037 – year: 2018 ident: 800_CR26 publication-title: Oper. Res. doi: 10.1007/s12351-018-0383-4 – volume: 6 start-page: 893 issue: 5 year: 2012 ident: 800_CR13 publication-title: Optim. Lett. doi: 10.1007/s11590-011-0315-1 – volume: 48 start-page: 25 year: 1997 ident: 800_CR22 publication-title: J. Oper. Res. Soc. doi: 10.1057/palgrave.jors.2600322 – ident: 800_CR20 doi: 10.1109/IFSA-NAFIPS.2013.6608401 – volume: 21 start-page: 625 issue: 3 year: 2013 ident: 800_CR30 publication-title: Eur. J. Oper. Res. doi: 10.1007/s10100-012-0252-9 – volume: 21 start-page: 1418 issue: 5 year: 2019 ident: 800_CR10 publication-title: Int. J. Fuzzy Syst. doi: 10.1007/s40815-019-00655-5 – volume: 42 start-page: 501 issue: 2 year: 2015 ident: 800_CR4 publication-title: Chiang Mai. J. Sci. – volume-title: Introduction to Interval Computations year: 1983 ident: 800_CR1 – volume: 15 start-page: 237 issue: 3 year: 2016 ident: 800_CR32 publication-title: Fuzzy Optim. Decis. Mak. doi: 10.1007/s10700-015-9226-4 – volume-title: Multicriteria Optimization year: 2005 ident: 800_CR11 – volume: 52 start-page: 345 year: 1991 ident: 800_CR21 publication-title: Eur. J. Oper. Res. doi: 10.1016/0377-2217(91)90169-V – ident: 800_CR12 – volume: 21 start-page: 72 issue: 1 year: 2018 ident: 800_CR39 publication-title: Int. J. Fuzzy Syst. doi: 10.1007/s40815-018-0541-0 – ident: 800_CR16 – volume: 86 start-page: 526 year: 1995 ident: 800_CR23 publication-title: Eur. J. Oper. Res. doi: 10.1016/0377-2217(94)00092-Q – volume: 24 start-page: 159 year: 1993 ident: 800_CR19 publication-title: Int. J. Syst. Sci. doi: 10.1080/00207729308949477 – volume: 78 start-page: 321 year: 1996 ident: 800_CR24 publication-title: Fuzzy Sets Syst. doi: 10.1016/0165-0114(95)00169-7 – volume: 42 start-page: 482 issue: 3 year: 2013 ident: 800_CR28 publication-title: Kybernetes doi: 10.1108/03684921311323707 – volume: 8 start-page: 375 year: 2014 ident: 800_CR14 publication-title: Optim. Lett. doi: 10.1007/s11590-012-0589-y – volume: 18 start-page: 500 year: 2009 ident: 800_CR34 publication-title: Electron J. Linear Algebra – volume: 66 start-page: 301 year: 1994 ident: 800_CR36 publication-title: Fuzzy Sets Syst. doi: 10.1016/0165-0114(94)90097-3 – start-page: 85 volume-title: Linear Programming, New Frontiers in Theory and Applications, Chapter 2 year: 2012 ident: 800_CR15 – volume: 21 start-page: 1511 issue: 5 year: 2019 ident: 800_CR38 publication-title: Int. J. Fuzzy Syst. doi: 10.1007/s40815-019-00646-6 – volume: 486 start-page: 1 year: 2019 ident: 800_CR9 publication-title: Inf. Sci. doi: 10.1016/j.ins.2019.02.012 – volume: 25 start-page: 1659 issue: 5 year: 2015 ident: 800_CR31 publication-title: Int. Trans. Oper. Res. doi: 10.1111/itor.12216 – volume: 199 start-page: 323 year: 2009 ident: 800_CR40 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2008.12.019 – volume: 438 start-page: 4156 issue: 11 year: 2013 ident: 800_CR17 publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2013.02.012 – volume: 4 start-page: 13 year: 1993 ident: 800_CR33 publication-title: Interval Comput. – volume: 281 start-page: 85 year: 2014 ident: 800_CR37 publication-title: Inf. Sci. doi: 10.1016/j.ins.2014.05.019 |
| SSID | ssib031263563 ssib053833614 ssib026410675 ssj0002147029 ssib008679421 |
| Score | 2.2200205 |
| Snippet | In this paper, we consider interval multi-objective linear programming (IMOLP) models which are used to deal with uncertainties of real-world problems. So far,... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 873 |
| SubjectTerms | Artificial Intelligence Computational Intelligence Engineering Linear programming Management Science Methods Multiple objective analysis Operations Research Optimization |
| SummonAdditionalLinks | – databaseName: SpringerLINK Contemporary 1997-Present dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT8MwDLZgcIADb8R4KQduEKltkj6OCG3igMbES7tVSZpIINjQNvj9OOljAwESnJNGre3YTuPvM8CJsFyg67U0jGRAOQ8UlSJMqWHSRNpmTPlqwoerpNdLB4OsX4HCJnW1e30l6T11A3bjGL0cmtghoTHNoWIRljDcpa5hw83tQ2NFjkJuDr2JEd_RpDVWy0LHvzIjncIdz1gVpLz_dp17At_eDM82EY14klVom-9f43NEm6WpX25WfcDqrv_vUzdgrUpQyXlpUZuwYIZbsDpHW7gN99dqWjaWIB3PQIGBizT_18jIEv-fEW2YeHwvHamn0q8SPPri1iL9sirsxS3RL1vaTHbgvtu5u7ikVXsGqlmcTClLlZKOrkdZpYUKA1S7kKkJtCkKWWRaxIXSYWw0ppXWZkLbRHEmBeM4YGO2C63haGj2gBSxYNJKITPriNOFipRUiTUFZ4onxrYhrEWc64q73LXQeM4b1mUvshxFlnuR5aINp80zryVzx6-zD2vN5dUunuSYCjntByxtw1mtqdnwz6vt_236AaxEXtmuIOgQWtPxmzmCZf0-fZyMj711fwD8Ye1- priority: 102 providerName: Springer Nature |
| Title | Obtaining Efficient Solutions of Interval Multi-objective Linear Programming Problems |
| URI | https://link.springer.com/article/10.1007/s40815-020-00800-5 https://www.proquest.com/docview/2932479038 |
| Volume | 22 |
| WOSCitedRecordID | wos000516485700001&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: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 2199-3211 dateEnd: 20241212 omitProxy: false ssIdentifier: ssj0002147029 issn: 1562-2479 databaseCode: P5Z dateStart: 20150301 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 2199-3211 dateEnd: 20241212 omitProxy: false ssIdentifier: ssj0002147029 issn: 1562-2479 databaseCode: K7- dateStart: 20150301 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 2199-3211 dateEnd: 20241212 omitProxy: false ssIdentifier: ssj0002147029 issn: 1562-2479 databaseCode: M7S dateStart: 20150301 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 2199-3211 dateEnd: 20241212 omitProxy: false ssIdentifier: ssj0002147029 issn: 1562-2479 databaseCode: BENPR dateStart: 20150301 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 2199-3211 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0002147029 issn: 1562-2479 databaseCode: RSV dateStart: 20150301 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT9wwEB4VlgMcaHmpC3TlAzewSGI7jxOi1a4qtVoiHqsVl8h2bAlEd4Hd9vczdrxZilQuveTixFEy45nxeOb7AI6E5QJNr6VxIiPKeaSoFHFODZMm0bZgylcTjn5mw2E-HhdlSLjNQlnlwiZ6Q11PtcuRn6JbSnhWRCw_e3yijjXKna4GCo0V6DiUhNiX7l21-uTA5F71caLvd4Bprf6y2CGxLOGncO0zFtyVt-SOwyfyRGe4y0moe3_ou_HddxzdqWtvdq3ZGHdR8bdvWwasb85YvesafPzfj_4EmyFoJeeNlm3BBzPZho1XUIY7cHOh5g3ZBOl7VAp0ZqTNuZGpJT73iHpNfM8vnar7xtYS3A7jciNlUyn2y01RNjQ3s124GfSvv32ngbKBapZmc8pypaSD8FFWaaHiCFVByNxE2tS1rAst0lrpODUaQ01rC6FtpjiTgnEcsCnbg9XJdGI-A6lTwaSVQhbWgakLlSipMmtqzhTPjO1CvPjZlQ545o5W46FqkZi9gCoUUOUFVIkuHLfPPDZoHu_efbiQShVW9qxaiqQLJwu5Lof_Pdv--7MdwHriVckVBR3C6vz5t_kCa_rP_G723IPO1_6wvOzByo-M9ryW47UUt3i9vBq9AKCg_D4 |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LT9wwEB5RqNRyoC9Qt9DWh_bUWiSxnccBVRUPgXa73QNU3FLbsSVQuwvsQtU_1d_IjPNYilRuHHp2Morjbx62Z74BeKe8VGh6PY8THXEpI8O1inPuhHaJ9YUwIZvw2yAbDvPj42K0AH_aWhhKq2xtYjDU1cTSGfkmuqVEZkUk8k9n55y6RtHtattCo4ZF3_3-hVu26dbBDq7v-yTZ2z3c3udNVwFuRZrNuMiN0cQyY7yxysQRfq3SuYusqypdFVallbFx6ixGQ94XyvrMSKGVkDjgU4FyH8CSFHlGetXPeIdfIq-7UTeKsQYRtHX6ImJifpnTXaGtEaJxj8FzUM-gKDRWw11Vwmm-TZ1PqPaT6L6pnJpKwTHO4-pvXzoPkG_d6QZXuffkf_vJT2GlCcrZ51qLnsGCGz-H5RtUjS_g6KuZ1c002G5g3UBnzbozRTbxLJytot6yUNPMJ-a09iUMt_s4JTaqM-F-kohR3cZnugpH9zKvNVgcT8buJbAqVUJ7rXThiSxemcRok3lXSWFk5nwP4nZxS9vwtVPbkB9lxzQdAFEiIMoAiFL14EP3zlnNVnLn0xstCsrGck3LOQR68LHF0Xz439Je3S3tLTzaP_wyKAcHw_46PE4CjCkBagMWZxeX7jU8tFezk-nFm6BTDL7fN76uAcw4WGk |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1bS8MwFD7oFNEH7-K85sE3DbZN0suj6IbimAN17K0kaQKKbmOr_n6TtOumqCA-Jw3tyZeck-Z83wE4YZoys_Vq7Afcw5R6AnPmx1gRrgKpEyJcNmG3FbXbca-XdGZY_C7bfXIlWXAarEpTPz8fZvq8Ir5R48kss9iyok3Ig9k8LFCbSG_P6_fdClFWTm6GyWm8v5VMqxBMfKvFMhWgMqufkNJhub3cVvHxXKkzc84JcECjpGTefP8an73bNGT9csvqnFdz7f-fvQ6rZeCKLgqkbcCc6m_Cyoyc4RY83om8KDiBGk6ZwoyMqv9uaKCR-_9osI0c7xcPxHOx3yJzJDZLDnWKbLFXO0SnKHUz3obHZuPh8hqXZRuwJGGUYxILwa2Mj9BCMuF7Bg6Mx8qTKst4lkgWZkL6oZIm3NQ6YVJHghLOCDUNOiQ7UOsP-moXUBYywjVnPNFWUJ2JQHARaZVRImikdB38iblTWWqa29IaL2mlxuxMlhqTpc5kKavDafXMsFD0-LX3wWQW03J1j1MTIlkkeCSuw9lk1qbNP4-297fux7DUuWqmrZv27T4sB27ebc7QAdTy0Zs6hEX5nj-NR0cO9B9vbflG |
| 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=Obtaining+Efficient+Solutions+of+Interval+Multi-objective+Linear+Programming+Problems&rft.jtitle=International+journal+of+fuzzy+systems&rft.au=Batamiz%2C+Aida&rft.au=Allahdadi%2C+Mehdi&rft.au=Hlad%C3%ADk%2C+Milan&rft.date=2020-04-01&rft.pub=Springer+Nature+B.V&rft.issn=1562-2479&rft.eissn=2199-3211&rft.volume=22&rft.issue=3&rft.spage=873&rft.epage=890&rft_id=info:doi/10.1007%2Fs40815-020-00800-5 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1562-2479&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1562-2479&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1562-2479&client=summon |