On the algebraic solution of fuzzy linear systems based on interval theory

In this paper, fuzzy linear systems involving a crisp square matrix and a fuzzy right-hand side vector are considered. A new approach to solve such systems based on interval theory and the new concept “interval inclusion linear system” is proposed. Also, new necessary and sufficient conditions are d...

Full description

Saved in:
Bibliographic Details
Published inApplied mathematical modelling Vol. 36; no. 11; pp. 5360 - 5379
Main Authors Allahviranloo, T., Ghanbari, M.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.11.2012
Subjects
Algebra
Algebraic solution
Crisps
Fuzzy
Fuzzy linear system
Fuzzy logic
Fuzzy number
Fuzzy set theory
Interval inclusion linear system
Interval linear system
Interval number
Intervals
Linear systems
Mathematical models
Interval linear system
Interval inclusion linear system
Algebraic solution
Fuzzy number
Fuzzy linear system
Interval number
Online AccessGet full text

Cover

Abstract In this paper, fuzzy linear systems involving a crisp square matrix and a fuzzy right-hand side vector are considered. A new approach to solve such systems based on interval theory and the new concept “interval inclusion linear system” is proposed. Also, new necessary and sufficient conditions are derived for obtaining the unique algebraic solution. Numerical examples are given to illustrate the efficiency of the proposed method.
AbstractList In this paper, fuzzy linear systems involving a crisp square matrix and a fuzzy right-hand side vector are considered. A new approach to solve such systems based on interval theory and the new concept "interval inclusion linear system" is proposed. Also, new necessary and sufficient conditions are derived for obtaining the unique algebraic solution. Numerical examples are given to illustrate the efficiency of the proposed method.
Author Ghanbari, M.
Allahviranloo, T.
Author_xml – sequence: 1
  givenname: T.
  surname: Allahviranloo
  fullname: Allahviranloo, T.
  email: tofigh@allahviranloo.com
– sequence: 2
  givenname: M.
  surname: Ghanbari
  fullname: Ghanbari, M.
BookMark eNp9kE1LAzEQhnOoYFv9Ad5y9LLrJGmbFE9S_KTQi4K3kE0nmrKb1GS3sP31bqlnmcMw8LwvzDMhoxADEnLDoGTAFne70uybkgPjJbASgI_IGATIYgmzz0syyXkHAPPhGpO3TaDtN1JTf2GVjLc0x7prfQw0Ouq647GntQ9oEs19brHJtDIZt3QAfGgxHUx9KoipvyIXztQZr__2lHw8Pb6vXor15vl19bAurJCiLaTjshLWcmWB2ZniitulVAsDCxCOKyGdk6oSwFEYRKFgPhesQoVGqqVBMSW35959ij8d5lY3PlusaxMwdlkzUJwzoYaZEnZGbYo5J3R6n3xjUj9A-uRK7_TgSp9caWB6cDVk7s8ZHH44eEw6W4_B4tYntK3eRv9P-hc-znVr
CitedBy_id crossref_primary_10_1142_S021848851350030X
crossref_primary_10_1016_j_fss_2024_108862
crossref_primary_10_1016_j_ins_2017_03_029
crossref_primary_10_1016_j_ins_2024_120619
crossref_primary_10_3233_JIFS_191927
crossref_primary_10_1155_2013_178209
crossref_primary_10_1155_2013_593274
crossref_primary_10_1016_j_engappai_2021_104287
crossref_primary_10_1016_j_fss_2015_03_018
crossref_primary_10_1007_s00500_012_0858_9
crossref_primary_10_3390_math12070946
crossref_primary_10_3934_math_2023368
crossref_primary_10_1155_2012_713617
crossref_primary_10_3390_app122110725
crossref_primary_10_1016_j_fss_2021_06_003
crossref_primary_10_3233_JIFS_200084
crossref_primary_10_1016_j_ins_2014_02_014
crossref_primary_10_1007_s00500_014_1243_7
crossref_primary_10_1007_s00500_016_2294_8
crossref_primary_10_1016_j_procs_2021_08_055
crossref_primary_10_1016_j_fss_2018_04_015
crossref_primary_10_1016_j_fss_2024_108997
crossref_primary_10_1016_j_ins_2023_119832
crossref_primary_10_1007_s40314_020_01156_0
crossref_primary_10_1007_s00158_019_02356_x
crossref_primary_10_1016_j_fss_2017_11_007
crossref_primary_10_1007_s40314_020_01386_2
crossref_primary_10_1016_j_fiae_2014_12_005
crossref_primary_10_1016_j_fss_2017_07_004
crossref_primary_10_3390_math10152822
crossref_primary_10_1016_j_fss_2021_04_007
crossref_primary_10_1080_16168658_2022_2152950
crossref_primary_10_1016_j_apm_2012_10_020
crossref_primary_10_1108_GS_01_2018_0007
crossref_primary_10_1007_s12190_018_1204_x
crossref_primary_10_1016_j_ins_2024_120179
crossref_primary_10_1016_j_asoc_2020_106196
crossref_primary_10_3390_e18030068
Cites_doi 10.1017/S096249291000005X
10.1023/A:1009975421252
10.1016/j.ins.2008.11.031
10.1137/S0895479894268075
10.1016/j.amc.2005.07.033
10.1016/0165-0114(84)90069-1
10.1137/080729621
10.1016/j.amc.2005.11.124
10.1016/S0096-3003(03)00793-8
10.1016/j.cam.2010.05.009
10.1016/j.fss.2011.02.010
10.1137/0716070
10.1016/j.ejor.2008.11.008
10.1016/S0168-9274(98)00112-3
10.1007/BF02390519
10.1016/S0165-0114(96)00270-9
10.1007/BF01386090
10.1016/j.cam.2005.07.033
10.1016/j.matcom.2003.11.006
10.1016/j.apm.2010.02.026
10.1016/S0377-0427(02)00693-3
10.1016/S0377-0427(00)00619-1
10.1016/j.cam.2010.02.042
10.1016/j.cam.2004.03.012
10.1016/S0377-0427(00)00342-3
10.1016/0024-3795(93)90120-D
10.1016/0165-0114(91)90030-T
10.1016/S0024-3795(98)10044-7
10.1016/j.amc.2009.03.041
ContentType Journal Article
Copyright 2012 Elsevier Inc.
Copyright_xml – notice: 2012 Elsevier Inc.
DBID 6I.
AAFTH
AAYXX
CITATION
7SC
8FD
JQ2
L7M
L~C
L~D
DOI 10.1016/j.apm.2012.01.002
DatabaseName ScienceDirect Open Access Titles
Elsevier:ScienceDirect:Open Access
CrossRef
Computer and Information Systems Abstracts
Technology Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Computer and Information Systems Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Advanced Technologies Database with Aerospace
ProQuest Computer Science Collection
Computer and Information Systems Abstracts Professional
DatabaseTitleList Computer and Information Systems Abstracts
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EndPage 5379
ExternalDocumentID 10_1016_j_apm_2012_01_002
S0307904X12000170
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
1B1
1RT
1~.
1~5
23M
4.4
457
4G.
5GY
5VS
6I.
7-5
71M
8P~
9JN
AACTN
AAEDT
AAEDW
AAFTH
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AAXUO
ABAOU
ABEFU
ABFNM
ABMAC
ABVKL
ABXDB
ABYKQ
ACAZW
ACDAQ
ACGFS
ACNNM
ACRLP
ADBBV
ADEZE
ADMUD
ADTZH
AEBSH
AECPX
AEKER
AENEX
AEXQZ
AFFNX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHJVU
AIEXJ
AIGVJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
ARUGR
ASPBG
AVWKF
AXJTR
AZFZN
BJAXD
BKOJK
BLXMC
CS3
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FDB
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
GBLVA
HZ~
IHE
IXB
J1W
JJJVA
KOM
LG9
LY7
M26
M41
MHUIS
MO0
MVM
N9A
NCXOZ
O-L
O9-
OAUVE
OK1
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
ROL
RPZ
SDF
SDG
SES
SEW
SPC
SPCBC
SST
SSW
SSZ
T5K
TN5
WH7
WUQ
XJT
XPP
ZMT
~02
~G-
0SF
AAXKI
AAYXX
ADVLN
AFJKZ
AKRWK
CITATION
7SC
8FD
JQ2
L7M
L~C
L~D
ID FETCH-LOGICAL-c373t-7f27b3cc28c01c48282c9786a0603f2837ff78b302e3aee3805531be8ea789ae3
IEDL.DBID AIKHN
ISSN 0307-904X
IngestDate Fri Oct 25 05:53:44 EDT 2024
Thu Sep 26 19:06:10 EDT 2024
Fri Feb 23 02:30:53 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 11
Keywords Interval linear system
Interval inclusion linear system
Algebraic solution
Fuzzy number
Fuzzy linear system
Interval number
Language English
License http://www.elsevier.com/open-access/userlicense/1.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c373t-7f27b3cc28c01c48282c9786a0603f2837ff78b302e3aee3805531be8ea789ae3
Notes ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
OpenAccessLink https://www.sciencedirect.com/science/article/pii/S0307904X12000170
PQID 1082213838
PQPubID 23500
PageCount 20
ParticipantIDs proquest_miscellaneous_1082213838
crossref_primary_10_1016_j_apm_2012_01_002
elsevier_sciencedirect_doi_10_1016_j_apm_2012_01_002
PublicationCentury 2000
PublicationDate November 2012
2012-11-00
20121101
PublicationDateYYYYMMDD 2012-11-01
PublicationDate_xml – month: 11
  year: 2012
  text: November 2012
PublicationDecade 2010
PublicationTitle Applied mathematical modelling
PublicationYear 2012
Publisher Elsevier Inc
Publisher_xml – name: Elsevier Inc
References Moore, Kearfott, Cloud (b0055) 2009
Dehghan, Hashemi, Ghatee (b0040) 2006; 179
Allahviranloo (b0015) 2004; 155
Cope, Rust (b0090) 1979; 16
Alefeld, Mayer (b0125) 2000; 121
Garloff (b0155) 2009; 30
Ferreira, Patrìcio, Oliveira (b0145) 2001; 136
Friedman, Ming, Kandel (b0005) 1998; 96
Beaumont (b0120) 1998; 281
Rump (b0065) 2010; 19
Mayer (b0080) 2007; 199
Baker Kearfott (b0195) 1996
Oettli (b0105) 1965; 2
Neumaier (b0100) 1990
Kaleva, Seikkala (b0185) 1984; 12
Markov (b0150) 1999; 30
Alefeld, Herzberger (b0175) 1983
Oettli, Prager (b0085) 1964; 6
Allahviranloo, Ghanbari, Hosseinzadeh, Haghi, Nuraei (b0010) 2011; 177
Alefeld, Mayer (b0115) 1995; 16
Allahviranloo, Salahshour, Khezerloo (b0045) 2011; 235
Allahviranloo, Ghanbari (b0020) 2010; 8
(b0070) 1996
Hansen, Walster (b0050) 2004
Alefeld, Kreinovich, Mayer (b0130) 2003; 152
Shary (b0190) 1997; 3
Alefeld, Mayer (b0110) 1993; 194
Moore (b0060) 1966
Dehghan, Hashemi (b0035) 2006; 175
Ferreira, Patrìcio, Oliveira (b0140) 2005; 173
Kreinovich, Lakeyev, Noskov (b0095) 1993; 1
Nikas, Grapsa (b0160) 2009; 213
Ghanbari, Mahdavi-Amiri (b0030) 2010; 34
(b0075) 2006
Kupriyanova (b0200) 1995; 1
Prokopyev, Butenko, Trapp (b0165) 2009; 199
Polyak, Nazin (b0135) 2004; 66
Sevastjanov, Dymova (b0170) 2009; 179
Allahviranloo, Salahshour (b0025) 2011; 235
Wu, Ming (b0180) 1991; 44
Oettli (10.1016/j.apm.2012.01.002_b0105) 1965; 2
Beaumont (10.1016/j.apm.2012.01.002_b0120) 1998; 281
Nikas (10.1016/j.apm.2012.01.002_b0160) 2009; 213
Rump (10.1016/j.apm.2012.01.002_b0065) 2010; 19
Mayer (10.1016/j.apm.2012.01.002_b0080) 2007; 199
Garloff (10.1016/j.apm.2012.01.002_b0155) 2009; 30
Markov (10.1016/j.apm.2012.01.002_b0150) 1999; 30
Baker Kearfott (10.1016/j.apm.2012.01.002_b0195) 1996
Allahviranloo (10.1016/j.apm.2012.01.002_b0010) 2011; 177
Alefeld (10.1016/j.apm.2012.01.002_b0125) 2000; 121
Ferreira (10.1016/j.apm.2012.01.002_b0140) 2005; 173
Moore (10.1016/j.apm.2012.01.002_b0055) 2009
Alefeld (10.1016/j.apm.2012.01.002_b0130) 2003; 152
Allahviranloo (10.1016/j.apm.2012.01.002_b0020) 2010; 8
Sevastjanov (10.1016/j.apm.2012.01.002_b0170) 2009; 179
Ghanbari (10.1016/j.apm.2012.01.002_b0030) 2010; 34
Ferreira (10.1016/j.apm.2012.01.002_b0145) 2001; 136
Polyak (10.1016/j.apm.2012.01.002_b0135) 2004; 66
Cope (10.1016/j.apm.2012.01.002_b0090) 1979; 16
Kupriyanova (10.1016/j.apm.2012.01.002_b0200) 1995; 1
Neumaier (10.1016/j.apm.2012.01.002_b0100) 1990
Alefeld (10.1016/j.apm.2012.01.002_b0115) 1995; 16
Wu (10.1016/j.apm.2012.01.002_b0180) 1991; 44
Friedman (10.1016/j.apm.2012.01.002_b0005) 1998; 96
Dehghan (10.1016/j.apm.2012.01.002_b0040) 2006; 179
Kreinovich (10.1016/j.apm.2012.01.002_b0095) 1993; 1
Allahviranloo (10.1016/j.apm.2012.01.002_b0015) 2004; 155
(10.1016/j.apm.2012.01.002_b0070) 1996
Shary (10.1016/j.apm.2012.01.002_b0190) 1997; 3
Dehghan (10.1016/j.apm.2012.01.002_b0035) 2006; 175
Kaleva (10.1016/j.apm.2012.01.002_b0185) 1984; 12
Allahviranloo (10.1016/j.apm.2012.01.002_b0025) 2011; 235
Alefeld (10.1016/j.apm.2012.01.002_b0175) 1983
Allahviranloo (10.1016/j.apm.2012.01.002_b0045) 2011; 235
Oettli (10.1016/j.apm.2012.01.002_b0085) 1964; 6
Moore (10.1016/j.apm.2012.01.002_b0060) 1966
Hansen (10.1016/j.apm.2012.01.002_b0050) 2004
(10.1016/j.apm.2012.01.002_b0075) 2006
Alefeld (10.1016/j.apm.2012.01.002_b0110) 1993; 194
Prokopyev (10.1016/j.apm.2012.01.002_b0165) 2009; 199
References_xml – volume: 3
  start-page: 103
  year: 1997
  end-page: 135
  ident: b0190
  article-title: Algebraic approach in the “outer problem” for interval linear equations
  publication-title: Reliable Computing
  contributor:
    fullname: Shary
– year: 1996
  ident: b0195
  article-title: Rigorous Global Search: Continuous Problems
  contributor:
    fullname: Baker Kearfott
– year: 1983
  ident: b0175
  article-title: Introduction to Interval Computations
  contributor:
    fullname: Herzberger
– year: 2004
  ident: b0050
  article-title: Global Optimization Using Interval Analysis
  contributor:
    fullname: Walster
– volume: 16
  start-page: 1223
  year: 1995
  end-page: 1240
  ident: b0115
  article-title: On the symmetric and unsymmetric solution set of interval systems
  publication-title: SIAM J. Matrix Anal. Appl.
  contributor:
    fullname: Mayer
– year: 2009
  ident: b0055
  article-title: Introduction to Interval Analysis
  contributor:
    fullname: Cloud
– volume: 173
  start-page: 295
  year: 2005
  end-page: 302
  ident: b0140
  article-title: On the computation of solutions of systems of interval polynomial equations
  publication-title: Journal of Computational and Applied Mathematics
  contributor:
    fullname: Oliveira
– volume: 16
  start-page: 950
  year: 1979
  end-page: 963
  ident: b0090
  article-title: Bounds on solutions of linear systems with inaccurate data
  publication-title: SIAM J. Numer. Anal.
  contributor:
    fullname: Rust
– volume: 1
  start-page: 15
  year: 1995
  end-page: 31
  ident: b0200
  article-title: Inner estimation of the united solution set of interval linear algebraic system
  publication-title: Reliable Computing
  contributor:
    fullname: Kupriyanova
– volume: 44
  start-page: 33
  year: 1991
  end-page: 38
  ident: b0180
  article-title: on embedding problem of fuzzy number space: Part 1
  publication-title: Fuzzy Sets and Systems
  contributor:
    fullname: Ming
– volume: 179
  start-page: 328
  year: 2006
  end-page: 343
  ident: b0040
  article-title: Computational methods for solving fully fuzzy linear systems
  publication-title: Applied Mathematics and Computation
  contributor:
    fullname: Ghatee
– volume: 179
  start-page: 925
  year: 2009
  end-page: 937
  ident: b0170
  article-title: A new method for solving interval and fuzzy equations: Linear case
  publication-title: Information Sciences
  contributor:
    fullname: Dymova
– year: 1966
  ident: b0060
  article-title: Interval Analysis
  contributor:
    fullname: Moore
– year: 1996
  ident: b0070
  publication-title: Applications of Interval Computations
– year: 2006
  ident: b0075
  publication-title: Linear Optimization Problems with Inexact Datam
– volume: 175
  start-page: 645
  year: 2006
  end-page: 674
  ident: b0035
  article-title: Iterative solution of fuzzy linear systems
  publication-title: Applied Mathematics and Computation
  contributor:
    fullname: Hashemi
– volume: 30
  start-page: 225
  year: 1999
  end-page: 239
  ident: b0150
  article-title: An iterative method for algebraic solution to interval equations
  publication-title: Applied Numerical Mathematics
  contributor:
    fullname: Markov
– volume: 235
  start-page: 4652
  year: 2011
  end-page: 4662
  ident: b0045
  article-title: Maximal- and minimal symmetric solutions of fully fuzzy linear systems
  publication-title: Journal of Computational and Applied Mathematics
  contributor:
    fullname: Khezerloo
– volume: 194
  start-page: 161
  year: 1993
  end-page: 182
  ident: b0110
  article-title: The Cholesky method for interval data
  publication-title: Linear Algebra Appl.
  contributor:
    fullname: Mayer
– volume: 199
  start-page: 117
  year: 2009
  end-page: 121
  ident: b0165
  article-title: Checking solvability of systems of interval linear equations and inequalities via mixed integer programming
  publication-title: European Journal of Operational Research
  contributor:
    fullname: Trapp
– volume: 235
  start-page: 4545
  year: 2011
  end-page: 4553
  ident: b0025
  article-title: Fuzzy symmetric solution of fuzzy linear systems
  publication-title: Journal of Computational and Applied Mathematics
  contributor:
    fullname: Salahshour
– volume: 2
  start-page: 115
  year: 1965
  end-page: 118
  ident: b0105
  article-title: On the solution set of a linear system with inaccurate coefficients
  publication-title: SIAM J. Numer. Anal.
  contributor:
    fullname: Oettli
– volume: 8
  start-page: 24
  year: 2010
  end-page: 30
  ident: b0020
  article-title: Solving Fuzzy Linear Systems by Homotopy Perturbation Method
  publication-title: International Journal of Computational Cognition
  contributor:
    fullname: Ghanbari
– volume: 96
  start-page: 201
  year: 1998
  end-page: 209
  ident: b0005
  article-title: Fuzzy linear systems
  publication-title: Fuzzy Sets and Systems
  contributor:
    fullname: Kandel
– volume: 213
  start-page: 466
  year: 2009
  end-page: 478
  ident: b0160
  article-title: Bounding the zeros of an interval equation
  publication-title: Applied Mathematics and Computation
  contributor:
    fullname: Grapsa
– volume: 1
  start-page: 6
  year: 1993
  end-page: 14
  ident: b0095
  article-title: Optimal solution of interval linear systems is intractable (NP-hard)
  publication-title: Interval Comput.
  contributor:
    fullname: Noskov
– volume: 30
  start-page: 1761
  year: 2009
  end-page: 1772
  ident: b0155
  article-title: Interval Gaussian elimination with pivot tightening
  publication-title: SIAM J. MATRIX ANAL. APPL.
  contributor:
    fullname: Garloff
– volume: 177
  start-page: 87
  year: 2011
  end-page: 92
  ident: b0010
  article-title: A note on “Fuzzy linear systems”
  publication-title: Fuzzy Sets and Systems
  contributor:
    fullname: Nuraei
– volume: 34
  start-page: 3363
  year: 2010
  end-page: 3375
  ident: b0030
  article-title: New solutions of LR fuzzy linear systems using ranking functions and ABS algorithms
  publication-title: Applied Mathematical Modelling
  contributor:
    fullname: Mahdavi-Amiri
– year: 1990
  ident: b0100
  article-title: Interval Methods for Systems of Equations
  contributor:
    fullname: Neumaier
– volume: 199
  start-page: 220
  year: 2007
  end-page: 228
  ident: b0080
  article-title: On regular and singular interval systems
  publication-title: Journal of Computational and Applied Mathematics
  contributor:
    fullname: Mayer
– volume: 136
  start-page: 271
  year: 2001
  end-page: 281
  ident: b0145
  article-title: A priori estimates for the zeros of interval polynomials
  publication-title: J. Comput. Appl. Math.
  contributor:
    fullname: Oliveira
– volume: 66
  start-page: 207
  year: 2004
  end-page: 217
  ident: b0135
  article-title: Interval solutions for interval algebraic equations
  publication-title: Mathematics and Computers in Simulation
  contributor:
    fullname: Nazin
– volume: 281
  start-page: 293
  year: 1998
  end-page: 309
  ident: b0120
  article-title: Solving interval linear systems with linear programming techniques
  publication-title: Linear Algebra and its Applications
  contributor:
    fullname: Beaumont
– volume: 121
  start-page: 421
  year: 2000
  end-page: 464
  ident: b0125
  article-title: Interval analysis: theory and applications
  publication-title: Journal of Computational and Applied Mathematics
  contributor:
    fullname: Mayer
– volume: 152
  start-page: 1
  year: 2003
  end-page: 15
  ident: b0130
  article-title: On the solution sets of particular classes of linear interval systems
  publication-title: J. Comput. Appl. Math.
  contributor:
    fullname: Mayer
– volume: 155
  start-page: 493
  year: 2004
  end-page: 502
  ident: b0015
  article-title: Numerical methods for fuzzy system of linear equations
  publication-title: Applied Mathematics and Computation
  contributor:
    fullname: Allahviranloo
– volume: 12
  start-page: 215
  year: 1984
  end-page: 229
  ident: b0185
  article-title: On fuzzy metric spaces
  publication-title: Fuzzy Sets and Systems
  contributor:
    fullname: Seikkala
– volume: 19
  start-page: 287
  year: 2010
  end-page: 449
  ident: b0065
  article-title: Verification methods: Rigorous results using floating-point arithmetic
  publication-title: Acta Numerica
  contributor:
    fullname: Rump
– volume: 6
  start-page: 405
  year: 1964
  end-page: 409
  ident: b0085
  article-title: Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
  publication-title: Numer. Math.
  contributor:
    fullname: Prager
– volume: 19
  start-page: 287
  year: 2010
  ident: 10.1016/j.apm.2012.01.002_b0065
  article-title: Verification methods: Rigorous results using floating-point arithmetic
  publication-title: Acta Numerica
  doi: 10.1017/S096249291000005X
  contributor:
    fullname: Rump
– volume: 3
  start-page: 103
  issue: 2
  year: 1997
  ident: 10.1016/j.apm.2012.01.002_b0190
  article-title: Algebraic approach in the “outer problem” for interval linear equations
  publication-title: Reliable Computing
  doi: 10.1023/A:1009975421252
  contributor:
    fullname: Shary
– volume: 179
  start-page: 925
  year: 2009
  ident: 10.1016/j.apm.2012.01.002_b0170
  article-title: A new method for solving interval and fuzzy equations: Linear case
  publication-title: Information Sciences
  doi: 10.1016/j.ins.2008.11.031
  contributor:
    fullname: Sevastjanov
– volume: 16
  start-page: 1223
  year: 1995
  ident: 10.1016/j.apm.2012.01.002_b0115
  article-title: On the symmetric and unsymmetric solution set of interval systems
  publication-title: SIAM J. Matrix Anal. Appl.
  doi: 10.1137/S0895479894268075
  contributor:
    fullname: Alefeld
– volume: 175
  start-page: 645
  year: 2006
  ident: 10.1016/j.apm.2012.01.002_b0035
  article-title: Iterative solution of fuzzy linear systems
  publication-title: Applied Mathematics and Computation
  doi: 10.1016/j.amc.2005.07.033
  contributor:
    fullname: Dehghan
– volume: 12
  start-page: 215
  year: 1984
  ident: 10.1016/j.apm.2012.01.002_b0185
  article-title: On fuzzy metric spaces
  publication-title: Fuzzy Sets and Systems
  doi: 10.1016/0165-0114(84)90069-1
  contributor:
    fullname: Kaleva
– volume: 30
  start-page: 1761
  year: 2009
  ident: 10.1016/j.apm.2012.01.002_b0155
  article-title: Interval Gaussian elimination with pivot tightening
  publication-title: SIAM J. MATRIX ANAL. APPL.
  doi: 10.1137/080729621
  contributor:
    fullname: Garloff
– year: 1966
  ident: 10.1016/j.apm.2012.01.002_b0060
  contributor:
    fullname: Moore
– volume: 179
  start-page: 328
  year: 2006
  ident: 10.1016/j.apm.2012.01.002_b0040
  article-title: Computational methods for solving fully fuzzy linear systems
  publication-title: Applied Mathematics and Computation
  doi: 10.1016/j.amc.2005.11.124
  contributor:
    fullname: Dehghan
– volume: 8
  start-page: 24
  issue: 2
  year: 2010
  ident: 10.1016/j.apm.2012.01.002_b0020
  article-title: Solving Fuzzy Linear Systems by Homotopy Perturbation Method
  publication-title: International Journal of Computational Cognition
  contributor:
    fullname: Allahviranloo
– year: 2009
  ident: 10.1016/j.apm.2012.01.002_b0055
  contributor:
    fullname: Moore
– volume: 155
  start-page: 493
  year: 2004
  ident: 10.1016/j.apm.2012.01.002_b0015
  article-title: Numerical methods for fuzzy system of linear equations
  publication-title: Applied Mathematics and Computation
  doi: 10.1016/S0096-3003(03)00793-8
  contributor:
    fullname: Allahviranloo
– volume: 235
  start-page: 4652
  issue: 16
  year: 2011
  ident: 10.1016/j.apm.2012.01.002_b0045
  article-title: Maximal- and minimal symmetric solutions of fully fuzzy linear systems
  publication-title: Journal of Computational and Applied Mathematics
  doi: 10.1016/j.cam.2010.05.009
  contributor:
    fullname: Allahviranloo
– volume: 177
  start-page: 87
  year: 2011
  ident: 10.1016/j.apm.2012.01.002_b0010
  article-title: A note on “Fuzzy linear systems”
  publication-title: Fuzzy Sets and Systems
  doi: 10.1016/j.fss.2011.02.010
  contributor:
    fullname: Allahviranloo
– volume: 2
  start-page: 115
  year: 1965
  ident: 10.1016/j.apm.2012.01.002_b0105
  article-title: On the solution set of a linear system with inaccurate coefficients
  publication-title: SIAM J. Numer. Anal.
  contributor:
    fullname: Oettli
– volume: 16
  start-page: 950
  year: 1979
  ident: 10.1016/j.apm.2012.01.002_b0090
  article-title: Bounds on solutions of linear systems with inaccurate data
  publication-title: SIAM J. Numer. Anal.
  doi: 10.1137/0716070
  contributor:
    fullname: Cope
– volume: 199
  start-page: 117
  year: 2009
  ident: 10.1016/j.apm.2012.01.002_b0165
  article-title: Checking solvability of systems of interval linear equations and inequalities via mixed integer programming
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2008.11.008
  contributor:
    fullname: Prokopyev
– year: 2004
  ident: 10.1016/j.apm.2012.01.002_b0050
  contributor:
    fullname: Hansen
– volume: 30
  start-page: 225
  year: 1999
  ident: 10.1016/j.apm.2012.01.002_b0150
  article-title: An iterative method for algebraic solution to interval equations
  publication-title: Applied Numerical Mathematics
  doi: 10.1016/S0168-9274(98)00112-3
  contributor:
    fullname: Markov
– volume: 1
  start-page: 15
  issue: 1
  year: 1995
  ident: 10.1016/j.apm.2012.01.002_b0200
  article-title: Inner estimation of the united solution set of interval linear algebraic system
  publication-title: Reliable Computing
  doi: 10.1007/BF02390519
  contributor:
    fullname: Kupriyanova
– volume: 96
  start-page: 201
  year: 1998
  ident: 10.1016/j.apm.2012.01.002_b0005
  article-title: Fuzzy linear systems
  publication-title: Fuzzy Sets and Systems
  doi: 10.1016/S0165-0114(96)00270-9
  contributor:
    fullname: Friedman
– volume: 6
  start-page: 405
  year: 1964
  ident: 10.1016/j.apm.2012.01.002_b0085
  article-title: Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
  publication-title: Numer. Math.
  doi: 10.1007/BF01386090
  contributor:
    fullname: Oettli
– volume: 199
  start-page: 220
  year: 2007
  ident: 10.1016/j.apm.2012.01.002_b0080
  article-title: On regular and singular interval systems
  publication-title: Journal of Computational and Applied Mathematics
  doi: 10.1016/j.cam.2005.07.033
  contributor:
    fullname: Mayer
– volume: 66
  start-page: 207
  year: 2004
  ident: 10.1016/j.apm.2012.01.002_b0135
  article-title: Interval solutions for interval algebraic equations
  publication-title: Mathematics and Computers in Simulation
  doi: 10.1016/j.matcom.2003.11.006
  contributor:
    fullname: Polyak
– volume: 34
  start-page: 3363
  year: 2010
  ident: 10.1016/j.apm.2012.01.002_b0030
  article-title: New solutions of LR fuzzy linear systems using ranking functions and ABS algorithms
  publication-title: Applied Mathematical Modelling
  doi: 10.1016/j.apm.2010.02.026
  contributor:
    fullname: Ghanbari
– volume: 152
  start-page: 1
  year: 2003
  ident: 10.1016/j.apm.2012.01.002_b0130
  article-title: On the solution sets of particular classes of linear interval systems
  publication-title: J. Comput. Appl. Math.
  doi: 10.1016/S0377-0427(02)00693-3
  contributor:
    fullname: Alefeld
– year: 1996
  ident: 10.1016/j.apm.2012.01.002_b0070
– year: 2006
  ident: 10.1016/j.apm.2012.01.002_b0075
– volume: 136
  start-page: 271
  year: 2001
  ident: 10.1016/j.apm.2012.01.002_b0145
  article-title: A priori estimates for the zeros of interval polynomials
  publication-title: J. Comput. Appl. Math.
  doi: 10.1016/S0377-0427(00)00619-1
  contributor:
    fullname: Ferreira
– year: 1990
  ident: 10.1016/j.apm.2012.01.002_b0100
  contributor:
    fullname: Neumaier
– volume: 235
  start-page: 4545
  issue: 16
  year: 2011
  ident: 10.1016/j.apm.2012.01.002_b0025
  article-title: Fuzzy symmetric solution of fuzzy linear systems
  publication-title: Journal of Computational and Applied Mathematics
  doi: 10.1016/j.cam.2010.02.042
  contributor:
    fullname: Allahviranloo
– year: 1996
  ident: 10.1016/j.apm.2012.01.002_b0195
  contributor:
    fullname: Baker Kearfott
– volume: 173
  start-page: 295
  year: 2005
  ident: 10.1016/j.apm.2012.01.002_b0140
  article-title: On the computation of solutions of systems of interval polynomial equations
  publication-title: Journal of Computational and Applied Mathematics
  doi: 10.1016/j.cam.2004.03.012
  contributor:
    fullname: Ferreira
– volume: 121
  start-page: 421
  year: 2000
  ident: 10.1016/j.apm.2012.01.002_b0125
  article-title: Interval analysis: theory and applications
  publication-title: Journal of Computational and Applied Mathematics
  doi: 10.1016/S0377-0427(00)00342-3
  contributor:
    fullname: Alefeld
– volume: 194
  start-page: 161
  year: 1993
  ident: 10.1016/j.apm.2012.01.002_b0110
  article-title: The Cholesky method for interval data
  publication-title: Linear Algebra Appl.
  doi: 10.1016/0024-3795(93)90120-D
  contributor:
    fullname: Alefeld
– year: 1983
  ident: 10.1016/j.apm.2012.01.002_b0175
  contributor:
    fullname: Alefeld
– volume: 44
  start-page: 33
  year: 1991
  ident: 10.1016/j.apm.2012.01.002_b0180
  article-title: on embedding problem of fuzzy number space: Part 1
  publication-title: Fuzzy Sets and Systems
  doi: 10.1016/0165-0114(91)90030-T
  contributor:
    fullname: Wu
– volume: 281
  start-page: 293
  year: 1998
  ident: 10.1016/j.apm.2012.01.002_b0120
  article-title: Solving interval linear systems with linear programming techniques
  publication-title: Linear Algebra and its Applications
  doi: 10.1016/S0024-3795(98)10044-7
  contributor:
    fullname: Beaumont
– volume: 213
  start-page: 466
  year: 2009
  ident: 10.1016/j.apm.2012.01.002_b0160
  article-title: Bounding the zeros of an interval equation
  publication-title: Applied Mathematics and Computation
  doi: 10.1016/j.amc.2009.03.041
  contributor:
    fullname: Nikas
– volume: 1
  start-page: 6
  year: 1993
  ident: 10.1016/j.apm.2012.01.002_b0095
  article-title: Optimal solution of interval linear systems is intractable (NP-hard)
  publication-title: Interval Comput.
  contributor:
    fullname: Kreinovich
SSID ssj0005904
Score 2.290714
Snippet In this paper, fuzzy linear systems involving a crisp square matrix and a fuzzy right-hand side vector are considered. A new approach to solve such systems...
SourceID proquest
crossref
elsevier
SourceType Aggregation Database
Publisher
StartPage 5360
SubjectTerms Algebra
Algebraic solution
Crisps
Fuzzy
Fuzzy linear system
Fuzzy logic
Fuzzy number
Fuzzy set theory
Interval inclusion linear system
Interval linear system
Interval number
Intervals
Linear systems
Mathematical models
Title On the algebraic solution of fuzzy linear systems based on interval theory
URI https://dx.doi.org/10.1016/j.apm.2012.01.002
https://search.proquest.com/docview/1082213838
Volume 36
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV05T8MwFH6CdoEBcYqzMhITUqgT53DGtgL1gDJwKGKx7MSRwpBWtB3agd_Ocw4QCDEw2oqT6PPzO-z3PgNcoJfsBSphVuKzxHLRxlno5StLUa68ROsgLni278Z-_8kdRl60Br26FsakVVa6v9TphbauetoVmu1plrUfjHiG1I1sp2SBWYdmcUjUgGZnMOqPvzI9QurWfIhmQH24WaR5yampRzc7gvbn5sov5umHoi6sz802bFVuI-mUf7YDazrfhc27T87V2R4M73OCTWIu7sAQOItJLVZkkpJ0sVotifEp5Rsp6ZtnxJiwhOADWZH5iB8o6hqX-_B0c_3Y61vVTQlWzAI2t4LUCRSLY4fH1I5djKKcGMNDX1KfstQQ3KRpwBWjjmZSa8aph2tPaa5lwEOp2QE08kmuD4Fos-xTFerAlS73kjDh3FOKejrRGNrII7isARLTkhBD1JlirwLRFAZNQW2BaB6BW0Movs2qQIX917DzGm6B0m6OMGSuJ4uZoTN1HBujan78v1efwIZpldWEp9CYvy30GboVc9WC9at3u4XC030e3bYqIcLeQdTF1rgX3b98AAwzz7g
link.rule.ids 315,783,787,3515,4511,24130,27583,27938,27939,45599,45677,45693,45888
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV05T8MwFLZKOwAD4hTlNBITUlQndmpnLBWo9GKgRd0sO3GkMKRVj6H99TznKAIhBsY4cRJ9fn6H_d5nhO7BS_a5jqgTNWnkMLBxDnj52tFEaD8yhocZz_Zg2OyMWXfiTyqoXdbC2LTKQvfnOj3T1kVLo0CzMUuSxpsVz4CwievlLDA7qAbeAIcIrNZ6fO_1vzI9AsJKPkTbodzczNK81MzWo9sVQXe7uPKLefqhqDPr83yIDgq3EbfyPztCFZMeo_3BlnN1cYK6rymGS2wP7oAQOAlxKVZ4GuN4tdmssfUp1Rzn9M0LbE1YhOGBJMt8hA9kdY3rUzR-fhq1O05xUoITUk6XDo89rmkYeiIkbsggivJCCA-bijQJjS3BTRxzoSnxDFXGUEF8mHvaCKO4CJShZ6iaTlNzjrCx0z7WgeFMMeFHQSSErzXxTWQgtFF19FACJGc5IYYsM8U-JKApLZqSuBLQrCNWQii_jaoEhf1Xt7sSbgnSbrcwVGqmq4WlM_U8F6JqcfG_V9-i3c5o0Jf9l2HvEu3ZO3ll4RWqLucrcw0uxlLfFCL0CXlDzXU
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+the+algebraic+solution+of+fuzzy+linear+systems+based+on+interval+theory&rft.jtitle=Applied+mathematical+modelling&rft.au=Allahviranloo%2C+T.&rft.au=Ghanbari%2C+M.&rft.date=2012-11-01&rft.issn=0307-904X&rft.volume=36&rft.issue=11&rft.spage=5360&rft.epage=5379&rft_id=info:doi/10.1016%2Fj.apm.2012.01.002&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_apm_2012_01_002
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0307-904X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0307-904X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0307-904X&client=summon