A method for solving fuzzy matrix equations
There are many reported studies, in which researchers tried to solve a system of fuzzy linear equations numerically. In this paper, a numerical method for solving fuzzy system A X ~ B = C ~ of matrix equations is investigated. As it can be observed in the form of these equations, the unknown matrix...
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| Veröffentlicht in: | Soft computing (Berlin, Germany) Germany), 2018-04, Vol.22 (7), p.2095-2103 |
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| creator | Amirfakhrian, M. Fallah, M. Rodríguez-López, R. |
| description | There are many reported studies, in which researchers tried to solve a system of fuzzy linear equations numerically. In this paper, a numerical method for solving fuzzy system
A
X
~
B
=
C
~
of matrix equations is investigated. As it can be observed in the form of these equations, the unknown matrix
X
, which is the solution to these equations, has a left-hand coefficient matrix
A
and a right-hand coefficient matrix
B
. Such character makes these equations different from other equations in the form of
A
X
~
=
B
~
. In the aforesaid equations,
A
and
B
are crisp matrices and
C
~
and
X
~
are matrices with fuzzy arrays. In this work using the parametric form of fuzzy linear equations and presenting an algorithm, two systems of equations will be developed and solved afterward. A comparison of the number of multiplications in this method with a different one will be drawn afterward. Some numerical examples are given to illustrate the effectiveness of the proposed method. |
| doi_str_mv | 10.1007/s00500-017-2680-x |
| format | Article |
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A
X
~
B
=
C
~
of matrix equations is investigated. As it can be observed in the form of these equations, the unknown matrix
X
, which is the solution to these equations, has a left-hand coefficient matrix
A
and a right-hand coefficient matrix
B
. Such character makes these equations different from other equations in the form of
A
X
~
=
B
~
. In the aforesaid equations,
A
and
B
are crisp matrices and
C
~
and
X
~
are matrices with fuzzy arrays. In this work using the parametric form of fuzzy linear equations and presenting an algorithm, two systems of equations will be developed and solved afterward. A comparison of the number of multiplications in this method with a different one will be drawn afterward. Some numerical examples are given to illustrate the effectiveness of the proposed method.</description><identifier>ISSN: 1432-7643</identifier><identifier>EISSN: 1433-7479</identifier><identifier>DOI: 10.1007/s00500-017-2680-x</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algorithms ; Artificial Intelligence ; Computational Intelligence ; Control ; Engineering ; Foundations ; Fuzzy sets ; Linear equations ; Mathematical analysis ; Mathematical Logic and Foundations ; Matrices (mathematics) ; Mechatronics ; Numerical methods ; Robotics</subject><ispartof>Soft computing (Berlin, Germany), 2018-04, Vol.22 (7), p.2095-2103</ispartof><rights>Springer-Verlag GmbH Germany 2017</rights><rights>Springer-Verlag GmbH Germany 2017.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-bb63b59e49cd77db573c006540dafdb08c3fc58f3183f04bee7f13f579e4ee8e3</citedby><cites>FETCH-LOGICAL-c316t-bb63b59e49cd77db573c006540dafdb08c3fc58f3183f04bee7f13f579e4ee8e3</cites><orcidid>0000-0001-9934-6412</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00500-017-2680-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2917939032?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,21388,27924,27925,33744,41488,42557,43805,51319,64385,64389,72469</link.rule.ids></links><search><creatorcontrib>Amirfakhrian, M.</creatorcontrib><creatorcontrib>Fallah, M.</creatorcontrib><creatorcontrib>Rodríguez-López, R.</creatorcontrib><title>A method for solving fuzzy matrix equations</title><title>Soft computing (Berlin, Germany)</title><addtitle>Soft Comput</addtitle><description>There are many reported studies, in which researchers tried to solve a system of fuzzy linear equations numerically. In this paper, a numerical method for solving fuzzy system
A
X
~
B
=
C
~
of matrix equations is investigated. As it can be observed in the form of these equations, the unknown matrix
X
, which is the solution to these equations, has a left-hand coefficient matrix
A
and a right-hand coefficient matrix
B
. Such character makes these equations different from other equations in the form of
A
X
~
=
B
~
. In the aforesaid equations,
A
and
B
are crisp matrices and
C
~
and
X
~
are matrices with fuzzy arrays. In this work using the parametric form of fuzzy linear equations and presenting an algorithm, two systems of equations will be developed and solved afterward. A comparison of the number of multiplications in this method with a different one will be drawn afterward. Some numerical examples are given to illustrate the effectiveness of the proposed method.</description><subject>Algorithms</subject><subject>Artificial Intelligence</subject><subject>Computational Intelligence</subject><subject>Control</subject><subject>Engineering</subject><subject>Foundations</subject><subject>Fuzzy sets</subject><subject>Linear equations</subject><subject>Mathematical analysis</subject><subject>Mathematical Logic and Foundations</subject><subject>Matrices (mathematics)</subject><subject>Mechatronics</subject><subject>Numerical methods</subject><subject>Robotics</subject><issn>1432-7643</issn><issn>1433-7479</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kEFLwzAYhoMoOKc_wFvBo0S_9Eua9jiGTmHgRc-hTZPZsTZb0sq2X29mBU-evvfwPu8HDyG3DB4YgHwMAAKAApM0zXKg-zMyYRyRSi6L85-cUplxvCRXIawBUiYFTsj9LGlN_-nqxDqfBLf5arpVYofj8ZC0Ze-bfWJ2Q9k3rgvX5MKWm2Bufu-UfDw_vc9f6PJt8TqfLalGlvW0qjKsRGF4oWsp60pI1ACZ4FCXtq4g12i1yC2yHC3wyhhpGVohI2JMbnBK7sbdrXe7wYRerd3gu_hSpQWTBRaAaWyxsaW9C8Ebq7a-aUt_UAzUyYkanajoRJ2cqH1k0pEJsdutjP9b_h_6BoJGZDY</recordid><startdate>20180401</startdate><enddate>20180401</enddate><creator>Amirfakhrian, M.</creator><creator>Fallah, M.</creator><creator>Rodríguez-López, R.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><orcidid>https://orcid.org/0000-0001-9934-6412</orcidid></search><sort><creationdate>20180401</creationdate><title>A method for solving fuzzy matrix equations</title><author>Amirfakhrian, M. ; Fallah, M. ; Rodríguez-López, R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-bb63b59e49cd77db573c006540dafdb08c3fc58f3183f04bee7f13f579e4ee8e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Algorithms</topic><topic>Artificial Intelligence</topic><topic>Computational Intelligence</topic><topic>Control</topic><topic>Engineering</topic><topic>Foundations</topic><topic>Fuzzy sets</topic><topic>Linear equations</topic><topic>Mathematical analysis</topic><topic>Mathematical Logic and Foundations</topic><topic>Matrices (mathematics)</topic><topic>Mechatronics</topic><topic>Numerical methods</topic><topic>Robotics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Amirfakhrian, M.</creatorcontrib><creatorcontrib>Fallah, M.</creatorcontrib><creatorcontrib>Rodríguez-López, R.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><jtitle>Soft computing (Berlin, Germany)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Amirfakhrian, M.</au><au>Fallah, M.</au><au>Rodríguez-López, R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A method for solving fuzzy matrix equations</atitle><jtitle>Soft computing (Berlin, Germany)</jtitle><stitle>Soft Comput</stitle><date>2018-04-01</date><risdate>2018</risdate><volume>22</volume><issue>7</issue><spage>2095</spage><epage>2103</epage><pages>2095-2103</pages><issn>1432-7643</issn><eissn>1433-7479</eissn><abstract>There are many reported studies, in which researchers tried to solve a system of fuzzy linear equations numerically. In this paper, a numerical method for solving fuzzy system
A
X
~
B
=
C
~
of matrix equations is investigated. As it can be observed in the form of these equations, the unknown matrix
X
, which is the solution to these equations, has a left-hand coefficient matrix
A
and a right-hand coefficient matrix
B
. Such character makes these equations different from other equations in the form of
A
X
~
=
B
~
. In the aforesaid equations,
A
and
B
are crisp matrices and
C
~
and
X
~
are matrices with fuzzy arrays. In this work using the parametric form of fuzzy linear equations and presenting an algorithm, two systems of equations will be developed and solved afterward. A comparison of the number of multiplications in this method with a different one will be drawn afterward. Some numerical examples are given to illustrate the effectiveness of the proposed method.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00500-017-2680-x</doi><tpages>9</tpages><orcidid>https://orcid.org/0000-0001-9934-6412</orcidid></addata></record> |
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| ispartof | Soft computing (Berlin, Germany), 2018-04, Vol.22 (7), p.2095-2103 |
| issn | 1432-7643 1433-7479 |
| language | eng |
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| source | ProQuest Central UK/Ireland; SpringerLink Journals - AutoHoldings; ProQuest Central |
| subjects | Algorithms Artificial Intelligence Computational Intelligence Control Engineering Foundations Fuzzy sets Linear equations Mathematical analysis Mathematical Logic and Foundations Matrices (mathematics) Mechatronics Numerical methods Robotics |
| title | A method for solving fuzzy matrix equations |
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