{"id":"https://openalex.org/W2196795176","doi":"https://doi.org/10.3233/ifs-151781","title":"An efficient method for solving LR fuzzy dual matrix systems","display_name":"An efficient method for solving LR fuzzy dual matrix systems","publication_year":2015,"publication_date":"2015-08-31","ids":{"openalex":"https://openalex.org/W2196795176","doi":"https://doi.org/10.3233/ifs-151781","mag":"2196795176"},"language":"lv","primary_location":{"id":"doi:10.3233/ifs-151781","is_oa":false,"landing_page_url":"https://doi.org/10.3233/ifs-151781","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Fuzzy Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083928443","display_name":"F. Babakordi","orcid":null},"institutions":[{"id":"https://openalex.org/I155419210","display_name":"Islamic Azad University, Science and Research Branch","ror":"https://ror.org/03187yj51","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I155419210"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"F. Babakordi","raw_affiliation_strings":["Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran","institution_ids":["https://openalex.org/I155419210"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073095019","display_name":"Tofigh Allahviranloo","orcid":"https://orcid.org/0000-0002-6673-3560"},"institutions":[{"id":"https://openalex.org/I155419210","display_name":"Islamic Azad University, Science and Research Branch","ror":"https://ror.org/03187yj51","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I155419210"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"T. Allahviranloo","raw_affiliation_strings":["Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran","institution_ids":["https://openalex.org/I155419210"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008474959","display_name":"M. Adabitabar Firozja","orcid":"https://orcid.org/0000-0001-9177-3882"},"institutions":[{"id":"https://openalex.org/I155419210","display_name":"Islamic Azad University, Science and Research Branch","ror":"https://ror.org/03187yj51","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I155419210"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"M. Adabitabar firozja","raw_affiliation_strings":["Department of Mathematics, Science and Research Branch, Islamic Azad University, Ghaemshahr, Iran","Fax: +98 214 4804172","E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Science and Research Branch, Islamic Azad University, Ghaemshahr, Iran","institution_ids":["https://openalex.org/I155419210"]},{"raw_affiliation_string":"Fax: +98 214 4804172","institution_ids":[]},{"raw_affiliation_string":"E-mail:","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073095019"],"corresponding_institution_ids":["https://openalex.org/I155419210"],"apc_list":null,"apc_paid":null,"fwci":0.6813,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.75096899,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"30","issue":"1","first_page":"575","last_page":"581"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9847999811172485,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.6926310062408447},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5805538892745972},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5414974093437195},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.531500518321991},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5238004922866821},{"id":"https://openalex.org/keywords/fuzzy-associative-matrix","display_name":"Fuzzy associative matrix","score":0.44848617911338806},{"id":"https://openalex.org/keywords/complex-matrix","display_name":"Complex matrix","score":0.4170020520687103},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4108726382255554},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.38416147232055664},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3725234866142273},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3510661721229553},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3132322430610657},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.24576762318611145},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1168944239616394},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.09084922075271606},{"id":"https://openalex.org/keywords/chromatography","display_name":"Chromatography","score":0.048523664474487305}],"concepts":[{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.6926310062408447},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5805538892745972},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5414974093437195},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.531500518321991},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5238004922866821},{"id":"https://openalex.org/C144170203","wikidata":"https://www.wikidata.org/wiki/Q5511099","display_name":"Fuzzy associative matrix","level":5,"score":0.44848617911338806},{"id":"https://openalex.org/C2988629283","wikidata":"https://www.wikidata.org/wiki/Q44337","display_name":"Complex matrix","level":2,"score":0.4170020520687103},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4108726382255554},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.38416147232055664},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3725234866142273},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3510661721229553},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3132322430610657},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.24576762318611145},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1168944239616394},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.09084922075271606},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.048523664474487305},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/ifs-151781","is_oa":false,"landing_page_url":"https://doi.org/10.3233/ifs-151781","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W18761891","https://openalex.org/W98520975","https://openalex.org/W1968027854","https://openalex.org/W1991563226","https://openalex.org/W1994178762","https://openalex.org/W1994564996","https://openalex.org/W1999926626","https://openalex.org/W2001671417","https://openalex.org/W2011925762","https://openalex.org/W2016429950","https://openalex.org/W2026963137","https://openalex.org/W2034996258","https://openalex.org/W2036102558","https://openalex.org/W2038857808","https://openalex.org/W2053292296","https://openalex.org/W2057691974","https://openalex.org/W2068497999","https://openalex.org/W2096768134","https://openalex.org/W2496352033","https://openalex.org/W4300491437"],"related_works":["https://openalex.org/W2024859344","https://openalex.org/W2954759830","https://openalex.org/W2155269963","https://openalex.org/W4234906133","https://openalex.org/W2358830440","https://openalex.org/W129962512","https://openalex.org/W2057887528","https://openalex.org/W1592580928","https://openalex.org/W2125337377","https://openalex.org/W2914616530"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,86,102,107,110,113,192],"fuzzy":[4,80,89],"dual":[5,90],"matrix":[6],"system":[7],"as":[8],"<mml:math":[9,54,65,116,150],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[10,55,66,117,151],"overflow=\"scroll\">":[11,56,67,118,152],"<mml:mi>A</mml:mi>":[12,119,154],"<mml:mover":[13,20,28,35,57,68,120,127,135,142,158,166,176],"accent=\"true\">":[14,21,29,36,58,69,121,128,136,143,159,167,177],"<mml:mi>x</mml:mi>":[15,30,122,137,160],"<mml:mo":[16,23,31,38,60,71,123,130,138,145,161,169,179],"stretchy=\"true\">\u02dc</mml:mo>":[17,24,32,39,61,72,124,131,139,146,162,170,180],"</mml:mover>":[18,25,33,40,62,73,125,132,140,147,163,171,181],"<mml:mo>+</mml:mo>":[19,34,126,141],"<mml:mi>B</mml:mi>":[22,59,129,178],"<mml:mo>=</mml:mo>":[26,133,164],"<mml:mi>C</mml:mi>":[27,134,156],"<mml:mi>D</mml:mi>":[37,70,144,168],"</mml:math>":[41,63,74,148,183],"in":[42],"which":[43],"A":[44],",":[45,64],"C":[46],"are":[47,75,188],"n":[48,50,76,78],"\u00d7":[49,77],"crisp":[51],"matrices":[52,81],"and":[53,96,149],"LR":[79],"is":[82],"studied.":[83],"To":[84],"obtain":[85],"solution":[87],"of":[88,112,115],"system,":[91],"we":[92,105],"initially":[93],"solve":[94],"1-cut":[95],"use":[97],"minimization":[98],"problem":[99],"to":[100,190],"calculate":[101],"spreads.":[103],"Afterwards,":[104],"explain":[106],"relationship":[108],"between":[109],"solutions":[111],"systems":[114],"<mml:mo>(</mml:mo>":[153,165],"<mml:mo>-</mml:mo>":[155],"<mml:mo>)</mml:mo>":[157,182],"<mml:munder>":[172],"<mml:mo>\u2296</mml:mo>":[173],"<mml:mi>h</mml:mi>":[174],"</mml:munder>":[175],".":[184],"Finally,":[185],"some":[186],"examples":[187],"solved":[189],"illustrate":[191],"proposed":[193],"method.":[194]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}