{"id":"https://openalex.org/W2888837581","doi":"https://doi.org/10.3390/g9030062","title":"Matrix Games with Interval-Valued 2-Tuple Linguistic Information","display_name":"Matrix Games with Interval-Valued 2-Tuple Linguistic Information","publication_year":2018,"publication_date":"2018-09-02","ids":{"openalex":"https://openalex.org/W2888837581","doi":"https://doi.org/10.3390/g9030062","mag":"2888837581"},"language":"en","primary_location":{"id":"doi:10.3390/g9030062","is_oa":true,"landing_page_url":"https://doi.org/10.3390/g9030062","pdf_url":"https://www.mdpi.com/2073-4336/9/3/62/pdf?version=1536230448","source":{"id":"https://openalex.org/S6552842","display_name":"Games","issn_l":"2073-4336","issn":["2073-4336"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Games","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-4336/9/3/62/pdf?version=1536230448","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101582339","display_name":"Anjali Singh","orcid":"https://orcid.org/0000-0003-1414-9255"},"institutions":[{"id":"https://openalex.org/I863896202","display_name":"Delhi Technological University","ror":"https://ror.org/01ztcvt22","country_code":"IN","type":"education","lineage":["https://openalex.org/I863896202"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Anjali Singh","raw_affiliation_strings":["Department of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi 110042, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi 110042, India","institution_ids":["https://openalex.org/I863896202"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067640234","display_name":"Anjana Gupta","orcid":"https://orcid.org/0000-0002-6514-0851"},"institutions":[{"id":"https://openalex.org/I863896202","display_name":"Delhi Technological University","ror":"https://ror.org/01ztcvt22","country_code":"IN","type":"education","lineage":["https://openalex.org/I863896202"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Anjana Gupta","raw_affiliation_strings":["Department of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi 110042, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi 110042, India","institution_ids":["https://openalex.org/I863896202"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067640234"],"corresponding_institution_ids":["https://openalex.org/I863896202"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.0302,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.79295539,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"9","issue":"3","first_page":"62","last_page":"62"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.996999979019165,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/mathematics","display_name":"Mathematics","score":0.6550627946853638},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5896484851837158},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5664844512939453},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.561122477054596},{"id":"https://openalex.org/keywords/tuple","display_name":"Tuple","score":0.4920751452445984},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.48966696858406067},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.4570044279098511},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.45076924562454224},{"id":"https://openalex.org/keywords/zero-sum-game","display_name":"Zero-sum game","score":0.42766863107681274},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4256208539009094},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.41279226541519165},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4023001790046692},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.3517817556858063},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3319008946418762},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3241501748561859},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22485411167144775},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1668902039527893},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15259695053100586}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6550627946853638},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5896484851837158},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5664844512939453},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.561122477054596},{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.4920751452445984},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.48966696858406067},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.4570044279098511},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.45076924562454224},{"id":"https://openalex.org/C136356330","wikidata":"https://www.wikidata.org/wiki/Q156612","display_name":"Zero-sum game","level":3,"score":0.42766863107681274},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4256208539009094},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.41279226541519165},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4023001790046692},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.3517817556858063},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3319008946418762},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3241501748561859},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22485411167144775},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1668902039527893},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15259695053100586},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/g9030062","is_oa":true,"landing_page_url":"https://doi.org/10.3390/g9030062","pdf_url":"https://www.mdpi.com/2073-4336/9/3/62/pdf?version=1536230448","source":{"id":"https://openalex.org/S6552842","display_name":"Games","issn_l":"2073-4336","issn":["2073-4336"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Games","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:gam:jgames:v:9:y:2018:i:3:p:62-:d:167312","is_oa":false,"landing_page_url":"https://www.mdpi.com/2073-4336/9/3/62/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:343b892b8e7e44479c82c1b658eddddc","is_oa":true,"landing_page_url":"https://doaj.org/article/343b892b8e7e44479c82c1b658eddddc","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Games, Vol 9, Iss 3, p 62 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-4336/9/3/62/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/g9030062","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Games","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/g9030062","is_oa":true,"landing_page_url":"https://doi.org/10.3390/g9030062","pdf_url":"https://www.mdpi.com/2073-4336/9/3/62/pdf?version=1536230448","source":{"id":"https://openalex.org/S6552842","display_name":"Games","issn_l":"2073-4336","issn":["2073-4336"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Games","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Quality Education","score":0.46000000834465027,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2888837581.pdf","grobid_xml":"https://content.openalex.org/works/W2888837581.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W103580892","https://openalex.org/W148430901","https://openalex.org/W1965096608","https://openalex.org/W1967808599","https://openalex.org/W1976073056","https://openalex.org/W1982178237","https://openalex.org/W1984810795","https://openalex.org/W1987751188","https://openalex.org/W2019703543","https://openalex.org/W2053655527","https://openalex.org/W2066431549","https://openalex.org/W2084311211","https://openalex.org/W2095452642","https://openalex.org/W2109810797","https://openalex.org/W2115880485","https://openalex.org/W2117827905","https://openalex.org/W2216147994","https://openalex.org/W2408477877","https://openalex.org/W2586534073","https://openalex.org/W2888837581","https://openalex.org/W6713575793","https://openalex.org/W6732723677"],"related_works":["https://openalex.org/W4245395944","https://openalex.org/W2143551613","https://openalex.org/W2138823233","https://openalex.org/W1979740464","https://openalex.org/W2143345456","https://openalex.org/W1789991335","https://openalex.org/W2562731034","https://openalex.org/W4315705795","https://openalex.org/W2804582172","https://openalex.org/W1565282301"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,16,23,35,108],"two-player":[4,131],"constant-sum":[5,132],"interval-valued":[6,59,136],"2-tuple":[7,137],"linguistic":[8,17,28,39,49,54,60,84,138],"matrix":[9,18,85],"game":[10,19,86,133],"is":[11,20,44,72,99,104],"construed.":[12],"The":[13,67,102,123],"value":[14,61],"of":[15,26,37,57,62,65,70,79,81,115],"proven":[21],"as":[22],"non-decreasing":[24],"function":[25],"the":[27,31,48,53,58,77,82,96,113,116,120,130],"values":[29,80],"in":[30,119,129],"payoffs,":[32],"and,":[33],"hence,":[34],"pair":[36],"auxiliary":[38],"linear":[40],"programming":[41],"(LLP)":[42],"problems":[43,134],"formulated":[45],"to":[46,75,94,111],"obtain":[47],"lower":[50],"bound":[51,56],"and":[52,90],"upper":[55],"such":[63],"class":[64],"games.":[66],"duality":[68],"theorem":[69],"LLP":[71],"also":[73,100],"adopted":[74],"establish":[76],"equality":[78],"interval":[83],"for":[87],"players":[88],"I":[89],"II.":[91],"A":[92],"flowchart":[93],"summarize":[95],"proposed":[97,117],"algorithm":[98,125],"given.":[101],"methodology":[103],"then":[105],"illustrated":[106],"via":[107],"hypothetical":[109],"example":[110],"demonstrate":[112],"applicability":[114],"theory":[118],"real":[121],"world.":[122],"designed":[124],"demonstrates":[126],"acceptable":[127],"results":[128],"with":[135],"payoffs.":[139]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}