{"id":"https://openalex.org/W2148857004","doi":"https://doi.org/10.1016/j.fss.2009.04.012","title":"Bector\u2013Chandra type duality in fuzzy linear programming with exponential membership functions","display_name":"Bector\u2013Chandra type duality in fuzzy linear programming with exponential membership functions","publication_year":2009,"publication_date":"2009-05-09","ids":{"openalex":"https://openalex.org/W2148857004","doi":"https://doi.org/10.1016/j.fss.2009.04.012","mag":"2148857004"},"language":"en","primary_location":{"id":"doi:10.1016/j.fss.2009.04.012","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.fss.2009.04.012","pdf_url":null,"source":{"id":"https://openalex.org/S169411308","display_name":"Fuzzy Sets and Systems","issn_l":"0165-0114","issn":["0165-0114","1872-6801"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Sets and 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/A5100746367","display_name":"Pankaj Gupta","orcid":"https://orcid.org/0000-0002-1963-7998"},"institutions":[{"id":"https://openalex.org/I110166357","display_name":"University of Delhi","ror":"https://ror.org/04gzb2213","country_code":"IN","type":"education","lineage":["https://openalex.org/I110166357"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Pankaj Gupta","raw_affiliation_strings":["Department of Operational Research, University of Delhi, Delhi 110007, India"],"affiliations":[{"raw_affiliation_string":"Department of Operational Research, University of Delhi, Delhi 110007, India","institution_ids":["https://openalex.org/I110166357"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063421319","display_name":"Mukesh Kumar Mehlawat","orcid":"https://orcid.org/0000-0002-2516-009X"},"institutions":[{"id":"https://openalex.org/I110166357","display_name":"University of Delhi","ror":"https://ror.org/04gzb2213","country_code":"IN","type":"education","lineage":["https://openalex.org/I110166357"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Mukesh Kumar Mehlawat","raw_affiliation_strings":["Department of Operational Research, University of Delhi, Delhi 110007, India"],"affiliations":[{"raw_affiliation_string":"Department of Operational Research, University of Delhi, Delhi 110007, India","institution_ids":["https://openalex.org/I110166357"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100746367"],"corresponding_institution_ids":["https://openalex.org/I110166357"],"apc_list":{"value":2600,"currency":"USD","value_usd":2600},"apc_paid":null,"fwci":3.3365,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.92387543,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"160","issue":"22","first_page":"3290","last_page":"3308"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9986000061035156,"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"}},"topics":[{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9986000061035156,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.996399998664856,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8233155012130737},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.7886403799057007},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.666109561920166},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.6251701712608337},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5718635320663452},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5521135926246643},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5178864002227783},{"id":"https://openalex.org/keywords/membership-function","display_name":"Membership function","score":0.4634224474430084},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4611964225769043},{"id":"https://openalex.org/keywords/linear-fractional-programming","display_name":"Linear-fractional programming","score":0.42530566453933716},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.42029935121536255},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.39452075958251953},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3607821762561798},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32008302211761475},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.23974543809890747},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13116657733917236},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12651151418685913},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1084693968296051}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8233155012130737},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7886403799057007},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.666109561920166},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.6251701712608337},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5718635320663452},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5521135926246643},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5178864002227783},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.4634224474430084},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4611964225769043},{"id":"https://openalex.org/C205658194","wikidata":"https://www.wikidata.org/wiki/Q4168281","display_name":"Linear-fractional programming","level":3,"score":0.42530566453933716},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.42029935121536255},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.39452075958251953},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3607821762561798},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32008302211761475},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.23974543809890747},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13116657733917236},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12651151418685913},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1084693968296051},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.fss.2009.04.012","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.fss.2009.04.012","pdf_url":null,"source":{"id":"https://openalex.org/S169411308","display_name":"Fuzzy Sets and Systems","issn_l":"0165-0114","issn":["0165-0114","1872-6801"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Sets and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.41999998688697815}],"awards":[],"funders":[{"id":"https://openalex.org/F4320324131","display_name":"University of Delhi","ror":"https://ror.org/04gzb2213"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W51696563","https://openalex.org/W561707741","https://openalex.org/W965656746","https://openalex.org/W1480998404","https://openalex.org/W1527065579","https://openalex.org/W1536339261","https://openalex.org/W1964367769","https://openalex.org/W1966419780","https://openalex.org/W1972965943","https://openalex.org/W1974667273","https://openalex.org/W1979718274","https://openalex.org/W1991901402","https://openalex.org/W1992980798","https://openalex.org/W1994956719","https://openalex.org/W2009292267","https://openalex.org/W2014193286","https://openalex.org/W2015044099","https://openalex.org/W2015863315","https://openalex.org/W2022079630","https://openalex.org/W2022351043","https://openalex.org/W2022793254","https://openalex.org/W2023893673","https://openalex.org/W2032220291","https://openalex.org/W2043074703","https://openalex.org/W2058693307","https://openalex.org/W2074145107","https://openalex.org/W2084300620","https://openalex.org/W2090790440","https://openalex.org/W2090975713","https://openalex.org/W2096768134","https://openalex.org/W2107578669","https://openalex.org/W2131088269","https://openalex.org/W2133695364","https://openalex.org/W2171715801","https://openalex.org/W4292158025","https://openalex.org/W4298258403"],"related_works":["https://openalex.org/W2593555778","https://openalex.org/W2201555914","https://openalex.org/W2725387418","https://openalex.org/W2614523486","https://openalex.org/W640885572","https://openalex.org/W4220928172","https://openalex.org/W2089739134","https://openalex.org/W4205348974","https://openalex.org/W1991078291","https://openalex.org/W2053271671"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}