{"id":"https://openalex.org/W4388660517","doi":"https://doi.org/10.3390/axioms12111048","title":"Multi-Objective Non-Linear Programming Problems in Linear Diophantine Fuzzy Environment","display_name":"Multi-Objective Non-Linear Programming Problems in Linear Diophantine Fuzzy Environment","publication_year":2023,"publication_date":"2023-11-13","ids":{"openalex":"https://openalex.org/W4388660517","doi":"https://doi.org/10.3390/axioms12111048"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12111048","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms12111048","pdf_url":"https://www.mdpi.com/2075-1680/12/11/1048/pdf","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/11/1048/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023221951","display_name":"Salma Iqbal","orcid":"https://orcid.org/0009-0003-2896-7408"},"institutions":[{"id":"https://openalex.org/I195024194","display_name":"Riphah International University","ror":"https://ror.org/02kdm5630","country_code":"PK","type":"education","lineage":["https://openalex.org/I195024194"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Salma Iqbal","raw_affiliation_strings":["Department of Mathematics and Statistics, Riphah International University, Sector I-14, Islamabad 44000, Pakistan"],"raw_orcid":"https://orcid.org/0009-0003-2896-7408","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Riphah International University, Sector I-14, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026211730","display_name":"Naveed Yaqoob","orcid":"https://orcid.org/0000-0002-5362-9916"},"institutions":[{"id":"https://openalex.org/I195024194","display_name":"Riphah International University","ror":"https://ror.org/02kdm5630","country_code":"PK","type":"education","lineage":["https://openalex.org/I195024194"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Naveed Yaqoob","raw_affiliation_strings":["Department of Mathematics and Statistics, Riphah International University, Sector I-14, Islamabad 44000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-5362-9916","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Riphah International University, Sector I-14, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030602859","display_name":"Muhammad Gulistan","orcid":"https://orcid.org/0000-0002-0314-876X"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Muhammad Gulistan","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2R3, Canada"],"raw_orcid":"https://orcid.org/0000-0002-0314-876X","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2R3, Canada","institution_ids":["https://openalex.org/I154425047"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030602859"],"corresponding_institution_ids":["https://openalex.org/I154425047"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.2317,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.47667176,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"12","issue":"11","first_page":"1048","last_page":"1048"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9994000196456909,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9993000030517578,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9955000281333923,"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/diophantine-equation","display_name":"Diophantine equation","score":0.8392791152000427},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6191450357437134},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.6030324697494507},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5786025524139404},{"id":"https://openalex.org/keywords/linear-fractional-programming","display_name":"Linear-fractional programming","score":0.5681850910186768},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5657275319099426},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.5558308362960815},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4900621175765991},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3321380019187927},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.13531294465065002},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11172148585319519}],"concepts":[{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.8392791152000427},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6191450357437134},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.6030324697494507},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5786025524139404},{"id":"https://openalex.org/C205658194","wikidata":"https://www.wikidata.org/wiki/Q4168281","display_name":"Linear-fractional programming","level":3,"score":0.5681850910186768},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5657275319099426},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.5558308362960815},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4900621175765991},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3321380019187927},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.13531294465065002},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11172148585319519},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12111048","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms12111048","pdf_url":"https://www.mdpi.com/2075-1680/12/11/1048/pdf","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:0bd6658dc28240dfbd8360dd68870a77","is_oa":true,"landing_page_url":"https://doaj.org/article/0bd6658dc28240dfbd8360dd68870a77","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":"Axioms, Vol 12, Iss 11, p 1048 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/11/1048/","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12111048","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":"Axioms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12111048","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms12111048","pdf_url":"https://www.mdpi.com/2075-1680/12/11/1048/pdf","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7900000214576721}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4388660517.pdf","grobid_xml":"https://content.openalex.org/works/W4388660517.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1980564456","https://openalex.org/W1982109263","https://openalex.org/W2023290810","https://openalex.org/W2034406580","https://openalex.org/W2085888792","https://openalex.org/W2086393750","https://openalex.org/W2094463119","https://openalex.org/W2099867994","https://openalex.org/W2156056332","https://openalex.org/W2176210190","https://openalex.org/W2183108822","https://openalex.org/W2186554366","https://openalex.org/W2345111119","https://openalex.org/W2471786331","https://openalex.org/W2490197496","https://openalex.org/W2973775716","https://openalex.org/W3108507338","https://openalex.org/W3208668603","https://openalex.org/W4292158025","https://openalex.org/W4321602805","https://openalex.org/W6686656750","https://openalex.org/W6720584126","https://openalex.org/W6802320697"],"related_works":["https://openalex.org/W4205348974","https://openalex.org/W3182682721","https://openalex.org/W4386394964","https://openalex.org/W2080462934","https://openalex.org/W2182614003","https://openalex.org/W175643398","https://openalex.org/W2368660077","https://openalex.org/W4245568382","https://openalex.org/W90125000","https://openalex.org/W2130484549"],"abstract_inverted_index":{"Due":[0],"to":[1,24,40,56],"various":[2],"unpredictable":[3],"factors,":[4],"a":[5,27,58,62],"decision":[6],"maker":[7],"frequently":[8],"experiences":[9],"uncertainty":[10],"and":[11,31,79],"hesitation":[12],"when":[13],"dealing":[14],"with":[15],"real-world":[16],"practical":[17],"optimization":[18],"problems.":[19],"At":[20],"times,":[21],"it\u2019s":[22],"necessary":[23],"simultaneously":[25],"optimize":[26],"number":[28],"of":[29,52,74,93],"non-linear":[30],"competing":[32],"objectives.":[33],"Linear":[34],"Diophantine":[35,64,84],"fuzzy":[36,65,85],"numbers":[37,86],"are":[38,82],"used":[39],"address":[41],"the":[42,72,75,80,91,94],"uncertain":[43],"parameters":[44],"that":[45],"arise":[46],"in":[47],"these":[48],"circumstances.":[49],"The":[50],"objective":[51],"this":[53],"manuscript":[54],"is":[55,105],"present":[57],"method":[59],"for":[60],"solving":[61],"linear":[63,83],"multi-objective":[66,77],"nonlinear":[67,76,95],"programming":[68,96],"problem":[69,97],"(LDFMONLPP).":[70],"All":[71],"coefficients":[73],"functions":[78],"constraints":[81],"(LDFNs).":[87],"Here":[88],"we":[89],"find":[90],"solution":[92],"by":[98],"using":[99],"Karush-Kuhn-Tucker":[100],"condition.":[101],"A":[102],"numerical":[103],"example":[104],"presented.":[106]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}