{"id":"https://openalex.org/W3159501514","doi":"https://doi.org/10.1515/jisys-2020-0095","title":"On characterizing solution for multi-objective fractional two-stage solid transportation problem under fuzzy environment","display_name":"On characterizing solution for multi-objective fractional two-stage solid transportation problem under fuzzy environment","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3159501514","doi":"https://doi.org/10.1515/jisys-2020-0095","mag":"3159501514"},"language":"en","primary_location":{"id":"doi:10.1515/jisys-2020-0095","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jisys-2020-0095","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jisys-2020-0095/pdf","source":{"id":"https://openalex.org/S2764846071","display_name":"Journal of Intelligent Systems","issn_l":"0334-1860","issn":["0334-1860","2191-026X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315148","host_organization_name":"IlmuKomputer.Com","host_organization_lineage":["https://openalex.org/P4310315148"],"host_organization_lineage_names":["IlmuKomputer.Com"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.degruyter.com/document/doi/10.1515/jisys-2020-0095/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103023240","display_name":"Hamiden Abd El-Wahed Khalifa","orcid":null},"institutions":[{"id":"https://openalex.org/I145487455","display_name":"Cairo University","ror":"https://ror.org/03q21mh05","country_code":"EG","type":"education","lineage":["https://openalex.org/I145487455"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Hamiden Abd El-Wahed Khalifa","raw_affiliation_strings":["Operations Research Department, Faculty of Graduate Studies for Statistical Research, Cairo University , Giza , Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Operations Research Department, Faculty of Graduate Studies for Statistical Research, Cairo University , Giza , Egypt","institution_ids":["https://openalex.org/I145487455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101398697","display_name":"Pavan Kumar","orcid":"https://orcid.org/0000-0001-5340-7777"},"institutions":[{"id":"https://openalex.org/I464993","display_name":"Barkatullah University","ror":"https://ror.org/02ax13658","country_code":"IN","type":"education","lineage":["https://openalex.org/I464993"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Pavan Kumar","raw_affiliation_strings":["Mathematics Division, School of Advanced Science and Languages, VIT Bhopal University , Sehore , MP 466114 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Division, School of Advanced Science and Languages, VIT Bhopal University , Sehore , MP 466114 , India","institution_ids":["https://openalex.org/I464993"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075392453","display_name":"Majed Alharbi","orcid":null},"institutions":[{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Majed. G. Alharbi","raw_affiliation_strings":["Mathematics Department, College of Science and Arts, El-Methnab, Qassim University , Methnab , Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, College of Science and Arts, El-Methnab, Qassim University , Methnab , Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101398697"],"corresponding_institution_ids":["https://openalex.org/I464993"],"apc_list":{"value":1000,"currency":"EUR","value_usd":1078},"apc_paid":{"value":1000,"currency":"EUR","value_usd":1078},"fwci":1.4887,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.81637007,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"30","issue":"1","first_page":"620","last_page":"635"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9535999894142151,"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":0.5067771077156067},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3977581560611725},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33772850036621094},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32886213064193726},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32441097497940063},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11648750305175781}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5067771077156067},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3977581560611725},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33772850036621094},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32886213064193726},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32441097497940063},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11648750305175781}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/jisys-2020-0095","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jisys-2020-0095","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jisys-2020-0095/pdf","source":{"id":"https://openalex.org/S2764846071","display_name":"Journal of Intelligent Systems","issn_l":"0334-1860","issn":["0334-1860","2191-026X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315148","host_organization_name":"IlmuKomputer.Com","host_organization_lineage":["https://openalex.org/P4310315148"],"host_organization_lineage_names":["IlmuKomputer.Com"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:594e308dfada4afd8c6011f997580ec1","is_oa":true,"landing_page_url":"https://doaj.org/article/594e308dfada4afd8c6011f997580ec1","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":"Journal of Intelligent Systems, Vol 30, Iss 1, Pp 620-635 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/jisys-2020-0095","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jisys-2020-0095","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jisys-2020-0095/pdf","source":{"id":"https://openalex.org/S2764846071","display_name":"Journal of Intelligent Systems","issn_l":"0334-1860","issn":["0334-1860","2191-026X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315148","host_organization_name":"IlmuKomputer.Com","host_organization_lineage":["https://openalex.org/P4310315148"],"host_organization_lineage_names":["IlmuKomputer.Com"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320324403","display_name":"Qassim University","ror":"https://ror.org/01wsfe280"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3159501514.pdf","grobid_xml":"https://content.openalex.org/works/W3159501514.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1966757346","https://openalex.org/W1967677376","https://openalex.org/W1972038524","https://openalex.org/W1992089421","https://openalex.org/W1992773137","https://openalex.org/W1994997349","https://openalex.org/W2003610871","https://openalex.org/W2045029812","https://openalex.org/W2055098718","https://openalex.org/W2061608598","https://openalex.org/W2077646062","https://openalex.org/W2102618289","https://openalex.org/W2111979370","https://openalex.org/W2156577211","https://openalex.org/W2172782373","https://openalex.org/W2186295708","https://openalex.org/W2302349006","https://openalex.org/W2330022088","https://openalex.org/W2463017232","https://openalex.org/W2500362673","https://openalex.org/W2588269456","https://openalex.org/W2903840207","https://openalex.org/W2933200186","https://openalex.org/W2943864676","https://openalex.org/W3001553400","https://openalex.org/W3014207952","https://openalex.org/W4211007335","https://openalex.org/W6702266818"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W2271181815"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"article":[2],"attempts":[3],"to":[4,128,139,179],"study":[5],"cost":[6,15],"minimizing":[7],"multi-objective":[8,147],"fractional":[9],"solid":[10],"transportation":[11],"problem":[12,132],"with":[13],"fuzzy":[14,39,59,79,99],"coefficients":[16],"<m:math":[17,42,61,81],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[18,43,62,82],"<m:msubsup>":[19],"<m:mrow>":[20,27,32,45,52,64,71,84,91],"<m:mover":[21,46,65,85],"accent=\"true\">":[22,47,66,86],"<m:mi>c</m:mi>":[23],"<m:mo>\u02dc</m:mo>":[24,49,68,88],"</m:mover>":[25,50,69,89],"</m:mrow>":[26,31,34,51,54,70,73,90,93],"<m:mi>i</m:mi>":[28,53],"<m:mi>j</m:mi>":[29,72],"<m:mi>k</m:mi>":[30,92],"<m:mi>r</m:mi>":[33],"</m:msubsup>":[35],"</m:math>":[36,56,75,95],"{\\tilde{c}}_{ijk}^{r}":[37],",":[38,58,77],"supply":[40],"quantities":[41],"<m:msub>":[44,63,83],"<m:mi>a</m:mi>":[48],"</m:msub>":[55,74,94],"{\\tilde{a}}_{i}":[57],"demands":[60],"<m:mi>b</m:mi>":[67],"{\\tilde{b}}_{j}":[76],"and/or":[78],"conveyances":[80],"<m:mi>e</m:mi>":[87],"{\\tilde{e}}_{k}":[96],".":[97],"The":[98,160],"efficient":[100,108],"concept":[101],"is":[102,110,120,126,158,167,174],"introduced":[103],"in":[104],"which":[105],"the":[106,118,130,141,155,164,181,184],"crisp":[107,131],"solution":[109,119,144],"extended.":[111],"A":[112,150,171],"necessary":[113],"and":[114,169,178],"sufficient":[115],"condition":[116],"for":[117,154,176],"established.":[121],"Fuzzy":[122],"geometric":[123],"programming":[124],"approach":[125],"applied":[127],"solve":[129],"by":[133],"defining":[134],"membership":[135,152],"function":[136,153,157],"so":[137],"as":[138],"obtain":[140],"optimal":[142],"compromise":[143],"of":[145,163,183],"a":[146],"two-stage":[148],"problem.":[149],"linear":[151],"objective":[156],"defined.":[159],"stability":[161],"set":[162],"first":[165],"kind":[166],"defined":[168],"determined.":[170],"numerical":[172],"example":[173],"given":[175],"illustration":[177],"check":[180],"validity":[182],"proposed":[185],"approach.":[186]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}