{"id":"https://openalex.org/W4386051102","doi":"https://doi.org/10.3390/sym15081617","title":"Novel Approach to Multi-Criteria Decision-Making Based on the n,mPR-Fuzzy Weighted Power Average Operator","display_name":"Novel Approach to Multi-Criteria Decision-Making Based on the n,mPR-Fuzzy Weighted Power Average Operator","publication_year":2023,"publication_date":"2023-08-21","ids":{"openalex":"https://openalex.org/W4386051102","doi":"https://doi.org/10.3390/sym15081617"},"language":"en","primary_location":{"id":"doi:10.3390/sym15081617","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15081617","pdf_url":"https://www.mdpi.com/2073-8994/15/8/1617/pdf?version=1692628399","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/8/1617/pdf?version=1692628399","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009403196","display_name":"Tareq Hamadneh","orcid":"https://orcid.org/0000-0003-1867-8111"},"institutions":[{"id":"https://openalex.org/I145019703","display_name":"Al-Zaytoonah University of Jordan","ror":"https://ror.org/04a5b0p13","country_code":"JO","type":"education","lineage":["https://openalex.org/I145019703"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Tareq Hamadneh","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Al Zaytoonah University of Jordan, Amman 11733, Jordan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Al Zaytoonah University of Jordan, Amman 11733, Jordan","institution_ids":["https://openalex.org/I145019703"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088345458","display_name":"Hariwan Z. Ibrahim","orcid":"https://orcid.org/0000-0001-9417-2695"},"institutions":[{"id":"https://openalex.org/I36162470","display_name":"University of Zakho","ror":"https://ror.org/05sd1pz50","country_code":"IQ","type":"education","lineage":["https://openalex.org/I36162470"]}],"countries":["IQ"],"is_corresponding":true,"raw_author_name":"Hariwan Z. Ibrahim","raw_affiliation_strings":["Department of Mathematics, Faculty of Education, University of Zakho, Zakho 42002, Iraq"],"raw_orcid":"https://orcid.org/0000-0001-9417-2695","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Education, University of Zakho, Zakho 42002, Iraq","institution_ids":["https://openalex.org/I36162470"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038992753","display_name":"Mayada Abualhomos","orcid":null},"institutions":[{"id":"https://openalex.org/I146367977","display_name":"Applied Science Private University","ror":"https://ror.org/01ah6nb52","country_code":"JO","type":"education","lineage":["https://openalex.org/I146367977"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Mayada Abualhomos","raw_affiliation_strings":["Department Basic Science, Applied Science Private University Applied Science Research Center (ASRC), Amman 11733, Jordan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department Basic Science, Applied Science Private University Applied Science Research Center (ASRC), Amman 11733, Jordan","institution_ids":["https://openalex.org/I146367977"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047802215","display_name":"Maha Mohammed Saeed","orcid":"https://orcid.org/0000-0001-6416-8097"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Maha Mohammed Saeed","raw_affiliation_strings":["Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-6416-8097","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039588198","display_name":"Gharib Gharib","orcid":null},"institutions":[{"id":"https://openalex.org/I153687341","display_name":"Zarqa University","ror":"https://ror.org/01wf1es90","country_code":"JO","type":"education","lineage":["https://openalex.org/I153687341"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Gharib Gharib","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan","institution_ids":["https://openalex.org/I153687341"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089688788","display_name":"Maha Al Soudi","orcid":null},"institutions":[{"id":"https://openalex.org/I146367977","display_name":"Applied Science Private University","ror":"https://ror.org/01ah6nb52","country_code":"JO","type":"education","lineage":["https://openalex.org/I146367977"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Maha Al Soudi","raw_affiliation_strings":["Department of Basic Scientific Sciences, Applied Science Private University, Amman 11931, Jordan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Basic Scientific Sciences, Applied Science Private University, Amman 11931, Jordan","institution_ids":["https://openalex.org/I146367977"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073384990","display_name":"Abdallah Al-Husban","orcid":"https://orcid.org/0000-0002-1682-7809"},"institutions":[{"id":"https://openalex.org/I97864281","display_name":"Irbid National University","ror":"https://ror.org/00xfxvy87","country_code":"JO","type":"education","lineage":["https://openalex.org/I97864281"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Abdallah Al-Husban","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 21110, Jordan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 21110, Jordan","institution_ids":["https://openalex.org/I97864281"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5088345458"],"corresponding_institution_ids":["https://openalex.org/I36162470"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.2466,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.5841242,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"15","issue":"8","first_page":"1617","last_page":"1617"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9889000058174133,"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":0.984499990940094,"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":0.6872303485870361},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6117745637893677},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.604744553565979},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5654044151306152},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.476483553647995},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.47398725152015686},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.46571803092956543},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4489978849887848},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.4216911196708679},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24663114547729492},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22604301571846008},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.04999402165412903}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6872303485870361},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6117745637893677},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.604744553565979},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5654044151306152},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.476483553647995},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.47398725152015686},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.46571803092956543},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4489978849887848},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.4216911196708679},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24663114547729492},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22604301571846008},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.04999402165412903},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15081617","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15081617","pdf_url":"https://www.mdpi.com/2073-8994/15/8/1617/pdf?version=1692628399","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:47f44ebd8aae42c8b75669bd46b9ed39","is_oa":true,"landing_page_url":"https://doaj.org/article/47f44ebd8aae42c8b75669bd46b9ed39","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 8, p 1617 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/8/1617/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15081617","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15081617","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15081617","pdf_url":"https://www.mdpi.com/2073-8994/15/8/1617/pdf?version=1692628399","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.47999998927116394}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386051102.pdf","grobid_xml":"https://content.openalex.org/works/W4386051102.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W1829951598","https://openalex.org/W1971875039","https://openalex.org/W1975978615","https://openalex.org/W1980564456","https://openalex.org/W1981107087","https://openalex.org/W1991446918","https://openalex.org/W2013932252","https://openalex.org/W2048524688","https://openalex.org/W2079457935","https://openalex.org/W2274512035","https://openalex.org/W2414387118","https://openalex.org/W2514754342","https://openalex.org/W2550247067","https://openalex.org/W2557959610","https://openalex.org/W2789613617","https://openalex.org/W2791638390","https://openalex.org/W2803228996","https://openalex.org/W2951141814","https://openalex.org/W2953509089","https://openalex.org/W2993467904","https://openalex.org/W2994797833","https://openalex.org/W2996837744","https://openalex.org/W3005435758","https://openalex.org/W3149124570","https://openalex.org/W3200407878","https://openalex.org/W3216781731","https://openalex.org/W4211007335","https://openalex.org/W4224098431","https://openalex.org/W4248851180","https://openalex.org/W4295308538","https://openalex.org/W4296079518","https://openalex.org/W4300972290","https://openalex.org/W4319159741","https://openalex.org/W4320502365","https://openalex.org/W4327517853","https://openalex.org/W4361291544","https://openalex.org/W4372219029","https://openalex.org/W4377223753","https://openalex.org/W6774250644"],"related_works":["https://openalex.org/W2674573885","https://openalex.org/W2253053392","https://openalex.org/W2184441312","https://openalex.org/W2331106272","https://openalex.org/W2614887008","https://openalex.org/W1542808721","https://openalex.org/W2121560876","https://openalex.org/W1485268022","https://openalex.org/W1486684451","https://openalex.org/W4361984403"],"abstract_inverted_index":{"A":[0],"significant":[1],"addition":[2],"to":[3,19,41,119,174],"fuzzy":[4,16,28,33,66,81,85,92,108,136,145,159,212,221,228,237],"set":[5,67],"theory":[6],"for":[7],"expressing":[8],"uncertain":[9,38],"data":[10],"is":[11,71],"an":[12,62,79],"n,m-th":[13,30,63,105,133,142,156],"power":[14,22,31,64,90,106,134,138,143,157,214,219,223,230,239],"root":[15,32,65,91,107,135,144,158,220],"set.":[17,93],"Compared":[18],"the":[20,51,58,75,132,164,176,179,190,203,206,210,217,226,234],"nth":[21,89,218],"root,":[23],"Fermatean,":[24],"Pythagorean,":[25],"and":[26,87,147,166,184,233],"intuitionistic":[27,80],"sets,":[29,160],"sets":[34,109,146],"can":[35,188],"cover":[36],"more":[37,56,72],"situations":[39],"due":[40],"their":[42,115],"greater":[43],"range":[44],"of":[45,61,78,101,114,150,182,205],"displayed":[46],"membership":[47],"grades.":[48],"When":[49],"discussing":[50],"symmetry":[52],"between":[53],"two":[54],"or":[55],"objects,":[57],"innovative":[59],"concept":[60],"over":[68],"dual":[69],"universes":[70],"flexible":[73],"than":[74],"current":[76],"notion":[77],"set,":[82,86],"a":[83,88,99,112,126],"Pythagorean":[84],"In":[94],"this":[95,172],"study,":[96],"we":[97,124,161,170,187,201],"demonstrate":[98,148],"number":[100,113],"additional":[102],"operations":[103],"on":[104],"along":[110],"with":[111,121,178,209],"special":[116],"aspects.":[117],"Additionally,":[118],"deal":[120],"choice":[122],"information,":[123],"create":[125],"novel":[127],"weighted":[128,137,213,222,229,238],"aggregated":[129],"operator":[130,173,208],"called":[131],"average":[139,215,224,231,240],"(FWPAmn)":[140],"across":[141],"some":[149],"its":[151],"fundamental":[152],"features.":[153],"To":[154],"rank":[155],"also":[162],"define":[163],"score":[165,198],"accuracy":[167],"functions.":[168],"Moreover,":[169],"use":[171],"identify":[175],"countries":[177],"best":[180,191],"standards":[181],"living":[183],"show":[185],"how":[186],"select":[189],"option":[192],"by":[193],"contrasting":[194],"aggregate":[195],"results":[196,204],"using":[197],"values.":[199],"Finally,":[200],"contrast":[202],"FWPAmn":[207],"square-root":[211],"(SR-FWPA),":[216],"(nPR-FWPA),":[225],"Fermatean":[227],"(FFWPA),":[232],"n,m-rung":[235],"orthopair":[236],"(n,m-ROFWPA)":[241],"operators.":[242]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
