{"id":"https://openalex.org/W4416456292","doi":"https://doi.org/10.3390/sym17112013","title":"Belief Entropy-Based MAGDM Algorithm Under Double Hierarchy Quantum-like Bayesian Networks and Its Application to Wastewater Reuse","display_name":"Belief Entropy-Based MAGDM Algorithm Under Double Hierarchy Quantum-like Bayesian Networks and Its Application to Wastewater Reuse","publication_year":2025,"publication_date":"2025-11-20","ids":{"openalex":"https://openalex.org/W4416456292","doi":"https://doi.org/10.3390/sym17112013"},"language":"en","primary_location":{"id":"doi:10.3390/sym17112013","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17112013","pdf_url":null,"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"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/sym17112013","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065888879","display_name":"Juxiang Wang","orcid":"https://orcid.org/0000-0002-2591-0807"},"institutions":[{"id":"https://openalex.org/I118987531","display_name":"Anhui Jianzhu University","ror":"https://ror.org/0108wjw08","country_code":"CN","type":"education","lineage":["https://openalex.org/I118987531"]},{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Juxiang Wang","raw_affiliation_strings":["School of Management, Hefei University of Technology, Hefei 230009, China","School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China"],"affiliations":[{"raw_affiliation_string":"School of Management, Hefei University of Technology, Hefei 230009, China","institution_ids":["https://openalex.org/I16365422"]},{"raw_affiliation_string":"School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China","institution_ids":["https://openalex.org/I118987531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103909819","display_name":"Yaping Li","orcid":"https://orcid.org/0009-0000-4703-939X"},"institutions":[{"id":"https://openalex.org/I118987531","display_name":"Anhui Jianzhu University","ror":"https://ror.org/0108wjw08","country_code":"CN","type":"education","lineage":["https://openalex.org/I118987531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yaping Li","raw_affiliation_strings":["School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China","institution_ids":["https://openalex.org/I118987531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100633188","display_name":"Xin Wang","orcid":"https://orcid.org/0009-0006-4174-2811"},"institutions":[{"id":"https://openalex.org/I118987531","display_name":"Anhui Jianzhu University","ror":"https://ror.org/0108wjw08","country_code":"CN","type":"education","lineage":["https://openalex.org/I118987531"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xin Wang","raw_affiliation_strings":["School of Economics and Management, Anhui Jianzhu University, Hefei 230601, China"],"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Anhui Jianzhu University, Hefei 230601, China","institution_ids":["https://openalex.org/I118987531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101965830","display_name":"Yanjun Wang","orcid":"https://orcid.org/0000-0003-3702-5693"},"institutions":[{"id":"https://openalex.org/I118987531","display_name":"Anhui Jianzhu University","ror":"https://ror.org/0108wjw08","country_code":"CN","type":"education","lineage":["https://openalex.org/I118987531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanjun Wang","raw_affiliation_strings":["School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China","institution_ids":["https://openalex.org/I118987531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5065888879","https://openalex.org/A5100633188"],"corresponding_institution_ids":["https://openalex.org/I118987531","https://openalex.org/I16365422"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.41310367,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"11","first_page":"2013","last_page":"2013"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.7322999835014343,"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":0.7322999835014343,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.0754999965429306,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11781","display_name":"Wastewater Treatment and Reuse","score":0.027699999511241913,"subfield":{"id":"https://openalex.org/subfields/2311","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6783999800682068},{"id":"https://openalex.org/keywords/analytic-hierarchy-process","display_name":"Analytic hierarchy process","score":0.6297000050544739},{"id":"https://openalex.org/keywords/interference","display_name":"Interference (communication)","score":0.6110000014305115},{"id":"https://openalex.org/keywords/bayesian-network","display_name":"Bayesian network","score":0.5291000008583069},{"id":"https://openalex.org/keywords/reuse","display_name":"Reuse","score":0.521399974822998},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4959000051021576},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.444599986076355},{"id":"https://openalex.org/keywords/group-decision-making","display_name":"Group decision-making","score":0.43689998984336853}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7585999965667725},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6783999800682068},{"id":"https://openalex.org/C87345402","wikidata":"https://www.wikidata.org/wiki/Q485202","display_name":"Analytic hierarchy process","level":2,"score":0.6297000050544739},{"id":"https://openalex.org/C32022120","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference (communication)","level":3,"score":0.6110000014305115},{"id":"https://openalex.org/C33724603","wikidata":"https://www.wikidata.org/wiki/Q812540","display_name":"Bayesian network","level":2,"score":0.5291000008583069},{"id":"https://openalex.org/C206588197","wikidata":"https://www.wikidata.org/wiki/Q846574","display_name":"Reuse","level":2,"score":0.521399974822998},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4959000051021576},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45239999890327454},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.444599986076355},{"id":"https://openalex.org/C20701700","wikidata":"https://www.wikidata.org/wiki/Q388791","display_name":"Group decision-making","level":2,"score":0.43689998984336853},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.3970000147819519},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36550000309944153},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.35760000348091125},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.32760000228881836},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.3206999897956848},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.30090001225471497},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.29919999837875366},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.29789999127388},{"id":"https://openalex.org/C4727928","wikidata":"https://www.wikidata.org/wiki/Q17164759","display_name":"Social network (sociolinguistics)","level":3,"score":0.2939999997615814},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.2919999957084656},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2854999899864197},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.274399995803833},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.26840001344680786},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.263700008392334},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.25690001249313354}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17112013","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17112013","pdf_url":null,"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"}],"best_oa_location":{"id":"doi:10.3390/sym17112013","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17112013","pdf_url":null,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1989440127","https://openalex.org/W2031558795","https://openalex.org/W2042255315","https://openalex.org/W2279097834","https://openalex.org/W2291805171","https://openalex.org/W2474884296","https://openalex.org/W2507975617","https://openalex.org/W2750667128","https://openalex.org/W2756442192","https://openalex.org/W2767622660","https://openalex.org/W2783891841","https://openalex.org/W2791665655","https://openalex.org/W2806437363","https://openalex.org/W2887079029","https://openalex.org/W2901135652","https://openalex.org/W2912214273","https://openalex.org/W2970690932","https://openalex.org/W2998354321","https://openalex.org/W3092968205","https://openalex.org/W3108339430","https://openalex.org/W3121070152","https://openalex.org/W3124374074","https://openalex.org/W3133848806","https://openalex.org/W3154525851","https://openalex.org/W3159060543","https://openalex.org/W3179958725","https://openalex.org/W4245152641","https://openalex.org/W4253746549","https://openalex.org/W4297179788","https://openalex.org/W4302773705","https://openalex.org/W4319019086","https://openalex.org/W4321071964","https://openalex.org/W4385462584","https://openalex.org/W4386962834","https://openalex.org/W4387380864","https://openalex.org/W4399006685","https://openalex.org/W4405808783","https://openalex.org/W4408989407","https://openalex.org/W4410031799","https://openalex.org/W4410214348"],"related_works":[],"abstract_inverted_index":{"The":[0,34],"traditional":[1],"multi-attribute":[2],"group":[3],"decision-making":[4,25],"(MAGDM)":[5],"method":[6,83,163],"easily":[7],"ignores":[8],"the":[9,21,24,29,101,108,122,126,130,137,153,156,161],"interference":[10,31,86,117,147],"effect":[11],"among":[12,32],"decision-makers":[13],"(DMs),":[14],"while":[15],"quantum":[16,53,73],"theory":[17,74],"can":[18,42],"effectively":[19],"portray":[20],"uncertainty":[22],"in":[23,39],"process":[26],"and":[27,63,75,79,107,158],"quantify":[28],"preference":[30],"DMs.":[33],"asymmetry":[35],"of":[36,160,170],"evaluation":[37],"information":[38],"social":[40,76],"networks":[41],"have":[43],"a":[44,52,64,81,93,142],"significant":[45],"impact":[46],"on":[47,57,89,100,136,152],"decision-making.":[48],"In":[49],"this":[50],"paper,":[51],"MAGDM":[54,145],"algorithm":[55],"based":[56,88,99,135,151],"probabilistic":[58,102,143],"linguistic":[59,103,144],"term":[60],"sets":[61],"(PLTSs)":[62],"quantum-like":[65],"Bayesian":[66],"network":[67,77,96],"(QLBN)":[68],"is":[69,97,119,149],"proposed":[70,120,150],"(PL-QLBN),":[71],"utilizing":[72],"concepts":[78],"introducing":[80],"novel":[82],"for":[84,121],"calculating":[85],"effects":[87,148],"belief":[90],"entropy.":[91],"Firstly,":[92],"complete":[94],"trust":[95,104,113],"constructed":[98],"transfer":[105],"operator":[106],"minimum":[109],"path":[110],"method.":[111,140],"A":[112],"aggregation":[114],"method,":[115],"considering":[116,146],"effects,":[118],"QLBN":[123],"to":[124],"determine":[125],"DM":[127],"weights.":[128],"Next,":[129],"attribute":[131],"weights":[132],"are":[133,164],"calculated":[134],"entropy":[138],"weight":[139],"Then,":[141],"QLBN.":[154],"Finally,":[155],"feasibility":[157],"validity":[159],"provided":[162],"verified":[165],"through":[166],"Hefei":[167],"City\u2019s":[168],"selection":[169],"wastewater":[171],"reuse":[172],"alternatives.":[173]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-11-23T00:00:00"}
