{"id":"https://openalex.org/W4285819387","doi":"https://doi.org/10.1109/tfuzz.2022.3191359","title":"Pythagorean Fuzzy Sets to Solve Z-Numbers in Decision-Making Model","display_name":"Pythagorean Fuzzy Sets to Solve Z-Numbers in Decision-Making Model","publication_year":2022,"publication_date":"2022-07-18","ids":{"openalex":"https://openalex.org/W4285819387","doi":"https://doi.org/10.1109/tfuzz.2022.3191359"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2022.3191359","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2022.3191359","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Fuzzy 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/A5017585981","display_name":"Qianlei Jia","orcid":"https://orcid.org/0000-0003-3827-3832"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qianlei Jia","raw_affiliation_strings":["School of Automation, Northwestern Polytechnical University, Xi&#x0027;an, China"],"affiliations":[{"raw_affiliation_string":"School of Automation, Northwestern Polytechnical University, Xi&#x0027;an, China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076657750","display_name":"Enrique Herrera\u2010Viedma","orcid":"https://orcid.org/0000-0002-7922-4984"},"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"]},{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]},{"id":"https://openalex.org/I4210095677","display_name":"Instituto Andaluz de Ciencias de la Tierra","ror":"https://ror.org/00v0g9w49","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210095677"]}],"countries":["ES","SA"],"is_corresponding":false,"raw_author_name":"Enrique Herrera-Viedma","raw_affiliation_strings":["Andalusian Research Institute in Data Science and Computational Intelligence and the Department of Computer Science and Artificial Intelligence, University of Granada, Granada, Spain","Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Andalusian Research Institute in Data Science and Computational Intelligence and the Department of Computer Science and Artificial Intelligence, University of Granada, Granada, Spain","institution_ids":["https://openalex.org/I4210095677","https://openalex.org/I173304897"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017585981"],"corresponding_institution_ids":["https://openalex.org/I17145004"],"apc_list":null,"apc_paid":null,"fwci":3.4371,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.92887128,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"31","issue":"3","first_page":"890","last_page":"904"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9987000226974487,"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":0.9987000226974487,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.982200026512146,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9182999730110168,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.7016725540161133},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6224796772003174},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5138819217681885},{"id":"https://openalex.org/keywords/pythagorean-triple","display_name":"Pythagorean triple","score":0.4960273206233978},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4302602708339691},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3848378658294678},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3717750012874603},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3622574806213379},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32661640644073486},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.20341730117797852},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15980884432792664}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.7016725540161133},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6224796772003174},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5138819217681885},{"id":"https://openalex.org/C80918210","wikidata":"https://www.wikidata.org/wiki/Q208225","display_name":"Pythagorean triple","level":3,"score":0.4960273206233978},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4302602708339691},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3848378658294678},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3717750012874603},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3622574806213379},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32661640644073486},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.20341730117797852},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15980884432792664},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tfuzz.2022.3191359","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2022.3191359","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8399999737739563,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G2623827249","display_name":null,"funder_award_id":"62073266","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3246653735","display_name":null,"funder_award_id":"61374032","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W826623024","https://openalex.org/W1668569279","https://openalex.org/W1829951598","https://openalex.org/W1997952930","https://openalex.org/W1997967425","https://openalex.org/W2013932252","https://openalex.org/W2042774699","https://openalex.org/W2083199031","https://openalex.org/W2125268144","https://openalex.org/W2282407434","https://openalex.org/W2292359941","https://openalex.org/W2343846868","https://openalex.org/W2345848912","https://openalex.org/W2396040005","https://openalex.org/W2509038672","https://openalex.org/W2514754342","https://openalex.org/W2521399310","https://openalex.org/W2574155231","https://openalex.org/W2586751834","https://openalex.org/W2744102091","https://openalex.org/W2744594184","https://openalex.org/W2747160131","https://openalex.org/W2756214476","https://openalex.org/W2758653053","https://openalex.org/W2765614740","https://openalex.org/W2787991310","https://openalex.org/W2790388419","https://openalex.org/W2794273717","https://openalex.org/W2803497498","https://openalex.org/W2884661192","https://openalex.org/W2890735275","https://openalex.org/W2902274251","https://openalex.org/W2902418216","https://openalex.org/W2904970805","https://openalex.org/W2941877913","https://openalex.org/W2942289617","https://openalex.org/W2948447020","https://openalex.org/W2955987323","https://openalex.org/W2982447614","https://openalex.org/W3028762139","https://openalex.org/W3030646047","https://openalex.org/W3094458853","https://openalex.org/W3126088291","https://openalex.org/W3128472026","https://openalex.org/W3134857105","https://openalex.org/W3135853097","https://openalex.org/W3137348704","https://openalex.org/W3156123292","https://openalex.org/W3182515817","https://openalex.org/W3192561886","https://openalex.org/W3195478544","https://openalex.org/W3216367135","https://openalex.org/W4205585509","https://openalex.org/W4211007335","https://openalex.org/W4245152641"],"related_works":["https://openalex.org/W3038906685","https://openalex.org/W2392975301","https://openalex.org/W2259363500","https://openalex.org/W2387543012","https://openalex.org/W2620974800","https://openalex.org/W2790200812","https://openalex.org/W2368479431","https://openalex.org/W4280581009","https://openalex.org/W4287077343","https://openalex.org/W3182949439"],"abstract_inverted_index":{"Since":[0],"the":[1,10,24,67,83,89,92,99,108,117,120,126,147,155,166,181,188],"concept":[2],"of":[3,12,26,57,112,149],"Z-numbers":[4,22,45,79,113],"was":[5],"proposed,":[6,115],"it":[7],"has":[8],"attracted":[9],"attention":[11],"scholars.":[13],"In":[14,64],"this":[15,62,65],"article,":[16],"we":[17],"are":[18,80,177],"committed":[19],"to":[20,43,46,97,179],"solving":[21,196],"from":[23],"perspective":[25],"coordinate":[27,39,156],"system":[28,40],"and":[29,73,86,116,173,193],"q-rung":[30],"orthopedic":[31],"fuzzy":[32,51],"sets":[33],"(q-ROFSs).":[34],"First,":[35],"a":[36,54,141,159],"new":[37,167],"layout":[38],"is":[41,59,95,114,138,144,162,191],"defined":[42,145],"map":[44],"q-ROFSs.":[47],"For":[48],"convenience,":[49],"Pythagorean":[50],"set":[52],"(PFS),":[53],"special":[55],"form":[56],"q-ROFSs,":[58],"employed":[60],"in":[61,78,154,195],"article.":[63],"way,":[66],"parameters":[68],"<inline-formula":[69,74,133],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[70,75,134],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[71,76,135],"notation=\"LaTeX\">$A$</tex-math></inline-formula>":[72],"notation=\"LaTeX\">$B$</tex-math></inline-formula>":[77],"transformed":[81],"into":[82],"corresponding":[84],"membership":[85],"nonmembership.":[87],"At":[88],"same":[90],"time,":[91],"genetic":[93],"algorithm":[94],"adopted":[96,178],"derive":[98],"potential":[100],"probability":[101],"distribution.":[102],"Next,":[103],"an":[104],"approach":[105],"for":[106],"calculating":[107],"weighted":[109,129],"information":[110],"entropy":[111],"theorem":[118],"proves":[119],"rationality.":[121],"To":[122],"integrate":[123],"multiple":[124],"Z-information,":[125],"linguistic":[127],"Z-PFS":[128],"aggregation":[130],"operator":[131],"(":[132],"notation=\"LaTeX\">$LZPFSPWAO$</tex-math></inline-formula>":[136],")":[137],"presented.":[139],"Also,":[140],"score":[142],"function":[143],"with":[146],"help":[148],"curve":[150],"length":[151],"calculation":[152],"formula":[153],"system.":[157],"Finally,":[158],"decision-making":[160],"model":[161],"constructed":[163],"based":[164],"on":[165],"solution.":[168],"Two":[169],"examples,":[170],"UAV":[171],"firefighting":[172],"energy":[174],"investment":[175],"selection,":[176],"demonstrate":[180],"validity.":[182],"The":[183],"comparison":[184],"results":[185],"show":[186],"that":[187],"proposed":[189],"method":[190],"effective":[192],"beneficial":[194],"Z-information.":[197]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}