{"id":"https://openalex.org/W3036071020","doi":"https://doi.org/10.1007/s40815-020-00877-y","title":"Pythagorean Fuzzy Entropy and Its Application in Multiple-Criteria Decision-Making","display_name":"Pythagorean Fuzzy Entropy and Its Application in Multiple-Criteria Decision-Making","publication_year":2020,"publication_date":"2020-06-15","ids":{"openalex":"https://openalex.org/W3036071020","doi":"https://doi.org/10.1007/s40815-020-00877-y","mag":"3036071020"},"language":"en","primary_location":{"id":"doi:10.1007/s40815-020-00877-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40815-020-00877-y","pdf_url":null,"source":{"id":"https://openalex.org/S18792341","display_name":"International Journal of Fuzzy Systems","issn_l":"1562-2479","issn":["1562-2479","2199-3211"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of 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/A5071755219","display_name":"Tingting Xu","orcid":"https://orcid.org/0000-0002-0516-873X"},"institutions":[{"id":"https://openalex.org/I4472751","display_name":"Anhui Normal University","ror":"https://ror.org/05fsfvw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I4472751"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ting-Ting Xu","raw_affiliation_strings":["School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241003, Anhui, People\u2019s Republic of China","School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241003, Anhui, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241003, Anhui, People\u2019s Republic of China","institution_ids":["https://openalex.org/I4472751"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241003, Anhui, People's Republic of China","institution_ids":["https://openalex.org/I4472751"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100672023","display_name":"Hui Zhang","orcid":"https://orcid.org/0000-0003-0630-2010"},"institutions":[{"id":"https://openalex.org/I4472751","display_name":"Anhui Normal University","ror":"https://ror.org/05fsfvw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I4472751"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hui Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241003, Anhui, People\u2019s Republic of China","School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241003, Anhui, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241003, Anhui, People\u2019s Republic of China","institution_ids":["https://openalex.org/I4472751"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241003, Anhui, People's Republic of China","institution_ids":["https://openalex.org/I4472751"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060856608","display_name":"Bo\u2010Quan Li","orcid":"https://orcid.org/0000-0002-9544-5795"},"institutions":[{"id":"https://openalex.org/I4472751","display_name":"Anhui Normal University","ror":"https://ror.org/05fsfvw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I4472751"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo-Quan Li","raw_affiliation_strings":["School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241003, Anhui, People\u2019s Republic of China","School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241003, Anhui, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241003, Anhui, People\u2019s Republic of China","institution_ids":["https://openalex.org/I4472751"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241003, Anhui, People's Republic of China","institution_ids":["https://openalex.org/I4472751"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071755219"],"corresponding_institution_ids":["https://openalex.org/I4472751"],"apc_list":{"value":2690,"currency":"EUR","value_usd":3490},"apc_paid":null,"fwci":4.488,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.9486456,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"22","issue":"5","first_page":"1552","last_page":"1564"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9696000218391418,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.954200029373169,"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/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.8516594171524048},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5381940007209778},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5138981342315674},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.4759942293167114},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.46956896781921387},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4200512170791626},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37717747688293457},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3685857057571411}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.8516594171524048},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5381940007209778},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5138981342315674},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.4759942293167114},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.46956896781921387},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4200512170791626},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37717747688293457},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3685857057571411},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40815-020-00877-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40815-020-00877-y","pdf_url":null,"source":{"id":"https://openalex.org/S18792341","display_name":"International Journal of Fuzzy Systems","issn_l":"1562-2479","issn":["1562-2479","2199-3211"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.8199999928474426}],"awards":[{"id":"https://openalex.org/G7579574524","display_name":null,"funder_award_id":"No.1908085MA07","funder_id":"https://openalex.org/F4320334897","funder_display_name":"Natural Science Foundation of Anhui Province"}],"funders":[{"id":"https://openalex.org/F4320334897","display_name":"Natural Science Foundation of Anhui Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W35369483","https://openalex.org/W194786220","https://openalex.org/W1546303393","https://openalex.org/W1829951598","https://openalex.org/W1980564456","https://openalex.org/W1996937753","https://openalex.org/W2013932252","https://openalex.org/W2014417436","https://openalex.org/W2025632392","https://openalex.org/W2026244788","https://openalex.org/W2029074979","https://openalex.org/W2040121225","https://openalex.org/W2044313855","https://openalex.org/W2065258344","https://openalex.org/W2079457935","https://openalex.org/W2104077967","https://openalex.org/W2168936936","https://openalex.org/W2306008351","https://openalex.org/W2396040005","https://openalex.org/W2506768821","https://openalex.org/W2589233777","https://openalex.org/W2593530789","https://openalex.org/W2732135403","https://openalex.org/W2765614740","https://openalex.org/W2811195812","https://openalex.org/W2899511870","https://openalex.org/W2912565176","https://openalex.org/W4211007335","https://openalex.org/W4245699803","https://openalex.org/W4255037432","https://openalex.org/W6604285789"],"related_works":["https://openalex.org/W2995447873","https://openalex.org/W1802380781","https://openalex.org/W4210969441","https://openalex.org/W4313271080","https://openalex.org/W4378767041","https://openalex.org/W2050612014","https://openalex.org/W3166167233","https://openalex.org/W2943864676","https://openalex.org/W2774486171","https://openalex.org/W2106711308"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}