{"id":"https://openalex.org/W2889948901","doi":"https://doi.org/10.3390/e20090672","title":"Entropy, Measures of Distance and Similarity of Q-Neutrosophic Soft Sets and Some Applications","display_name":"Entropy, Measures of Distance and Similarity of Q-Neutrosophic Soft Sets and Some Applications","publication_year":2018,"publication_date":"2018-09-05","ids":{"openalex":"https://openalex.org/W2889948901","doi":"https://doi.org/10.3390/e20090672","mag":"2889948901","pmid":"https://pubmed.ncbi.nlm.nih.gov/33265761","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/7513197"},"language":"en","primary_location":{"id":"doi:10.3390/e20090672","doi":"https://doi.org/10.3390/e20090672","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e20090672","pdf_url":"https://www.mdpi.com/1099-4300/20/9/672/pdf?version=1536643711","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","norway-1","poland-100","russia-white-list-2","vabb-shw"],"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":"Entropy","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","datacite","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/20/9/672/pdf?version=1536643711","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035371154","display_name":"Majdoleen Abu Qamar","orcid":"https://orcid.org/0000-0002-0758-6062","observed_orcids":["https://orcid.org/0000-0002-0758-6062"]},"institutions":[{"id":"https://openalex.org/I885383172","display_name":"National University of Malaysia","ror":"https://ror.org/00bw8d226","country_code":"MY","type":"education","lineage":["https://openalex.org/I885383172"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Majdoleen Abu Qamar","raw_affiliation_strings":["School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Selangor 43600, Malaysia"],"raw_orcid":"https://orcid.org/0000-0002-0758-6062","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Selangor 43600, Malaysia","institution_ids":["https://openalex.org/I885383172"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034562310","display_name":"Nasruddin Hassan","orcid":"https://orcid.org/0000-0002-1659-7089","observed_orcids":["https://orcid.org/0000-0002-1659-7089"]},"institutions":[{"id":"https://openalex.org/I885383172","display_name":"National University of Malaysia","ror":"https://ror.org/00bw8d226","country_code":"MY","type":"education","lineage":["https://openalex.org/I885383172"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Nasruddin Hassan","raw_affiliation_strings":["School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Selangor 43600, Malaysia"],"raw_orcid":"https://orcid.org/0000-0002-1659-7089","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Selangor 43600, Malaysia","institution_ids":["https://openalex.org/I885383172"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034562310"],"corresponding_institution_ids":["https://openalex.org/I885383172"],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":3.4292,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.92602972,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"20","issue":"9","first_page":"672","last_page":"672"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":1.0,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":1.0,"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":0.0,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/neutrosophic-soft-sets","display_name":"neutrosophic soft sets","score":0.902999997138977},{"id":"https://openalex.org/keywords/entropy-measures","display_name":"entropy measures","score":0.8259999752044678},{"id":"https://openalex.org/keywords/distance-metrics","display_name":"distance measures","score":0.7649999856948853},{"id":"https://openalex.org/keywords/similarity-measures","display_name":"similarity measures","score":0.9959999918937683},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.9039999842643738},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.9980000257492065},{"id":"https://openalex.org/keywords/degree-of-fuzziness","display_name":"degree of fuzziness","score":0.8029999732971191},{"id":"https://openalex.org/keywords/diagnosis","display_name":"diagnosis","score":0.8500000238418579},{"id":"https://openalex.org/keywords/decision-making","display_name":"decision-making","score":0.8149999976158142}],"concepts":[{"id":"https://openalex.org/C2777037408","wikidata":"https://www.wikidata.org/wiki/Q4310193","display_name":"Soft set","level":3,"score":0.7344856858253479},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.6999210119247437},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6493345499038696},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.5829691886901855},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5755029916763306},{"id":"https://openalex.org/C2776517306","wikidata":"https://www.wikidata.org/wiki/Q29017317","display_name":"Similarity measure","level":2,"score":0.5540263056755066},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.46285951137542725},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.4460068941116333},{"id":"https://openalex.org/C2639959","wikidata":"https://www.wikidata.org/wiki/Q1344778","display_name":"Distance measures","level":2,"score":0.442452996969223},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3804588317871094},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3267919719219208},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31395792961120605},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29881638288497925},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2753814458847046},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.14293980598449707},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.082712322473526},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.3390/e20090672","doi":"https://doi.org/10.3390/e20090672","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e20090672","pdf_url":"https://www.mdpi.com/1099-4300/20/9/672/pdf?version=1536643711","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","norway-1","poland-100","russia-white-list-2","vabb-shw"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:33265761","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33265761","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":"Journal Article"},{"id":"pmh:oai:pubmedcentral.nih.gov:7513197","doi":null,"is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC7513197/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:07824108f55a40c59a87793849f0bbf0","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/07824108f55a40c59a87793849f0bbf0","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,"listed_in":[],"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":"Entropy, Vol 20, Iss 9, p 672 (2018)","raw_type":"article"},{"id":"pmh:oai:zenodo.org:3050755","doi":null,"is_oa":true,"landing_page_url":"https://zenodo.org/record/3050755","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.5281/zenodo.3050754","doi":"https://doi.org/10.5281/zenodo.3050754","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.3050754","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.3050755","doi":"https://doi.org/10.5281/zenodo.3050755","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.3050755","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.3390/e20090672","doi":"https://doi.org/10.3390/e20090672","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e20090672","pdf_url":"https://www.mdpi.com/1099-4300/20/9/672/pdf?version=1536643711","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","norway-1","poland-100","russia-white-list-2","vabb-shw"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G5238610532","display_name":null,"funder_award_id":"GUP-2017-105","funder_id":"https://openalex.org/F4320322699","funder_display_name":"Universiti Kebangsaan Malaysia"}],"funders":[{"id":"https://openalex.org/F4320322699","display_name":"Universiti Kebangsaan Malaysia","ror":"https://ror.org/00bw8d226"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2889948901.pdf","grobid_xml":"https://content.openalex.org/works/W2889948901.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W21455131","https://openalex.org/W1578428442","https://openalex.org/W1595461165","https://openalex.org/W1637935307","https://openalex.org/W1924732356","https://openalex.org/W1978352585","https://openalex.org/W1980564456","https://openalex.org/W2007508233","https://openalex.org/W2015415636","https://openalex.org/W2029074979","https://openalex.org/W2038190934","https://openalex.org/W2040121225","https://openalex.org/W2044193890","https://openalex.org/W2062064638","https://openalex.org/W2131390763","https://openalex.org/W2153696615","https://openalex.org/W2155976821","https://openalex.org/W2162501341","https://openalex.org/W2293737317","https://openalex.org/W2511459981","https://openalex.org/W2565613390","https://openalex.org/W2587969203","https://openalex.org/W2753957617","https://openalex.org/W2775083246","https://openalex.org/W2782371983","https://openalex.org/W2789453065","https://openalex.org/W2793390658","https://openalex.org/W2802854050","https://openalex.org/W2804099896","https://openalex.org/W2804792520","https://openalex.org/W2808069851","https://openalex.org/W2808106424","https://openalex.org/W2887058281","https://openalex.org/W2963635008","https://openalex.org/W4211007335","https://openalex.org/W4291270071","https://openalex.org/W6693091319","https://openalex.org/W6725980889","https://openalex.org/W6986727158"],"related_works":["https://openalex.org/W1637935307","https://openalex.org/W233938478","https://openalex.org/W7098259803","https://openalex.org/W2949104085","https://openalex.org/W4406073565","https://openalex.org/W6926480305","https://openalex.org/W7143374098","https://openalex.org/W1578428442","https://openalex.org/W2793390658","https://openalex.org/W4200487299"],"abstract_inverted_index":{"The":[0,67,86,108],"idea":[1,103],"of":[2,59,61,69,74,104,118,125,128],"the":[3,9,15,49,53,57,102,116,126,136],"Q-neutrosophic":[4,62,81,105,129],"soft":[5,11,63,82,106,130],"set":[6,12],"emerges":[7],"from":[8],"neutrosophic":[10],"by":[13,132],"upgrading":[14],"membership":[16],"functions":[17],"to":[18,32,96,114,139],"a":[19,140],"two-dimensional":[20,35],"entity":[21],"which":[22],"indicate":[23],"uncertainty,":[24],"indeterminacy":[25],"and":[26,38,56,72,90,135,143],"falsity.":[27],"Hence,":[28],"it":[29],"is":[30,111],"able":[31],"deal":[33],"with":[34,101],"inconsistent,":[36],"imprecise,":[37],"indeterminate":[39],"information":[40],"appearing":[41],"in":[42],"real":[43],"life":[44],"situations.":[45],"In":[46],"this":[47],"study,":[48],"tools":[50],"that":[51],"measure":[52,110,117,138],"similarity,":[54],"distance":[55,109],"degree":[58],"fuzziness":[60],"sets":[64,131],"are":[65,76,94],"presented.":[66,85],"definitions":[68],"distance,":[70],"similarity":[71,137],"measures":[73,127],"entropy":[75,83,134],"introduced.":[77],"Some":[78],"formulas":[79],"for":[80],"were":[84],"known":[87],"Hamming,":[88],"Euclidean":[89],"their":[91],"normalized":[92],"distances":[93],"generalized":[95],"make":[97],"them":[98],"well":[99],"matched":[100],"set.":[107],"subsequently":[112],"used":[113],"define":[115],"similarity.":[119],"Lastly,":[120],"we":[121],"expound":[122],"three":[123],"applications":[124],"applying":[133],"medical":[141],"diagnosis":[142],"decision":[144],"making":[145],"problems.":[146]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":3}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2018-09-27T00:00:00"}
