{"id":"https://openalex.org/W2058847570","doi":"https://doi.org/10.1109/fskd.2013.6816171","title":"New fuzzy metric spaces based on gradual numbers","display_name":"New fuzzy metric spaces based on gradual numbers","publication_year":2013,"publication_date":"2013-07-01","ids":{"openalex":"https://openalex.org/W2058847570","doi":"https://doi.org/10.1109/fskd.2013.6816171","mag":"2058847570"},"language":"en","primary_location":{"id":"doi:10.1109/fskd.2013.6816171","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fskd.2013.6816171","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 10th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)","raw_type":"proceedings-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/A5102210862","display_name":"Cai-Li Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I43337087","display_name":"Hebei University","ror":"https://ror.org/01p884a79","country_code":"CN","type":"education","lineage":["https://openalex.org/I43337087"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Cai-Li Zhou","raw_affiliation_strings":["College of Mathematics and Computer Science, Hebei University, Baoding, China","College of Mathematics and Computer Science, Hebei University, Baoding, China 071002#TAB#"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Computer Science, Hebei University, Baoding, China","institution_ids":["https://openalex.org/I43337087"]},{"raw_affiliation_string":"College of Mathematics and Computer Science, Hebei University, Baoding, China 071002#TAB#","institution_ids":["https://openalex.org/I43337087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080244807","display_name":"Yinying Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I4210163890","display_name":"Langfang Normal University","ror":"https://ror.org/05kyq2m47","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210163890"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yin-Ying Zhou","raw_affiliation_strings":["Department of Mathematics and Information Sciences, Lang fang Teachers College, Langfang, China","Department of Mathematics and Information Sciences, Lang fang Teachers College, China 065000"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Information Sciences, Lang fang Teachers College, Langfang, China","institution_ids":["https://openalex.org/I4210163890"]},{"raw_affiliation_string":"Department of Mathematics and Information Sciences, Lang fang Teachers College, China 065000","institution_ids":["https://openalex.org/I4210163890"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085154156","display_name":"Junyan Bao","orcid":"https://orcid.org/0000-0002-8132-6998"},"institutions":[{"id":"https://openalex.org/I43337087","display_name":"Hebei University","ror":"https://ror.org/01p884a79","country_code":"CN","type":"education","lineage":["https://openalex.org/I43337087"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun-Yan Bao","raw_affiliation_strings":["College of Mathematics and Computer Science, Hebei University, Baoding, China","College of Mathematics and Computer Science, Hebei University, Baoding, China 071002#TAB#"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Computer Science, Hebei University, Baoding, China","institution_ids":["https://openalex.org/I43337087"]},{"raw_affiliation_string":"College of Mathematics and Computer Science, Hebei University, Baoding, China 071002#TAB#","institution_ids":["https://openalex.org/I43337087"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102210862"],"corresponding_institution_ids":["https://openalex.org/I43337087"],"apc_list":null,"apc_paid":null,"fwci":0.9294,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.74150636,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"160","issue":null,"first_page":"83","last_page":"87"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9379000067710876,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.7536816596984863},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7199575304985046},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6764209866523743},{"id":"https://openalex.org/keywords/equivalence-of-metrics","display_name":"Equivalence of metrics","score":0.5747801065444946},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5636739730834961},{"id":"https://openalex.org/keywords/t-norm","display_name":"T-norm","score":0.5602973103523254},{"id":"https://openalex.org/keywords/convex-metric-space","display_name":"Convex metric space","score":0.5369593501091003},{"id":"https://openalex.org/keywords/metric-map","display_name":"Metric map","score":0.5013177394866943},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.4736170470714569},{"id":"https://openalex.org/keywords/injective-metric-space","display_name":"Injective metric space","score":0.4656662940979004},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4357345700263977},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.40277010202407837},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39884355664253235},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.3199516534805298},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27723178267478943},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.2428031861782074},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18671870231628418},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.1478622853755951},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11388105154037476},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11015906929969788}],"concepts":[{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.7536816596984863},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7199575304985046},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6764209866523743},{"id":"https://openalex.org/C191226916","wikidata":"https://www.wikidata.org/wiki/Q5384710","display_name":"Equivalence of metrics","level":4,"score":0.5747801065444946},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5636739730834961},{"id":"https://openalex.org/C2721081","wikidata":"https://www.wikidata.org/wiki/Q2383161","display_name":"T-norm","level":5,"score":0.5602973103523254},{"id":"https://openalex.org/C196613150","wikidata":"https://www.wikidata.org/wiki/Q3966092","display_name":"Convex metric space","level":3,"score":0.5369593501091003},{"id":"https://openalex.org/C145084290","wikidata":"https://www.wikidata.org/wiki/Q2713824","display_name":"Metric map","level":4,"score":0.5013177394866943},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.4736170470714569},{"id":"https://openalex.org/C177547787","wikidata":"https://www.wikidata.org/wiki/Q6034319","display_name":"Injective metric space","level":3,"score":0.4656662940979004},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4357345700263977},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.40277010202407837},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39884355664253235},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3199516534805298},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27723178267478943},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.2428031861782074},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18671870231628418},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.1478622853755951},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11388105154037476},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11015906929969788},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fskd.2013.6816171","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fskd.2013.6816171","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 10th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.47999998927116394,"display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321949","display_name":"Department of Education of Hebei Province","ror":"https://ror.org/01jkyjd96"},{"id":"https://openalex.org/F4320322163","display_name":"Natural Science Foundation of Hebei Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W166627264","https://openalex.org/W1480981862","https://openalex.org/W1500905082","https://openalex.org/W1541374981","https://openalex.org/W1662542889","https://openalex.org/W1964093237","https://openalex.org/W1987761358","https://openalex.org/W1990043203","https://openalex.org/W1997679081","https://openalex.org/W2008230680","https://openalex.org/W2019441837","https://openalex.org/W2025174402","https://openalex.org/W2032769966","https://openalex.org/W2038300950","https://openalex.org/W2048795066","https://openalex.org/W2049226309","https://openalex.org/W2049442812","https://openalex.org/W2051734340","https://openalex.org/W2056207709","https://openalex.org/W2061904260","https://openalex.org/W2083089446","https://openalex.org/W2088532519","https://openalex.org/W2099285375","https://openalex.org/W2108028062","https://openalex.org/W2119964222","https://openalex.org/W2122781548","https://openalex.org/W2133452065","https://openalex.org/W2136708504","https://openalex.org/W2162021822","https://openalex.org/W2228857411","https://openalex.org/W6606734566","https://openalex.org/W6632670038","https://openalex.org/W6636797783"],"related_works":["https://openalex.org/W2255258360","https://openalex.org/W2610752199","https://openalex.org/W3039282288","https://openalex.org/W2740809164","https://openalex.org/W3009207718","https://openalex.org/W2029705245","https://openalex.org/W2226253657","https://openalex.org/W2802428694","https://openalex.org/W4210552450","https://openalex.org/W2783578794"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"deal":[4],"with":[5,55],"special":[6],"generalization":[7,34],"of":[8,23,35,47],"metric":[9,25,37,61],"spaces":[10,26,38,43,62],"by":[11],"considering":[12],"the":[13,21,45],"distances":[14],"between":[15],"objects":[16],"as":[17],"gradual":[18,24,40,60],"numbers.":[19],"Firstly,":[20],"concept":[22,31],"is":[27,32],"introduced.":[28],"The":[29],"new":[30],"a":[33],"classical":[36],"and":[39,49,65],"linear":[41],"normed":[42],"in":[44,59],"sense":[46],"Sadeqi":[48],"Azart.":[50],"And":[51],"then,":[52],"basic":[53],"concepts":[54],"respect":[56],"to":[57],"topology":[58],"are":[63,68],"presented":[64],"their":[66],"properties":[67],"discussed.":[69]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}