{"id":"https://openalex.org/W3033560154","doi":"https://doi.org/10.1007/s40314-020-01174-y","title":"Roughness of a set by $$(\\alpha , \\beta )$$-indiscernibility of Bipolar fuzzy relation","display_name":"Roughness of a set by $$(\\alpha , \\beta )$$-indiscernibility of Bipolar fuzzy relation","publication_year":2020,"publication_date":"2020-06-01","ids":{"openalex":"https://openalex.org/W3033560154","doi":"https://doi.org/10.1007/s40314-020-01174-y","mag":"3033560154"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-020-01174-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-020-01174-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":"Computational and Applied Mathematics","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/A5023804984","display_name":"Rizwan Gul","orcid":"https://orcid.org/0000-0002-6139-1872"},"institutions":[{"id":"https://openalex.org/I12469534","display_name":"Quaid-i-Azam University","ror":"https://ror.org/04s9hft57","country_code":"PK","type":"education","lineage":["https://openalex.org/I12469534"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Rizwan Gul","raw_affiliation_strings":["Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078902055","display_name":"Muhammad Shabir","orcid":"https://orcid.org/0000-0002-3161-8482"},"institutions":[{"id":"https://openalex.org/I12469534","display_name":"Quaid-i-Azam University","ror":"https://ror.org/04s9hft57","country_code":"PK","type":"education","lineage":["https://openalex.org/I12469534"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Shabir","raw_affiliation_strings":["Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023804984"],"corresponding_institution_ids":["https://openalex.org/I12469534"],"apc_list":null,"apc_paid":null,"fwci":1.4436,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.86031131,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"39","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9993000030517578,"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":0.9943000078201294,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.989799976348877,"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/beta","display_name":"BETA (programming language)","score":0.7844470739364624},{"id":"https://openalex.org/keywords/alpha","display_name":"Alpha (finance)","score":0.7837422490119934},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.7230550050735474},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.7183511257171631},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6461043953895569},{"id":"https://openalex.org/keywords/rough-set","display_name":"Rough set","score":0.6256990432739258},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5787546634674072},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.551841676235199},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.525533139705658},{"id":"https://openalex.org/keywords/surface-finish","display_name":"Surface finish","score":0.4841657280921936},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3552705645561218},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3303532600402832},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28749245405197144},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.2571089565753937},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2175796627998352},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12368234992027283},{"id":"https://openalex.org/keywords/mechanical-engineering","display_name":"Mechanical engineering","score":0.07662686705589294},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.05033639073371887}],"concepts":[{"id":"https://openalex.org/C2776174256","wikidata":"https://www.wikidata.org/wiki/Q830842","display_name":"BETA (programming language)","level":2,"score":0.7844470739364624},{"id":"https://openalex.org/C64943373","wikidata":"https://www.wikidata.org/wiki/Q2651003","display_name":"Alpha (finance)","level":4,"score":0.7837422490119934},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.7230550050735474},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.7183511257171631},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6461043953895569},{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.6256990432739258},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5787546634674072},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.551841676235199},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.525533139705658},{"id":"https://openalex.org/C71039073","wikidata":"https://www.wikidata.org/wiki/Q3439090","display_name":"Surface finish","level":2,"score":0.4841657280921936},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3552705645561218},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3303532600402832},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28749245405197144},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2571089565753937},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2175796627998352},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12368234992027283},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.07662686705589294},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.05033639073371887},{"id":"https://openalex.org/C49453240","wikidata":"https://www.wikidata.org/wiki/Q1592163","display_name":"Construct validity","level":3,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C171606756","wikidata":"https://www.wikidata.org/wiki/Q506132","display_name":"Psychometrics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-020-01174-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-020-01174-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5799999833106995}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W1496156369","https://openalex.org/W1542837303","https://openalex.org/W1551588360","https://openalex.org/W1580419169","https://openalex.org/W1754863686","https://openalex.org/W1965795249","https://openalex.org/W1971424330","https://openalex.org/W1978352585","https://openalex.org/W1979113938","https://openalex.org/W1979152784","https://openalex.org/W1980886530","https://openalex.org/W1999693983","https://openalex.org/W2005739429","https://openalex.org/W2007620983","https://openalex.org/W2013824873","https://openalex.org/W2027692378","https://openalex.org/W2032972115","https://openalex.org/W2035431054","https://openalex.org/W2036019995","https://openalex.org/W2042560256","https://openalex.org/W2043619358","https://openalex.org/W2055824572","https://openalex.org/W2069754181","https://openalex.org/W2074193720","https://openalex.org/W2074196524","https://openalex.org/W2076980303","https://openalex.org/W2083267403","https://openalex.org/W2090660539","https://openalex.org/W2153862588","https://openalex.org/W2171844048","https://openalex.org/W2181545555","https://openalex.org/W2191274632","https://openalex.org/W2263787491","https://openalex.org/W2296563105","https://openalex.org/W2315241089","https://openalex.org/W2323691484","https://openalex.org/W2409897897","https://openalex.org/W2463945886","https://openalex.org/W2591701982","https://openalex.org/W2767014154","https://openalex.org/W2784354918","https://openalex.org/W2796019338","https://openalex.org/W2796431025","https://openalex.org/W2890449512","https://openalex.org/W2906424845","https://openalex.org/W2912565176","https://openalex.org/W2920676258","https://openalex.org/W2938942452","https://openalex.org/W2944446010","https://openalex.org/W2983194979","https://openalex.org/W2989251093","https://openalex.org/W2990696050","https://openalex.org/W3000277635","https://openalex.org/W3036984811","https://openalex.org/W4211007335","https://openalex.org/W4255833381"],"related_works":["https://openalex.org/W2085182244","https://openalex.org/W2207330189","https://openalex.org/W1998654355","https://openalex.org/W1966362173","https://openalex.org/W1980846982","https://openalex.org/W2354026142","https://openalex.org/W2951050562","https://openalex.org/W2000627613","https://openalex.org/W1509844650","https://openalex.org/W3033560154"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
