{"id":"https://openalex.org/W2138152543","doi":"https://doi.org/10.1109/tsmcb.2008.2005527","title":"Generalized Rough Sets, Entropy, and Image Ambiguity Measures","display_name":"Generalized Rough Sets, Entropy, and Image Ambiguity Measures","publication_year":2008,"publication_date":"2008-12-08","ids":{"openalex":"https://openalex.org/W2138152543","doi":"https://doi.org/10.1109/tsmcb.2008.2005527","mag":"2138152543","pmid":"https://pubmed.ncbi.nlm.nih.gov/19150762"},"language":"en","primary_location":{"id":"doi:10.1109/tsmcb.2008.2005527","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmcb.2008.2005527","pdf_url":null,"source":{"id":"https://openalex.org/S4210170378","display_name":"IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)","issn_l":"1083-4419","issn":["1083-4419","1941-0492"],"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 Systems, Man, and Cybernetics, Part B (Cybernetics)","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5063471945","display_name":"Debashis Sen","orcid":"https://orcid.org/0000-0002-9756-1191"},"institutions":[{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"D. Sen","raw_affiliation_strings":["Center for Soft Computing Research, Indian Statistical Institute, Calcutta 700108, India. dsen_t@isical.ac.in","Center for Soft Comput. Res., Indian Stat. Inst., Calcutta"],"affiliations":[{"raw_affiliation_string":"Center for Soft Computing Research, Indian Statistical Institute, Calcutta 700108, India. dsen_t@isical.ac.in","institution_ids":["https://openalex.org/I6498739"]},{"raw_affiliation_string":"Center for Soft Comput. Res., Indian Stat. Inst., Calcutta","institution_ids":["https://openalex.org/I6498739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101770423","display_name":"Suparna Pal","orcid":"https://orcid.org/0000-0002-0749-7828"},"institutions":[{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"S.K. Pal","raw_affiliation_strings":["Center of Soft Computing Research, Indian Statistical Institute, Calcutta, India","Center for Soft Comput. Res., Indian Stat. Inst., Calcutta"],"affiliations":[{"raw_affiliation_string":"Center of Soft Computing Research, Indian Statistical Institute, Calcutta, India","institution_ids":["https://openalex.org/I6498739"]},{"raw_affiliation_string":"Center for Soft Comput. Res., Indian Stat. Inst., Calcutta","institution_ids":["https://openalex.org/I6498739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063471945"],"corresponding_institution_ids":["https://openalex.org/I6498739"],"apc_list":null,"apc_paid":null,"fwci":7.8202,"has_fulltext":false,"cited_by_count":97,"citation_normalized_percentile":{"value":0.97582195,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":100},"biblio":{"volume":"39","issue":"1","first_page":"117","last_page":"128"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9998999834060669,"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":0.9998999834060669,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9567000269889832,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T13882","display_name":"Research studies in Vietnam","score":0.9271000027656555,"subfield":{"id":"https://openalex.org/subfields/2303","display_name":"Ecology"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ambiguity","display_name":"Ambiguity","score":0.7784197330474854},{"id":"https://openalex.org/keywords/rough-set","display_name":"Rough set","score":0.6746301651000977},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6598597168922424},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.6124097108840942},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5949994921684265},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.49327319860458374},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.44471314549446106},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4383352994918823},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4095839858055115},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38223332166671753},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.37301939725875854},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3679828643798828},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.35168302059173584},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.346039354801178}],"concepts":[{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.7784197330474854},{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.6746301651000977},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6598597168922424},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.6124097108840942},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5949994921684265},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.49327319860458374},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.44471314549446106},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4383352994918823},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4095839858055115},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38223332166671753},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.37301939725875854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3679828643798828},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.35168302059173584},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.346039354801178},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007091","descriptor_name":"Image Processing, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007091","descriptor_name":"Image Processing, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007091","descriptor_name":"Image Processing, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D017143","descriptor_name":"Fuzzy Logic","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017143","descriptor_name":"Fuzzy Logic","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017143","descriptor_name":"Fuzzy Logic","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D019277","descriptor_name":"Entropy","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D019277","descriptor_name":"Entropy","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D019277","descriptor_name":"Entropy","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":3,"locations":[{"id":"doi:10.1109/tsmcb.2008.2005527","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmcb.2008.2005527","pdf_url":null,"source":{"id":"https://openalex.org/S4210170378","display_name":"IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)","issn_l":"1083-4419","issn":["1083-4419","1941-0492"],"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 Systems, Man, and Cybernetics, Part B (Cybernetics)","raw_type":"journal-article"},{"id":"pmid:19150762","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/19150762","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,"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":"IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.217.1068","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.217.1068","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.isical.ac.in/~sankar/paper/TSMC_B_09_DS_SKP.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W147723833","https://openalex.org/W1497916229","https://openalex.org/W1541067610","https://openalex.org/W1557923305","https://openalex.org/W1586017272","https://openalex.org/W1591618909","https://openalex.org/W1898259180","https://openalex.org/W1971707777","https://openalex.org/W1987469094","https://openalex.org/W1993361112","https://openalex.org/W1999612973","https://openalex.org/W2010560725","https://openalex.org/W2022262325","https://openalex.org/W2026898888","https://openalex.org/W2027654459","https://openalex.org/W2035567190","https://openalex.org/W2067191022","https://openalex.org/W2071200009","https://openalex.org/W2089783231","https://openalex.org/W2092179332","https://openalex.org/W2098434088","https://openalex.org/W2100115174","https://openalex.org/W2111499159","https://openalex.org/W2119929398","https://openalex.org/W2132839152","https://openalex.org/W2145023731","https://openalex.org/W2197021550","https://openalex.org/W3023411394","https://openalex.org/W4212783130","https://openalex.org/W6632430144","https://openalex.org/W6687403197"],"related_works":["https://openalex.org/W2353179089","https://openalex.org/W2978519593","https://openalex.org/W2131323062","https://openalex.org/W2102746356","https://openalex.org/W4390066334","https://openalex.org/W3041490575","https://openalex.org/W2970690932","https://openalex.org/W4321135767","https://openalex.org/W2069619724","https://openalex.org/W2106711308"],"abstract_inverted_index":{"Quantifying":[0],"ambiguities":[1,38,81],"in":[2,15,39,82,120],"images":[3,40,83],"using":[4,87],"fuzzy":[5,48],"set":[6,30,49,60],"theory":[7,31,61],"has":[8],"been":[9],"of":[10,18,28,47,54,98],"utmost":[11],"interest":[12],"to":[13,44,71],"researchers":[14],"the":[16,26,45,88,94,99],"field":[17],"image":[19,107,118],"processing.":[20],"In":[21],"this":[22,121],"paper,":[23],"we":[24],"present":[25],"use":[27,46],"rough":[29,59],"and":[32,41,62,66,79,96],"its":[33,63],"certain":[34,64],"generalizations":[35],"for":[36],"quantifying":[37],"compare":[42],"it":[43],"theory.":[50],"We":[51,92,110],"propose":[52,112],"classes":[53],"entropy":[55,90,101],"measures":[56,102],"based":[57],"on":[58],"generalizations,":[65],"perform":[67],"rigorous":[68],"theoretical":[69],"analysis":[70],"provide":[72],"some":[73,105],"properties":[74],"which":[75],"they":[76],"satisfy.":[77],"Grayness":[78],"spatial":[80],"are":[84],"then":[85],"quantified":[86],"proposed":[89,100],"measures.":[91],"demonstrate":[93],"utility":[95],"effectiveness":[97],"by":[103],"considering":[104],"elementary":[106],"processing":[108],"applications.":[109],"also":[111],"a":[113],"new":[114],"measure":[115],"called":[116],"average":[117],"ambiguity":[119],"context.":[122]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":14}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
