{"id":"https://openalex.org/W4405184339","doi":"https://doi.org/10.3390/axioms13120858","title":"A Novel Framework for Belief and Plausibility Measures in Intuitionistic Fuzzy Sets: Belief and Plausibility Distance, Similarity, and TOPSIS for Multicriteria Decision Making","display_name":"A Novel Framework for Belief and Plausibility Measures in Intuitionistic Fuzzy Sets: Belief and Plausibility Distance, Similarity, and TOPSIS for Multicriteria Decision Making","publication_year":2024,"publication_date":"2024-12-07","ids":{"openalex":"https://openalex.org/W4405184339","doi":"https://doi.org/10.3390/axioms13120858"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13120858","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13120858","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/axioms13120858","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057610503","display_name":"Shahid Hussain","orcid":"https://orcid.org/0000-0001-5426-2290"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shahid Hussain","raw_affiliation_strings":["College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046124406","display_name":"Zahid Hussain","orcid":"https://orcid.org/0000-0002-6101-6685"},"institutions":[{"id":"https://openalex.org/I236232284","display_name":"Karakoram International University","ror":"https://ror.org/0324r4e56","country_code":"PK","type":"education","lineage":["https://openalex.org/I236232284"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Zahid Hussain","raw_affiliation_strings":["Department of Mathematical Sciences, Karakoram International University, Gilgit 15100, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Karakoram International University, Gilgit 15100, Pakistan","institution_ids":["https://openalex.org/I236232284"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101861699","display_name":"R. Jahir Hussain","orcid":"https://orcid.org/0000-0003-3260-7280"},"institutions":[{"id":"https://openalex.org/I236232284","display_name":"Karakoram International University","ror":"https://ror.org/0324r4e56","country_code":"PK","type":"education","lineage":["https://openalex.org/I236232284"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Rashid Hussain","raw_affiliation_strings":["Department of Mathematical Sciences, Karakoram International University, Gilgit 15100, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Karakoram International University, Gilgit 15100, Pakistan","institution_ids":["https://openalex.org/I236232284"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046121670","display_name":"Ahmed Bakhet","orcid":"https://orcid.org/0000-0001-5454-380X"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ahmad Bakhet","raw_affiliation_strings":["College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"],"raw_orcid":"https://orcid.org/0000-0001-5454-380X","affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Hussain Arafat","orcid":null},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hussain Arafat","raw_affiliation_strings":["College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060547119","display_name":"Mohammed Zakarya","orcid":"https://orcid.org/0000-0003-4312-8330"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Mohammed Zakarya","raw_affiliation_strings":["Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-4312-8330","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104542077","display_name":"Amirah Ayidh I Al-Thaqfan","orcid":null},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Amirah Ayidh I Al-Thaqfan","raw_affiliation_strings":["Department of Mathematics, College of Arts and Sciences, King Khalid University, P.O. Box 64512, Abha 62529, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Arts and Sciences, King Khalid University, P.O. Box 64512, Abha 62529, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022762018","display_name":"Maha Ali","orcid":null},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Maha Ali","raw_affiliation_strings":["Department of Mathematics, College of Arts and Sciences, King Khalid University, P.O. Box 64512, Abha 62529, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Arts and Sciences, King Khalid University, P.O. Box 64512, Abha 62529, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5046121670"],"corresponding_institution_ids":["https://openalex.org/I96908189"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.461,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.7105123,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"13","issue":"12","first_page":"858","last_page":"858"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","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/T10050","display_name":"Multi-Criteria Decision Making","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":0.9887999892234802,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.947700023651123,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.7487002015113831},{"id":"https://openalex.org/keywords/topsis","display_name":"TOPSIS","score":0.6508212685585022},{"id":"https://openalex.org/keywords/ambiguity","display_name":"Ambiguity","score":0.6074187159538269},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.594287097454071},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5479998588562012},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5062190890312195},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4528059959411621},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3781762719154358},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3340064287185669},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.09887170791625977},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.07741916179656982}],"concepts":[{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.7487002015113831},{"id":"https://openalex.org/C51566761","wikidata":"https://www.wikidata.org/wiki/Q1235853","display_name":"TOPSIS","level":2,"score":0.6508212685585022},{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.6074187159538269},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.594287097454071},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5479998588562012},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5062190890312195},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4528059959411621},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3781762719154358},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3340064287185669},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.09887170791625977},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.07741916179656982},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13120858","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13120858","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:44ba7a068c1d4ef0adda907740166d66","is_oa":true,"landing_page_url":"https://doaj.org/article/44ba7a068c1d4ef0adda907740166d66","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,"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":"Axioms, Vol 13, Iss 12, p 858 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13120858","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13120858","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7900000214576721}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W1177241668","https://openalex.org/W1528458083","https://openalex.org/W1976210939","https://openalex.org/W1978336073","https://openalex.org/W1978808568","https://openalex.org/W2035059039","https://openalex.org/W2045249520","https://openalex.org/W2053596247","https://openalex.org/W2055957797","https://openalex.org/W2079767857","https://openalex.org/W2084693411","https://openalex.org/W2089122143","https://openalex.org/W2094682318","https://openalex.org/W2105699261","https://openalex.org/W2142191316","https://openalex.org/W2188902638","https://openalex.org/W2398841771","https://openalex.org/W2406470551","https://openalex.org/W2559544114","https://openalex.org/W2597824611","https://openalex.org/W2622201814","https://openalex.org/W2748103251","https://openalex.org/W2769008644","https://openalex.org/W2794329837","https://openalex.org/W2799466028","https://openalex.org/W2904831720","https://openalex.org/W2913813006","https://openalex.org/W2936825285","https://openalex.org/W2946461872","https://openalex.org/W2967666729","https://openalex.org/W2969852833","https://openalex.org/W3048846577","https://openalex.org/W3121532256","https://openalex.org/W3170932440","https://openalex.org/W4200419627","https://openalex.org/W4211007335","https://openalex.org/W4255014856","https://openalex.org/W4281760542","https://openalex.org/W4281781240","https://openalex.org/W4283215232","https://openalex.org/W4295074053","https://openalex.org/W4379260611","https://openalex.org/W4386162760","https://openalex.org/W4386579178","https://openalex.org/W4386753638","https://openalex.org/W4387140882","https://openalex.org/W4392058616","https://openalex.org/W4393204095","https://openalex.org/W4396684100","https://openalex.org/W4401336255","https://openalex.org/W4401611875"],"related_works":["https://openalex.org/W2041949587","https://openalex.org/W2958553423","https://openalex.org/W2358217305","https://openalex.org/W2353179089","https://openalex.org/W2359186709","https://openalex.org/W4282827651","https://openalex.org/W3015638941","https://openalex.org/W4324117723","https://openalex.org/W2379805174","https://openalex.org/W2963268865"],"abstract_inverted_index":{"Dempster\u2013Shafer":[0],"Theory":[1],"(DST)":[2],"relies":[3],"significantly":[4],"on":[5,35],"belief":[6,36,58,123],"and":[7,13,24,37,43,59,66,69,76,86,100,111,120,124,132,146],"plausibility":[8,38,60,125],"measures":[9,88],"to":[10,20,89,113,135],"handle":[11],"ambiguity":[12],"uncertainty;":[14],"however,":[15],"DST":[16],"has":[17],"been":[18],"extended":[19],"fuzzy":[21,26,40,63],"sets":[22,27,64],"(FSs)":[23],"intuitionistic":[25,39,62],"(IFSs)":[28],"with":[29],"only":[30],"a":[31,53],"few":[32],"extensions":[33],"focusing":[34],"distance":[41,85,99],"(BP-distance)":[42],"similarity":[44,87],"(BP-similarity)":[45],"until":[46],"now.":[47],"In":[48],"this":[49],"work,":[50],"we":[51,121],"propose":[52],"novel":[54],"framework":[55],"for":[56],"the":[57,79,91,115,129,144],"of":[61,78,98,117,148],"(BP-IFSs)":[65],"their":[67],"BP-distance":[68],"BP-similarity":[70],"measures.":[71],"We":[72,102],"modified":[73],"steps":[74],"4":[75],"5":[77],"classical":[80],"TOPSIS":[81,126],"method,":[82],"utilizing":[83],"both":[84],"rank":[90],"alternatives":[92],"that":[93],"satisfy":[94],"all":[95],"necessary":[96],"axioms":[97],"similarity.":[101],"present":[103],"numerical":[104],"examples":[105],"involving":[106],"pattern":[107],"recognition,":[108],"linguistic":[109],"variables,":[110],"clustering":[112],"illustrate":[114],"efficiency":[116],"these":[118],"measures,":[119],"develop":[122],"(BP-TOPSIS)":[127],"using":[128],"proposed":[130],"criteria":[131],"apply":[133],"it":[134],"complex":[136],"multicriteria":[137],"decision-making":[138],"(MCDM)":[139],"challenges.":[140],"The":[141],"results":[142],"demonstrate":[143],"practicality":[145],"effectiveness":[147],"our":[149],"approach.":[150]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}