{"id":"https://openalex.org/W2521399310","doi":"https://doi.org/10.1109/tfuzz.2016.2612303","title":"Approximate Reasoning on a Basis of <italic>Z</italic>-Number-Valued If\u2013Then Rules","display_name":"Approximate Reasoning on a Basis of <italic>Z</italic>-Number-Valued If\u2013Then Rules","publication_year":2016,"publication_date":"2016-09-21","ids":{"openalex":"https://openalex.org/W2521399310","doi":"https://doi.org/10.1109/tfuzz.2016.2612303","mag":"2521399310"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2016.2612303","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2016.2612303","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"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 Fuzzy Systems","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/A5044050863","display_name":"Rafik Aziz Aliev","orcid":"https://orcid.org/0000-0001-8124-7600"},"institutions":[{"id":"https://openalex.org/I69050122","display_name":"Near East University","ror":"https://ror.org/02x8svs93","country_code":"CY","type":"education","lineage":["https://openalex.org/I69050122"]},{"id":"https://openalex.org/I136806742","display_name":"Azerbaijan State Oil and Industry University","ror":"https://ror.org/05mmnns11","country_code":"AZ","type":"education","lineage":["https://openalex.org/I136806742"]}],"countries":["AZ","CY"],"is_corresponding":true,"raw_author_name":"Rafik A. Aliev","raw_affiliation_strings":["Azerbaijan State University of Oil and Industry, Baku, Azerbaijan","Department of Computer Engineering, Near East University, Lefkosa, North Cyprus"],"affiliations":[{"raw_affiliation_string":"Azerbaijan State University of Oil and Industry, Baku, Azerbaijan","institution_ids":["https://openalex.org/I136806742"]},{"raw_affiliation_string":"Department of Computer Engineering, Near East University, Lefkosa, North Cyprus","institution_ids":["https://openalex.org/I69050122"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003799782","display_name":"Witold Pedrycz","orcid":"https://orcid.org/0000-0002-9335-9930"},"institutions":[{"id":"https://openalex.org/I66083562","display_name":"Systems Research Institute","ror":"https://ror.org/0111cp837","country_code":"PL","type":"facility","lineage":["https://openalex.org/I66083562","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"funder","lineage":["https://openalex.org/I99542240"]},{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["CA","PL","SA"],"is_corresponding":false,"raw_author_name":"Witold Pedrycz","raw_affiliation_strings":["Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah, Saudi Arabia","Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada","Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]},{"raw_affiliation_string":"Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland","institution_ids":["https://openalex.org/I66083562","https://openalex.org/I99542240"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052103867","display_name":"O. H. Huseynov","orcid":"https://orcid.org/0000-0003-3843-7403"},"institutions":[{"id":"https://openalex.org/I136806742","display_name":"Azerbaijan State Oil and Industry University","ror":"https://ror.org/05mmnns11","country_code":"AZ","type":"education","lineage":["https://openalex.org/I136806742"]}],"countries":["AZ"],"is_corresponding":false,"raw_author_name":"Oleg H. Huseynov","raw_affiliation_strings":["Research Laboratory of Intelligent Systems of Decision Making and Control in Industry and Economics, Azerbaijan State University of Oil and Industry, Baku, Azerbaijan"],"affiliations":[{"raw_affiliation_string":"Research Laboratory of Intelligent Systems of Decision Making and Control in Industry and Economics, Azerbaijan State University of Oil and Industry, Baku, Azerbaijan","institution_ids":["https://openalex.org/I136806742"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043276594","display_name":"\u015eerife Zihni Ey\u00fcpo\u011flu","orcid":"https://orcid.org/0000-0001-7678-1729"},"institutions":[{"id":"https://openalex.org/I69050122","display_name":"Near East University","ror":"https://ror.org/02x8svs93","country_code":"CY","type":"education","lineage":["https://openalex.org/I69050122"]}],"countries":["CY"],"is_corresponding":false,"raw_author_name":"Serife Zihni Eyupoglu","raw_affiliation_strings":["Department of Business Administration, Near East University, Lefkosa, North Cyprus"],"affiliations":[{"raw_affiliation_string":"Department of Business Administration, Near East University, Lefkosa, North Cyprus","institution_ids":["https://openalex.org/I69050122"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5044050863"],"corresponding_institution_ids":["https://openalex.org/I136806742","https://openalex.org/I69050122"],"apc_list":null,"apc_paid":null,"fwci":8.617,"has_fulltext":false,"cited_by_count":108,"citation_normalized_percentile":{"value":0.97749844,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"25","issue":"6","first_page":"1589","last_page":"1600"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9990000128746033,"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":0.9990000128746033,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9923999905586243,"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/fuzzy-set","display_name":"Fuzzy set","score":0.5812622308731079},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5552324652671814},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5125815272331238},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.5042036771774292},{"id":"https://openalex.org/keywords/possibility-theory","display_name":"Possibility theory","score":0.4634229242801666},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4541832506656647},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.44954365491867065},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.437746524810791},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4142327308654785},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3824999928474426},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.33128198981285095}],"concepts":[{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5812622308731079},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5552324652671814},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5125815272331238},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.5042036771774292},{"id":"https://openalex.org/C137912672","wikidata":"https://www.wikidata.org/wiki/Q1967096","display_name":"Possibility theory","level":4,"score":0.4634229242801666},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4541832506656647},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.44954365491867065},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.437746524810791},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4142327308654785},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3824999928474426},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33128198981285095},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tfuzz.2016.2612303","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2016.2612303","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"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 Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.6000000238418579,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":70,"referenced_works":["https://openalex.org/W43906595","https://openalex.org/W179611734","https://openalex.org/W202063358","https://openalex.org/W207279958","https://openalex.org/W312518228","https://openalex.org/W972800504","https://openalex.org/W1184059260","https://openalex.org/W1499455358","https://openalex.org/W1552255123","https://openalex.org/W1566211337","https://openalex.org/W1641109945","https://openalex.org/W1825902664","https://openalex.org/W1932235888","https://openalex.org/W1932542225","https://openalex.org/W1970922706","https://openalex.org/W1971649776","https://openalex.org/W1979707769","https://openalex.org/W1982865616","https://openalex.org/W1997952930","https://openalex.org/W2000301175","https://openalex.org/W2004139117","https://openalex.org/W2011719763","https://openalex.org/W2011781154","https://openalex.org/W2013198395","https://openalex.org/W2022628426","https://openalex.org/W2031760375","https://openalex.org/W2031955941","https://openalex.org/W2036891811","https://openalex.org/W2038190934","https://openalex.org/W2041280856","https://openalex.org/W2042774699","https://openalex.org/W2057656735","https://openalex.org/W2060921584","https://openalex.org/W2063943005","https://openalex.org/W2073237559","https://openalex.org/W2075090033","https://openalex.org/W2081305819","https://openalex.org/W2085238338","https://openalex.org/W2088758816","https://openalex.org/W2101401875","https://openalex.org/W2115922873","https://openalex.org/W2117223702","https://openalex.org/W2119774578","https://openalex.org/W2122361993","https://openalex.org/W2128313554","https://openalex.org/W2130902926","https://openalex.org/W2130915832","https://openalex.org/W2142422446","https://openalex.org/W2145320441","https://openalex.org/W2152319777","https://openalex.org/W2157041604","https://openalex.org/W2163982943","https://openalex.org/W2184468396","https://openalex.org/W2279545905","https://openalex.org/W2291196818","https://openalex.org/W2335720172","https://openalex.org/W2340270372","https://openalex.org/W2490295271","https://openalex.org/W2503329151","https://openalex.org/W2912565176","https://openalex.org/W4211007335","https://openalex.org/W4240278385","https://openalex.org/W4242600860","https://openalex.org/W4245152641","https://openalex.org/W4254628720","https://openalex.org/W4285719527","https://openalex.org/W4297946089","https://openalex.org/W4300014214","https://openalex.org/W6629974409","https://openalex.org/W6704063259"],"related_works":["https://openalex.org/W4361273540","https://openalex.org/W4361984403","https://openalex.org/W1486684451","https://openalex.org/W2801459815","https://openalex.org/W2099285375","https://openalex.org/W1546758909","https://openalex.org/W4240419148","https://openalex.org/W1579832019","https://openalex.org/W2553068980","https://openalex.org/W3048464822"],"abstract_inverted_index":{"Approximate":[0],"reasoning":[1,4,16,114,151],"is":[2,34,44,78,89,109,146],"about":[3],"with":[5,17,122,152],"imperfect":[6,32,187],"information.":[7,49,188],"Nowadays,":[8],"a":[9,59,79,83,90,99,143,155],"large":[10],"diversity":[11],"of":[12,38,52,58,70,82,85,93,96,101,119,157,164,196],"approaches":[13],"to":[14,46,106,136,148,167,172,179],"approximate":[15,113,150],"fuzzy":[18,21,39,71],"information":[19,23,33],"and":[20,40,74,87,125,171,181,194],"type-2":[22],"exists.":[24],"It":[25],"should":[26],"be":[27],"stressed,":[28],"however,":[29],"that":[30],"real-world":[31],"characterized":[35,185],"by":[36,186],"combination":[37],"probabilistic":[41],"uncertainties,":[42],"which":[43],"referred":[45],"as":[47,62,134],"bimodal":[48],"In":[50,140],"view":[51],"this,":[53],"Zadeh":[54,130],"introduced":[55],"the":[56,117,165,197],"concept":[57],"Z-number":[60],"regarded":[61],"an":[63,137,162],"ordered":[64],"pair":[65],"Z":[66],"=":[67],"(A,":[68],"B)":[69],"numbers":[72],"A":[73,77],"B,":[75],"where":[76],"linguistic":[80,91],"value":[81,92],"variable":[84],"interest,":[86],"B":[88],"probability":[94],"measure":[95],"A,":[97],"playing":[98],"role":[100],"its":[102],"reliability.":[103],"Unfortunately,":[104],"up":[105],"day,":[107],"there":[108],"no":[110],"research":[111],"on":[112,116,154],"realized":[115],"basis":[118,156],"if-then":[120],"rules":[121],"Z-number-valued":[123],"antecedents":[124],"consequents,":[126],"briefly,":[127],"Z-":[128],"rules.":[129],"addressed":[131],"this":[132,141],"problem":[133],"related":[135,178],"uncharted":[138],"territory.":[139],"paper,":[142],"new":[144],"approach":[145,166],"developed":[147],"study":[149],"Z-rules":[153],"linear":[158],"interpolation.":[159],"We":[160],"provide":[161],"application":[163],"job":[168],"satisfaction":[169],"evaluation":[170,176],"students'":[173],"educational":[174],"achievement":[175],"problems":[177],"psychological":[180],"perceptual":[182],"issues":[183],"naturally":[184],"The":[189],"obtained":[190],"results":[191],"show":[192],"applicability":[193],"validity":[195],"proposed":[198],"approach.":[199]},"counts_by_year":[{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":12}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}