{"id":"https://openalex.org/W2550584236","doi":"https://doi.org/10.1109/fuzz-ieee.2016.7737697","title":"On rational fuzzy implication functions","display_name":"On rational fuzzy implication functions","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2550584236","doi":"https://doi.org/10.1109/fuzz-ieee.2016.7737697","mag":"2550584236"},"language":"en","primary_location":{"id":"doi:10.1109/fuzz-ieee.2016.7737697","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz-ieee.2016.7737697","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)","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/A5017546076","display_name":"Sebasti\u00e0 Massanet","orcid":"https://orcid.org/0000-0001-8243-5013"},"institutions":[{"id":"https://openalex.org/I50441567","display_name":"Universitat de les Illes Balears","ror":"https://ror.org/03e10x626","country_code":"ES","type":"education","lineage":["https://openalex.org/I50441567"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Sebastia Massanet","raw_affiliation_strings":["Dept. Mathematics and Computer Science, University of the Balearic Islands, Palma, Spain"],"affiliations":[{"raw_affiliation_string":"Dept. Mathematics and Computer Science, University of the Balearic Islands, Palma, Spain","institution_ids":["https://openalex.org/I50441567"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005035399","display_name":"Juan Vicente Riera","orcid":"https://orcid.org/0000-0002-0878-8301"},"institutions":[{"id":"https://openalex.org/I50441567","display_name":"Universitat de les Illes Balears","ror":"https://ror.org/03e10x626","country_code":"ES","type":"education","lineage":["https://openalex.org/I50441567"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Juan Vicente Riera","raw_affiliation_strings":["Dept. Mathematics and Computer Science, University of the Balearic Islands, Palma, Spain"],"affiliations":[{"raw_affiliation_string":"Dept. Mathematics and Computer Science, University of the Balearic Islands, Palma, Spain","institution_ids":["https://openalex.org/I50441567"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041876130","display_name":"Daniel Ruiz-Aguilera","orcid":"https://orcid.org/0000-0001-9413-009X"},"institutions":[{"id":"https://openalex.org/I50441567","display_name":"Universitat de les Illes Balears","ror":"https://ror.org/03e10x626","country_code":"ES","type":"education","lineage":["https://openalex.org/I50441567"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Daniel Ruiz-Aguilera","raw_affiliation_strings":["Dept. Mathematics and Computer Science, University of the Balearic Islands, Palma, Spain"],"affiliations":[{"raw_affiliation_string":"Dept. Mathematics and Computer Science, University of the Balearic Islands, Palma, Spain","institution_ids":["https://openalex.org/I50441567"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5017546076"],"corresponding_institution_ids":["https://openalex.org/I50441567"],"apc_list":null,"apc_paid":null,"fwci":0.7181,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.78304912,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"272","last_page":"279"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9957000017166138,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6877739429473877},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6271454095840454},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.571919322013855},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.5643026828765869},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4996018409729004},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.4909079670906067},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4733465015888214},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.4520256519317627},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4236496686935425},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.349473774433136},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3490142822265625},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32830774784088135},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.3168942332267761},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28297847509384155},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15425145626068115}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6877739429473877},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6271454095840454},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.571919322013855},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.5643026828765869},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4996018409729004},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.4909079670906067},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4733465015888214},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.4520256519317627},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4236496686935425},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.349473774433136},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3490142822265625},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32830774784088135},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3168942332267761},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28297847509384155},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15425145626068115},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fuzz-ieee.2016.7737697","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz-ieee.2016.7737697","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W32776350","https://openalex.org/W377680676","https://openalex.org/W656973277","https://openalex.org/W1569422684","https://openalex.org/W1606108510","https://openalex.org/W1673969116","https://openalex.org/W2015620414","https://openalex.org/W2025021415","https://openalex.org/W2052215587","https://openalex.org/W2061539836","https://openalex.org/W2221355491","https://openalex.org/W2272156062","https://openalex.org/W2288230525","https://openalex.org/W2553658571","https://openalex.org/W4234672050","https://openalex.org/W4299417699","https://openalex.org/W6729877602"],"related_works":["https://openalex.org/W2773005380","https://openalex.org/W4388451300","https://openalex.org/W2060361571","https://openalex.org/W1879432897","https://openalex.org/W2256857057","https://openalex.org/W3167814444","https://openalex.org/W3176863924","https://openalex.org/W2023513928","https://openalex.org/W2182392910","https://openalex.org/W4361984403"],"abstract_inverted_index":{"The":[0],"proposal":[1],"of":[2,5,16,44,50,57,75,78,85,102,105,128,136,144],"new":[3],"classes":[4],"fuzzy":[6,29,58,65,92,114,122,145],"implication":[7,30,66,93,115,146],"functions":[8,31,67,147],"must":[9],"take":[10],"into":[11],"account":[12],"the":[13,17,42,55,73,100,103,106],"final":[14],"expression":[15,69],"operator":[18],"to":[19,89,99,110],"be":[20],"potentially":[21],"used":[22],"in":[23,52],"a":[24,91,113],"concrete":[25],"application.":[26],"In":[27,117],"particular,":[28],"with":[32,141],"simple":[33],"expressions":[34],"have":[35],"low":[36],"computational":[37],"cost":[38],"and":[39,139],"they":[40],"reduce":[41],"spreading":[43],"numerical":[45],"errors.":[46],"Following":[47],"this":[48,53],"line":[49],"research,":[51],"work,":[54],"class":[56],"rational":[59,123],"implications":[60,124,138],"is":[61,70],"introduced":[62],"as":[63],"those":[64],"whose":[68],"given":[71,109],"by":[72],"quotient":[74],"two":[76,79],"polynomials":[77,86,107,127],"variables.":[80],"Since":[81],"not":[82],"all":[83,121],"quotients":[84],"are":[87,108,148],"adequate":[88],"generate":[90],"function,":[94],"some":[95,129],"necessary":[96],"properties":[97],"related":[98],"values":[101],"coefficients":[104],"ensure":[111],"obtaining":[112],"function.":[116],"addition,":[118],"we":[119],"characterize":[120],"constructed":[125],"from":[126],"fixed":[130],"degrees.":[131],"Finally,":[132],"several":[133],"construction":[134],"methods":[135],"these":[137],"relationships":[140],"other":[142],"families":[143],"given.":[149]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-25T21:42:39.735039","created_date":"2025-10-10T00:00:00"}