{"id":"https://openalex.org/W2966467061","doi":"https://doi.org/10.3390/axioms8030095","title":"Why Triangular Membership Functions Are Successfully Used in F-Transform Applications: A Global Explanation to Supplement the Existing Local Ones","display_name":"Why Triangular Membership Functions Are Successfully Used in F-Transform Applications: A Global Explanation to Supplement the Existing Local Ones","publication_year":2019,"publication_date":"2019-08-05","ids":{"openalex":"https://openalex.org/W2966467061","doi":"https://doi.org/10.3390/axioms8030095","mag":"2966467061"},"language":"en","primary_location":{"id":"doi:10.3390/axioms8030095","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms8030095","pdf_url":"https://www.mdpi.com/2075-1680/8/3/95/pdf?version=1564990761","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://www.mdpi.com/2075-1680/8/3/95/pdf?version=1564990761","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075920182","display_name":"Olga Kosheleva","orcid":"https://orcid.org/0000-0003-2587-4209"},"institutions":[{"id":"https://openalex.org/I164936912","display_name":"The University of Texas at El Paso","ror":"https://ror.org/04d5vba33","country_code":"US","type":"education","lineage":["https://openalex.org/I164936912"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Olga Kosheleva","raw_affiliation_strings":["Department of Teacher Education, University of Texas at El Paso, El Paso, TX 79968, USA"],"affiliations":[{"raw_affiliation_string":"Department of Teacher Education, University of Texas at El Paso, El Paso, TX 79968, USA","institution_ids":["https://openalex.org/I164936912"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061275811","display_name":"\u0412\u043b\u0430\u0434\u0438\u043a \u041a\u0440\u0435\u0439\u043d\u043e\u0432\u0438\u0447","orcid":"https://orcid.org/0000-0002-1244-1650"},"institutions":[{"id":"https://openalex.org/I164936912","display_name":"The University of Texas at El Paso","ror":"https://ror.org/04d5vba33","country_code":"US","type":"education","lineage":["https://openalex.org/I164936912"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Vladik Kreinovich","raw_affiliation_strings":["Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA","institution_ids":["https://openalex.org/I164936912"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101981883","display_name":"Thach Ngoc Nguyen","orcid":"https://orcid.org/0000-0002-3814-7265"},"institutions":[{"id":"https://openalex.org/I3129629310","display_name":"Ho Chi Minh University of Banking","ror":"https://ror.org/03fsckq75","country_code":"VN","type":"education","lineage":["https://openalex.org/I3129629310"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Thach Ngoc Nguyen","raw_affiliation_strings":["Institute of Banking Research and Technology, Banking University of Ho Chi Minh City, 56 Hoang Dieu 2, Thu Duc, Ho Chi Minh City 71010, Vietnam"],"affiliations":[{"raw_affiliation_string":"Institute of Banking Research and Technology, Banking University of Ho Chi Minh City, 56 Hoang Dieu 2, Thu Duc, Ho Chi Minh City 71010, Vietnam","institution_ids":["https://openalex.org/I3129629310"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061275811"],"corresponding_institution_ids":["https://openalex.org/I164936912"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.388,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.636675,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"8","issue":"3","first_page":"95","last_page":"95"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9970999956130981,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9970999956130981,"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":0.9898999929428101,"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"}},{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9894000291824341,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.5717131495475769},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4793563485145569},{"id":"https://openalex.org/keywords/phenomenon","display_name":"Phenomenon","score":0.4638267755508423},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4330233633518219},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3848654329776764},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3658373951911926},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.14664465188980103}],"concepts":[{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.5717131495475769},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4793563485145569},{"id":"https://openalex.org/C50335755","wikidata":"https://www.wikidata.org/wiki/Q483247","display_name":"Phenomenon","level":2,"score":0.4638267755508423},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4330233633518219},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3848654329776764},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3658373951911926},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.14664465188980103},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms8030095","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms8030095","pdf_url":"https://www.mdpi.com/2075-1680/8/3/95/pdf?version=1564990761","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:d39fd7b982f749888c18730cb14a72eb","is_oa":true,"landing_page_url":"https://doaj.org/article/d39fd7b982f749888c18730cb14a72eb","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"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 8, Iss 3, p 95 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/8/3/95/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms8030095","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 8; Issue 3; Pages: 95","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms8030095","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms8030095","pdf_url":"https://www.mdpi.com/2075-1680/8/3/95/pdf?version=1564990761","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":[],"awards":[{"id":"https://openalex.org/G2981983478","display_name":null,"funder_award_id":"HRD-1242122","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6793870340","display_name":null,"funder_award_id":"1623190","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2966467061.pdf","grobid_xml":"https://content.openalex.org/works/W2966467061.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W564030374","https://openalex.org/W586186677","https://openalex.org/W1481101934","https://openalex.org/W1997196510","https://openalex.org/W2002918766","https://openalex.org/W2037138572","https://openalex.org/W2041144576","https://openalex.org/W2075594316","https://openalex.org/W2481995907","https://openalex.org/W2613291186","https://openalex.org/W2781044394","https://openalex.org/W2793334974","https://openalex.org/W2796751344","https://openalex.org/W2804212075","https://openalex.org/W2902062307","https://openalex.org/W2912565176","https://openalex.org/W2953712194","https://openalex.org/W4211007335","https://openalex.org/W4231804901","https://openalex.org/W4234976561","https://openalex.org/W4249816584","https://openalex.org/W4254931243","https://openalex.org/W4289127527","https://openalex.org/W6617208349"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4300450609","https://openalex.org/W4386931570","https://openalex.org/W2391010541","https://openalex.org/W2357367123","https://openalex.org/W4388930439","https://openalex.org/W2387276901","https://openalex.org/W1979597421","https://openalex.org/W2385953334","https://openalex.org/W2351303360"],"abstract_inverted_index":{"The":[0],"main":[1],"ideas":[2],"of":[3,42,55,77,108,113],"F-transform":[4,34,56],"came":[5],"from":[6],"representing":[7],"expert":[8],"rules.":[9],"It":[10],"would":[11],"be":[12,31],"therefore":[13],"reasonable":[14],"to":[15,46],"expect":[16],"that":[17,38,95,103],"the":[18,21,27,32,58,78,100,105,109,114],"more":[19,28],"accurately":[20],"membership":[22,48,62,97],"functions":[23,98],"describe":[24],"human":[25],"reasoning,":[26],"successful":[29,53],"will":[30],"corresponding":[33],"formulas.":[35],"We":[36],"know":[37],"an":[39],"adequate":[40],"description":[41],"our":[43],"reasoning":[44],"corresponds":[45],"complicated":[47],"functions\u2014however,":[49],"somewhat":[50],"surprisingly,":[51],"many":[52],"applications":[54],"use":[57],"simplest":[59],"possible":[60],"triangular":[61,96],"functions.":[63],"There":[64],"exist":[65],"some":[66],"explanations":[67,87],"for":[68],"this":[69,81],"phenomenon,":[70],"which":[71],"are":[72,99],"based":[73],"on":[74],"local":[75,86],"behavior":[76],"signal.":[79,115],"In":[80],"paper,":[82],"we":[83,93],"supplement":[84],"these":[85],"by":[88],"a":[89],"global":[90,111],"one:":[91],"namely,":[92],"prove":[94],"only":[101],"one":[102],"provide":[104],"exact":[106],"reconstruction":[107],"appropriate":[110],"characteristic":[112]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2019-08-13T00:00:00"}