{"id":"https://openalex.org/W3083358500","doi":"https://doi.org/10.1007/s00500-020-05238-3","title":"Approximation of two-variable functions using high-order Takagi\u2013Sugeno fuzzy systems, sparse regressions, and metaheuristic optimization","display_name":"Approximation of two-variable functions using high-order Takagi\u2013Sugeno fuzzy systems, sparse regressions, and metaheuristic optimization","publication_year":2020,"publication_date":"2020-09-05","ids":{"openalex":"https://openalex.org/W3083358500","doi":"https://doi.org/10.1007/s00500-020-05238-3","mag":"3083358500"},"language":"en","primary_location":{"id":"doi:10.1007/s00500-020-05238-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00500-020-05238-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00500-020-05238-3.pdf","source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00500-020-05238-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023446547","display_name":"Krzysztof Wiktorowicz","orcid":"https://orcid.org/0000-0001-8711-1659"},"institutions":[{"id":"https://openalex.org/I111664937","display_name":"Rzesz\u00f3w University of Technology","ror":"https://ror.org/056xse072","country_code":"PL","type":"education","lineage":["https://openalex.org/I111664937"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Krzysztof Wiktorowicz","raw_affiliation_strings":["Faculty of Electrical and Computer Engineering, Rzeszow University of Technology, al. Powstancow Warszawy 12, 35-959, Rzeszow, Poland"],"raw_orcid":"https://orcid.org/0000-0001-8711-1659","affiliations":[{"raw_affiliation_string":"Faculty of Electrical and Computer Engineering, Rzeszow University of Technology, al. Powstancow Warszawy 12, 35-959, Rzeszow, Poland","institution_ids":["https://openalex.org/I111664937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031387603","display_name":"Tomasz Krzeszowski","orcid":"https://orcid.org/0000-0001-7359-4637"},"institutions":[{"id":"https://openalex.org/I111664937","display_name":"Rzesz\u00f3w University of Technology","ror":"https://ror.org/056xse072","country_code":"PL","type":"education","lineage":["https://openalex.org/I111664937"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Tomasz Krzeszowski","raw_affiliation_strings":["Faculty of Electrical and Computer Engineering, Rzeszow University of Technology, al. Powstancow Warszawy 12, 35-959, Rzeszow, Poland"],"raw_orcid":"https://orcid.org/0000-0001-7359-4637","affiliations":[{"raw_affiliation_string":"Faculty of Electrical and Computer Engineering, Rzeszow University of Technology, al. Powstancow Warszawy 12, 35-959, Rzeszow, Poland","institution_ids":["https://openalex.org/I111664937"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023446547"],"corresponding_institution_ids":["https://openalex.org/I111664937"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.9385,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.81239883,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"24","issue":"20","first_page":"15113","last_page":"15127"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9994000196456909,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9937000274658203,"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/T10320","display_name":"Neural Networks and Applications","score":0.9879000186920166,"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/metaheuristic","display_name":"Metaheuristic","score":0.7269608974456787},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6029913425445557},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5837415456771851},{"id":"https://openalex.org/keywords/particle-swarm-optimization","display_name":"Particle swarm optimization","score":0.5236560702323914},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5183264017105103},{"id":"https://openalex.org/keywords/simulated-annealing","display_name":"Simulated annealing","score":0.5115102529525757},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3600490093231201},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3583333194255829},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33189982175827026}],"concepts":[{"id":"https://openalex.org/C109718341","wikidata":"https://www.wikidata.org/wiki/Q1385229","display_name":"Metaheuristic","level":2,"score":0.7269608974456787},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6029913425445557},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5837415456771851},{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.5236560702323914},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5183264017105103},{"id":"https://openalex.org/C126980161","wikidata":"https://www.wikidata.org/wiki/Q863783","display_name":"Simulated annealing","level":2,"score":0.5115102529525757},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3600490093231201},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3583333194255829},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33189982175827026}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00500-020-05238-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00500-020-05238-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00500-020-05238-3.pdf","source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00500-020-05238-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00500-020-05238-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00500-020-05238-3.pdf","source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3083358500.pdf","grobid_xml":"https://content.openalex.org/works/W3083358500.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W995630646","https://openalex.org/W1499209894","https://openalex.org/W1506806321","https://openalex.org/W1539238865","https://openalex.org/W1659842140","https://openalex.org/W1875348914","https://openalex.org/W1990521272","https://openalex.org/W1998326571","https://openalex.org/W2008175782","https://openalex.org/W2011272021","https://openalex.org/W2016698759","https://openalex.org/W2020329107","https://openalex.org/W2024060531","https://openalex.org/W2024723354","https://openalex.org/W2029399898","https://openalex.org/W2032663886","https://openalex.org/W2038289871","https://openalex.org/W2047028564","https://openalex.org/W2047094503","https://openalex.org/W2063978378","https://openalex.org/W2067811909","https://openalex.org/W2070459079","https://openalex.org/W2072245897","https://openalex.org/W2077562320","https://openalex.org/W2079325629","https://openalex.org/W2089299272","https://openalex.org/W2101036899","https://openalex.org/W2116957451","https://openalex.org/W2118030936","https://openalex.org/W2120845011","https://openalex.org/W2122825543","https://openalex.org/W2134246787","https://openalex.org/W2135046866","https://openalex.org/W2144630308","https://openalex.org/W2148948822","https://openalex.org/W2152195021","https://openalex.org/W2168366203","https://openalex.org/W2265085376","https://openalex.org/W2321496009","https://openalex.org/W2577476110","https://openalex.org/W2729976127","https://openalex.org/W2756946419","https://openalex.org/W2763689883","https://openalex.org/W2765981075","https://openalex.org/W2791929225","https://openalex.org/W2801014085","https://openalex.org/W2983710221","https://openalex.org/W4234698323"],"related_works":["https://openalex.org/W2789681586","https://openalex.org/W2794361564","https://openalex.org/W4243392960","https://openalex.org/W1939200287","https://openalex.org/W2082305040","https://openalex.org/W4381955380","https://openalex.org/W1980833393","https://openalex.org/W1967228184","https://openalex.org/W4327850430","https://openalex.org/W3095745430"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"proposes":[3],"a":[4,51,99],"new":[5],"hybrid":[6],"method":[7,54],"for":[8],"training":[9],"high-order":[10,33],"Takagi\u2013Sugeno":[11],"fuzzy":[12,21,27,39,42,107,146],"systems":[13],"using":[14,68],"sparse":[15,75,121,141],"regressions":[16,76,122,142],"and":[17,32,85,88,109,136],"metaheuristic":[18,52,124],"optimization.":[19],"The":[20,41,112],"system":[22],"is":[23,95],"considered":[24],"with":[25,132],"Gaussian":[26],"sets":[28,43],"in":[29,35],"the":[30,36,64,102,106,118,128,133,138,145,152],"antecedents":[31],"polynomials":[34,65],"consequents":[37],"of":[38,105,120,140,151],"rules.":[40],"can":[44,126],"be":[45],"chosen":[46],"manually":[47],"or":[48,60,74],"determined":[49],"by":[50,148],"optimization":[53,125],"(particle":[55],"swarm":[56],"optimization,":[57],"genetic":[58],"algorithm":[59],"simulated":[61],"annealing),":[62],"while":[63],"are":[66],"obtained":[67],"ordinary":[69],"least":[70,79,82],"squares,":[71],"ridge":[72],"regression":[73],"(forward":[77],"selection,":[78],"angle":[80],"regression,":[81],"absolute":[83],"shrinkage":[84],"selection":[86],"operator,":[87],"elastic":[89],"net":[90],"regression).":[91],"A":[92],"quality":[93],"criterion":[94],"proposed":[96],"that":[97],"expresses":[98],"compromise":[100],"between":[101],"prediction":[103],"ability":[104],"model":[108,147],"its":[110],"sparsity.":[111],"conducted":[113],"experiments":[114],"showed":[115],"that:":[116],"(a)":[117],"use":[119,139],"and/or":[123],"reduce":[127],"validation":[129],"error":[130],"compared":[131],"reference":[134],"method,":[135],"(b)":[137],"may":[143],"simplify":[144],"zeroing":[149],"some":[150],"coefficients.":[153]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}