{"id":"https://openalex.org/W2099426586","doi":"https://doi.org/10.1109/isspa.2007.4555483","title":"Continuity of product-sum-gravity method on L&lt;sup&gt;2&lt;/sup&gt; space using fuzzy number for premise variable","display_name":"Continuity of product-sum-gravity method on L&lt;sup&gt;2&lt;/sup&gt; space using fuzzy number for premise variable","publication_year":2007,"publication_date":"2007-02-01","ids":{"openalex":"https://openalex.org/W2099426586","doi":"https://doi.org/10.1109/isspa.2007.4555483","mag":"2099426586"},"language":"en","primary_location":{"id":"doi:10.1109/isspa.2007.4555483","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isspa.2007.4555483","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 9th International Symposium on Signal Processing and Its Applications","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/A5085141878","display_name":"Takashi Mitsuishi","orcid":null},"institutions":[{"id":"https://openalex.org/I59596033","display_name":"University of Marketing and Distribution Sciences","ror":"https://ror.org/05k4ves29","country_code":"JP","type":"education","lineage":["https://openalex.org/I59596033"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takashi Mitsuishi","raw_affiliation_strings":["Faculty of Information, University of Marketing and Distribution Sciences, Kobe, Japan","Fac. of Inf., Univ. of Marketing & Distrib. Sci., Kobe"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Information, University of Marketing and Distribution Sciences, Kobe, Japan","institution_ids":["https://openalex.org/I59596033"]},{"raw_affiliation_string":"Fac. of Inf., Univ. of Marketing & Distrib. Sci., Kobe","institution_ids":["https://openalex.org/I59596033"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055549852","display_name":"Yasunari Shidama","orcid":"https://orcid.org/0000-0001-5634-0838"},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yasunari Shidama","raw_affiliation_strings":["Faculty of Engineering, Shinshu University, Nagano, Japan","Shinshu University, Faculty of Engineering, 4-17-1 Wakasato, Nagano 380-8553 Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Shinshu University, Nagano, Japan","institution_ids":["https://openalex.org/I137975476"]},{"raw_affiliation_string":"Shinshu University, Faculty of Engineering, 4-17-1 Wakasato, Nagano 380-8553 Japan","institution_ids":["https://openalex.org/I137975476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9688,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.82534075,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"1","issue":null,"first_page":"1","last_page":"4"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9915000200271606,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9887999892234802,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.6892136931419373},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6589517593383789},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.6198551654815674},{"id":"https://openalex.org/keywords/premise","display_name":"Premise","score":0.5700279474258423},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5627702474594116},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5288202166557312},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.49173691868782043},{"id":"https://openalex.org/keywords/fuzzy-control-system","display_name":"Fuzzy control system","score":0.49118420481681824},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.4834190607070923},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.47944775223731995},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4757939577102661},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46784600615501404},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4556288421154022},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4266386032104492},{"id":"https://openalex.org/keywords/fuzzy-mathematics","display_name":"Fuzzy mathematics","score":0.4256085157394409},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2929750382900238},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2320423722267151},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1857582926750183},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13477370142936707}],"concepts":[{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.6892136931419373},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6589517593383789},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.6198551654815674},{"id":"https://openalex.org/C2778023277","wikidata":"https://www.wikidata.org/wiki/Q321703","display_name":"Premise","level":2,"score":0.5700279474258423},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5627702474594116},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5288202166557312},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.49173691868782043},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.49118420481681824},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.4834190607070923},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.47944775223731995},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4757939577102661},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46784600615501404},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4556288421154022},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4266386032104492},{"id":"https://openalex.org/C166586474","wikidata":"https://www.wikidata.org/wiki/Q5511129","display_name":"Fuzzy mathematics","level":5,"score":0.4256085157394409},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2929750382900238},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2320423722267151},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1857582926750183},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13477370142936707},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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":1,"locations":[{"id":"doi:10.1109/isspa.2007.4555483","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isspa.2007.4555483","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 9th International Symposium on Signal Processing and Its Applications","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":12,"referenced_works":["https://openalex.org/W1970104171","https://openalex.org/W2121146657","https://openalex.org/W2128523553","https://openalex.org/W2159582391","https://openalex.org/W2335062971","https://openalex.org/W2618704776","https://openalex.org/W2914019270","https://openalex.org/W3140062925","https://openalex.org/W3141151088","https://openalex.org/W4212771256","https://openalex.org/W6704218619","https://openalex.org/W6738107611"],"related_works":["https://openalex.org/W74364172","https://openalex.org/W2287021682","https://openalex.org/W2006645915","https://openalex.org/W2060486654","https://openalex.org/W2893993940","https://openalex.org/W2061828243","https://openalex.org/W2093064982","https://openalex.org/W1918299039","https://openalex.org/W3000504909","https://openalex.org/W2130941169"],"abstract_inverted_index":{"The":[0],"authors":[1],"present":[2],"a":[3,8,22,74],"mathematical":[4],"framework":[5],"for":[6],"studying":[7],"fuzzy":[9,19,28,43,105],"feedback":[10,95],"control":[11,96],"system,":[12],"which":[13],"is":[14,66,84],"constructed":[15],"by":[16,97],"if-then":[17,42],"type":[18],"rules":[20],"through":[21],"kind":[23],"of":[24,33,49,54,57,79,100,102,104],"product-sum-gravity":[25],"method.":[26],"Moreover,":[27],"numbers":[29],"are":[30],"used":[31],"instead":[32],"definite":[34],"values":[35],"(crisp":[36],"numbers)":[37],"as":[38],"premise":[39],"variables":[40],"in":[41,60],"rule.":[44],"To":[45],"guarantee":[46],"the":[47,52,55,77,90],"convergence":[48],"optimal":[50,94],"solution":[51],"compactness":[53,101],"set":[56,78],"membership":[58,80,106],"functions":[59],"L":[61],"<sup":[62],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[63],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[64],"space":[65],"proved.":[67,85],"And":[68],"assuming":[69],"approximate":[70],"reasoning":[71],"to":[72],"be":[73],"functional":[75],"on":[76],"functions,":[81],"its":[82],"continuity":[83],"Then,":[86],"we":[87],"show":[88],"that":[89],"system":[91],"has":[92],"an":[93],"essential":[98],"use":[99],"sets":[103],"functions.":[107]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
