{"id":"https://openalex.org/W2113659211","doi":"https://doi.org/10.1109/fuzz.2002.1005061","title":"Inequalities in De Morgan systems. I","display_name":"Inequalities in De Morgan systems. I","publication_year":2003,"publication_date":"2003-06-25","ids":{"openalex":"https://openalex.org/W2113659211","doi":"https://doi.org/10.1109/fuzz.2002.1005061","mag":"2113659211"},"language":"en","primary_location":{"id":"doi:10.1109/fuzz.2002.1005061","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz.2002.1005061","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2002 IEEE World Congress on Computational Intelligence. 2002 IEEE International Conference on Fuzzy Systems. FUZZ-IEEE'02. Proceedings (Cat. No.02CH37291)","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/A5110609480","display_name":"Carol L. Walker","orcid":null},"institutions":[{"id":"https://openalex.org/I10052268","display_name":"New Mexico State University","ror":"https://ror.org/00hpz7z43","country_code":"US","type":"education","lineage":["https://openalex.org/I10052268"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"C. Walker","raw_affiliation_strings":["New Mexico State University, Las Cruces, NM, USA","New Mexico State University , Las Cruces , NM , USA"],"affiliations":[{"raw_affiliation_string":"New Mexico State University, Las Cruces, NM, USA","institution_ids":["https://openalex.org/I10052268"]},{"raw_affiliation_string":"New Mexico State University , Las Cruces , NM , USA","institution_ids":["https://openalex.org/I10052268"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110062855","display_name":"E. Walker","orcid":null},"institutions":[{"id":"https://openalex.org/I10052268","display_name":"New Mexico State University","ror":"https://ror.org/00hpz7z43","country_code":"US","type":"education","lineage":["https://openalex.org/I10052268"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E. Walker","raw_affiliation_strings":["New Mexico State University, Las Cruces, NM, USA","New Mexico State University , Las Cruces , NM , USA"],"affiliations":[{"raw_affiliation_string":"New Mexico State University, Las Cruces, NM, USA","institution_ids":["https://openalex.org/I10052268"]},{"raw_affiliation_string":"New Mexico State University , Las Cruces , NM , USA","institution_ids":["https://openalex.org/I10052268"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110609480"],"corresponding_institution_ids":["https://openalex.org/I10052268"],"apc_list":null,"apc_paid":null,"fwci":1.4547,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.82676913,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"1","issue":null,"first_page":"607","last_page":"609"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9994000196456909,"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":0.9994000196456909,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9939000010490417,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9876000285148621,"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/negation","display_name":"Negation","score":0.8249943256378174},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5544513463973999},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5457831621170044},{"id":"https://openalex.org/keywords/boolean-algebra","display_name":"Boolean algebra","score":0.49985694885253906},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.49586281180381775},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.48656097054481506},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.43909427523612976},{"id":"https://openalex.org/keywords/unit-interval","display_name":"Unit interval","score":0.42768871784210205},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36754560470581055},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3207697868347168},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24199721217155457},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.07888656854629517},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.06975376605987549}],"concepts":[{"id":"https://openalex.org/C2185349","wikidata":"https://www.wikidata.org/wiki/Q190558","display_name":"Negation","level":2,"score":0.8249943256378174},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5544513463973999},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5457831621170044},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.49985694885253906},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.49586281180381775},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.48656097054481506},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.43909427523612976},{"id":"https://openalex.org/C128394911","wikidata":"https://www.wikidata.org/wiki/Q1987578","display_name":"Unit interval","level":2,"score":0.42768871784210205},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36754560470581055},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3207697868347168},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24199721217155457},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.07888656854629517},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.06975376605987549},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/fuzz.2002.1005061","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz.2002.1005061","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2002 IEEE World Congress on Computational Intelligence. 2002 IEEE International Conference on Fuzzy Systems. FUZZ-IEEE'02. Proceedings (Cat. No.02CH37291)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.205.3348","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.205.3348","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.nmsu.edu/%7Ehardy/wcci2002Honoluluelbert.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.6800000071525574}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W5908805","https://openalex.org/W1601200269","https://openalex.org/W1985204380","https://openalex.org/W1992093132","https://openalex.org/W2008679964","https://openalex.org/W2068402605","https://openalex.org/W2127350003","https://openalex.org/W2130030409","https://openalex.org/W2153181185","https://openalex.org/W2163160345","https://openalex.org/W4230159267","https://openalex.org/W4248692849","https://openalex.org/W6600244361","https://openalex.org/W6652643323"],"related_works":["https://openalex.org/W2059922809","https://openalex.org/W2387527986","https://openalex.org/W2479250593","https://openalex.org/W4283261428","https://openalex.org/W2131148043","https://openalex.org/W2092783274","https://openalex.org/W4318829426","https://openalex.org/W4391025849","https://openalex.org/W4384940451","https://openalex.org/W2389908864"],"abstract_inverted_index":{"In":[0],"a":[1,60],"Boolean":[2],"algebra,":[3],"every":[4],"element":[5],"has":[6],"two":[7,86],"canonical":[8],"forms,":[9],"its":[10,16,63],"disjunctive":[11],"normal":[12,18],"form":[13,19],"(BDNF)":[14],"and":[15,38,52,62,75],"conjunctive":[17],"(BCNF).":[20],"If":[21,48],"these":[22],"elements":[23],"are":[24,57],"viewed":[25],"in":[26,54,84],"the":[27,31,39,42,49,67,70,85],"algebra":[28,56],"consisting":[29],"of":[30],"unit":[32],"interval":[33],"with":[34],"operations":[35,50],"min,":[36],"max,":[37],"usual":[40,68],"negation,":[41,69],"inequality":[43,72],"BDNF/spl":[44],"les/BCNF":[45],"always":[46],"holds.":[47],"min":[51],"max":[53],"this":[55,81],"replaced":[58],"by":[59],"t-norm":[61],"t-conorm":[64],"dual":[65],"to":[66],"resulting":[71],"holds":[73],"sometimes":[74],"fails":[76],"sometimes.":[77],"The":[78],"paper":[79],"examines":[80],"phenomenon,":[82],"especially":[83],"variable":[87],"case.":[88]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}