{"id":"https://openalex.org/W2751230672","doi":"https://doi.org/10.1007/978-3-319-66824-6_20","title":"The Law of Contraposition and the Law of Importation for Probabilistic S-Implications","display_name":"The Law of Contraposition and the Law of Importation for Probabilistic S-Implications","publication_year":2017,"publication_date":"2017-08-29","ids":{"openalex":"https://openalex.org/W2751230672","doi":"https://doi.org/10.1007/978-3-319-66824-6_20","mag":"2751230672"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-66824-6_20","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-66824-6_20","pdf_url":null,"source":{"id":"https://openalex.org/S2764905038","display_name":"Advances in intelligent systems and computing","issn_l":"2194-5357","issn":["2194-5357","2194-5365"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Intelligent Systems and Computing","raw_type":"book-chapter"},"type":"book-chapter","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/A5091457078","display_name":"Piotr Helbin","orcid":"https://orcid.org/0000-0001-5961-3010"},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I864159182","display_name":"University of Silesia in Katowice","ror":"https://ror.org/0104rcc94","country_code":"PL","type":"education","lineage":["https://openalex.org/I864159182"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Piotr Helbin","raw_affiliation_strings":["Institute of Mathematics, University of Silesia, Bankowa 14, 40-007, Katowice, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Silesia, Bankowa 14, 40-007, Katowice, Poland","institution_ids":["https://openalex.org/I864159182","https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5091457078"],"corresponding_institution_ids":["https://openalex.org/I4210137370","https://openalex.org/I864159182"],"apc_list":null,"apc_paid":null,"fwci":1.0093,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.77706167,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"226","last_page":"237"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9955999851226807,"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":0.9955999851226807,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.984499990940094,"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":0.9408000111579895,"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/probabilistic-logic","display_name":"Probabilistic logic","score":0.884357213973999},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5588934421539307},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.5047527551651001},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.45843440294265747},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.384752094745636},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3815041780471802},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3396915793418884},{"id":"https://openalex.org/keywords/law-and-economics","display_name":"Law and economics","score":0.331493079662323},{"id":"https://openalex.org/keywords/sociology","display_name":"Sociology","score":0.26880496740341187},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.2687944769859314},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22852149605751038},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05652317404747009}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.884357213973999},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5588934421539307},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.5047527551651001},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.45843440294265747},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.384752094745636},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3815041780471802},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3396915793418884},{"id":"https://openalex.org/C190253527","wikidata":"https://www.wikidata.org/wiki/Q295354","display_name":"Law and economics","level":1,"score":0.331493079662323},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.26880496740341187},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.2687944769859314},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22852149605751038},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05652317404747009},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-319-66824-6_20","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-66824-6_20","pdf_url":null,"source":{"id":"https://openalex.org/S2764905038","display_name":"Advances in intelligent systems and computing","issn_l":"2194-5357","issn":["2194-5357","2194-5365"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Intelligent Systems and Computing","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6600000262260437,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W138381777","https://openalex.org/W656973277","https://openalex.org/W1606108510","https://openalex.org/W1830776758","https://openalex.org/W1923956138","https://openalex.org/W1989704856","https://openalex.org/W2112660043","https://openalex.org/W2913824272","https://openalex.org/W2915061287","https://openalex.org/W3158113069","https://openalex.org/W4232299526","https://openalex.org/W4234672050"],"related_works":["https://openalex.org/W2012531322","https://openalex.org/W2494523064","https://openalex.org/W2943623134","https://openalex.org/W2785900585","https://openalex.org/W2588219639","https://openalex.org/W2353730437","https://openalex.org/W2030292806","https://openalex.org/W2215759665","https://openalex.org/W2490303674","https://openalex.org/W2609066826"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}