{"corpus_id":122493437,"paper_sha":"0c8ae9ad721d9e5a89c52ab536b9828c76d4fae9","doi":"10.3390/books978-3-03897-323-2","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":null,"dblp_id":null,"acl_id":null,"title":"Fuzzy Mathematics","year":2018,"publication_date":"2018-11-21","venue":"","journal":null,"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":[],"reference_count":0,"citation_count":66,"influential_citation_count":0,"is_open_access":true,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":"https://openresearchlibrary.org/ext/api/media/8496b8c1-5c0e-42b7-9452-0ee468dfda2a/assets/external_content.pdf","s2_open_access_landing_url":"https://www.semanticscholar.org/paper/0c8ae9ad721d9e5a89c52ab536b9828c76d4fae9","s2_open_access_license":"CCBYNCND","s2_open_access_status":"GREEN","pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"Cl Fuzzy concepts are 'natural' generalizations of conventional mathematical concepts. Cl Probability and possibility are complementary. Cl Possibility theory is the attempt to be precise about uncertainty, to related statistical objects with rule-based and fuzzy concepts. Everything is a matter of degree.-The Fuzzy Principle Since almost all objects of mathematics can be described by sets (e.g., a function as a set of ordered pairs), one can establish fuzzy generalizations for nearly all of those. In the previous sections, we have seen that fuzzy mathematical concepts occur 'naturally', that is, considering the uncertainty involved in the application, the need to generalize creates fuzzy mathematical objects. We considered 0 fuzzy sets l fuzzy graphs 0 fuzzy mappings 0 fuzzy clustering l fuzzy relations and their composition l possibility measures and distributions To apply formal mathematical objects to an engineering problem, mathematical statements are formulated using propositional CUZCUZUS for which the standard logical connectives and their set-theoretic equivalents for propositions p and Q are: 197 Data Engineering: Fuzzy Mathematics in Systems Theory and Data Analysis.","claims":[{"public_id":"cl_a562859fb038ac7bb6cab3f7aa374152","status":"active","text":"Possibility theory attempts to formalize uncertainty by relating statistical objects to rule-based and fuzzy concepts.","confidence":0.6,"contributors":[{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["extraction"],"url":"https://sah.borca.ai/u/322360f1c1"},{"id":2,"public_id":"4715169a40","public_label":"AK 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