Editing Fuzzy logic (section)

{{short description|System for reasoning about vagueness}}
{{About|the scientific theory of that name||Fuzzy logic (disambiguation)}}
{{use dmy dates|date=November 2022}}
'''Fuzzy logic''' is a form of [[many-valued logic]] in which the [[truth value]] of variables may be any [[real number]] between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false.<ref>{{cite book |last1=Novák, V. |last2=Perfilieva, I. |last3=Močkoř, J.  |title=Mathematical principles of fuzzy logic |date=1999 |publisher=Kluwer Academic |location=Dordrecht |isbn=978-0-7923-8595-0 }}</ref> By contrast, in [[Boolean algebra|Boolean logic]], the truth values of variables may only be the [[integer]] values 0 or 1.

The term ''fuzzy logic'' was introduced with the 1965 proposal of [[fuzzy set theory]] by mathematician [[Lotfi A. Zadeh|Lotfi Zadeh]].<ref>{{cite encyclopedia |url=http://plato.stanford.edu/entries/logic-fuzzy/ |title=Fuzzy Logic |access-date=2008-09-30 |encyclopedia=Stanford Encyclopedia of Philosophy |publisher=Bryant University |date=2006-07-23 }}</ref><ref>{{cite Q | last1=Zadeh |first1=L. A. | author-link1 = Lotfi A. Zadeh | Q25938993 | journal = [[Information and Computation|Information and Control]] | doi-access = free }}</ref> Fuzzy logic had, however, been studied since the 1920s, as [[Łukasiewicz logic|infinite-valued logic]]—notably by [[Jan Łukasiewicz|Łukasiewicz]] and [[Alfred Tarski|Tarski]].<ref>{{cite journal | last1 = Pelletier | first1 = Francis Jeffry | year = 2000 | title = Review of ''Metamathematics of fuzzy logics'' | url = https://www.sfu.ca/~jeffpell/papers/ReviewHajek.pdf | journal = The Bulletin of Symbolic Logic | volume = 6 | issue = 3 | pages = 342–346 | jstor = 421060 | doi = 10.2307/421060 | url-status = live | archive-url = https://web.archive.org/web/20160303172812/http://www.sfu.ca/~jeffpell/papers/ReviewHajek.pdf | archive-date = 2016-03-03 }}</ref>

Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy models or fuzzy sets are mathematical means of representing [[vagueness]] and imprecise information (hence the term fuzzy). These models have the capability of recognising, representing, manipulating, interpreting, and using data and information that are vague and lack certainty.<ref>{{Cite web |title=What is Fuzzy Logic? "Mechanical Engineering Discussion Forum" |url=https://mechanicalsite.com/157/what-is-fuzzy-logic |url-status=usurped |archive-url=https://web.archive.org/web/20181111173944/https://mechanicalsite.com/157/what-is-fuzzy-logic |archive-date=2018-11-11 |access-date=2018-11-11 |website=mechanicalsite.com}}</ref><ref name="Babuška2012">{{cite book |author=Babuška |first=Robert |url=https://books.google.com/books?id=-nzrCAAAQBAJ |title=Fuzzy Modeling for Control |publisher=Springer Science & Business Media |year=1998 |isbn=978-94-011-4868-9}}</ref>

Fuzzy logic has been applied to many fields, from [[control theory]] to [[artificial intelligence]].