Editing Fuzzy logic (section)

==Overview==
[[Classical logic]] only permits conclusions that are either true or false. However, there are also [[proposition]]s with variable answers, which one might find when asking a group of people to identify a color. In such instances, the truth appears as the result of reasoning from inexact or partial knowledge in which the sampled answers are mapped on a spectrum.<ref>{{cite web| url-status = live| archive-url = https://web.archive.org/web/20211205194241/https://www.youtube.com/watch?v=cGdRB1r_iC0| archive-date = 2021-12-05| url = https://www.youtube.com/watch?v=cGdRB1r_iC0| title = Fuzzy Logic| website = [[YouTube]]| date=9 May 2013 | access-date = 2020-05-11}}</ref>

Both [[degree of truth|degrees of truth]] and [[probability|probabilities]] range between 0 and 1 and hence may seem identical at first, but fuzzy logic uses degrees of truth as a [[mathematical model]] of ''vagueness'', while [[probability]] is a mathematical model of ''ignorance''.<ref>{{Cite book|url=https://books.google.com/books?id=QBBADwAAQBAJ&q=Both+degrees+of+truth+and+probabilities+range+between+0+and+1+and+hence+may+seem+similar+at+first,+but+fuzzy+logic+uses+degrees+of+truth+as+a+mathematical+model+of+vagueness,+while+probability+is+a+mathematical+model+of+ignorance&pg=SA4-PA13|title=Handbook of Research for Fluid and Solid Mechanics: Theory, Simulation, and Experiment|last1=Asli|first1=Kaveh Hariri|last2=Aliyev|first2=Soltan Ali Ogli|last3=Thomas|first3=Sabu|last4=Gopakumar|first4=Deepu A.|date=2017-11-23|publisher=CRC Press|isbn=9781315341507|language=en}}</ref>

===Applying truth values===
A basic application might characterize various sub-ranges of a [[Variable (mathematics)|continuous variable]]. For instance, a temperature measurement for [[Anti-lock braking system|anti-lock brakes]] might have several separate membership functions defining particular temperature ranges needed to control the brakes properly. Each function maps the same temperature value to a truth value in the 0 to 1 range. These truth values can then be used to determine how the brakes should be controlled.<ref>{{Cite book|url=https://books.google.com/books?id=-ZXJDQAAQBAJ&q=For+instance,+a+temperature+measurement+for+anti-lock+brakes+might+have+several+separate+membership+functions+defining+particular+temperature+ranges+needed+to+control+the+brakes+properly.+Each+function+maps+the+same+temperature+value+to+a+truth+value+in+the+0+to+1+range.+These+truth+values+can+then+be+used+to+determine+how+the+brakes+should+be+controlled&pg=PA47|title=Optical Character Recognition Systems for Different Languages with Soft Computing|last1=Chaudhuri|first1=Arindam|last2=Mandaviya|first2=Krupa|last3=Badelia|first3=Pratixa|last4=Ghosh|first4=Soumya K.|date=2016-12-23|publisher=Springer|isbn=9783319502526|language=en}}</ref> Fuzzy set theory provides a means for representing uncertainty.

===Linguistic variables===
In fuzzy logic applications, non-numeric values are often used to facilitate the expression of rules and facts.<ref>{{cite book |last1=Zadeh |first1=L. A. |display-authors=etal |title=Fuzzy Sets, Fuzzy Logic, Fuzzy Systems |date=1996 |publisher=World Scientific Press |isbn=978-981-02-2421-9 }}</ref>

A linguistic variable such as ''age'' may accept values such as ''young'' and its antonym ''old''. Because natural languages do not always contain enough value terms to express a fuzzy value scale, it is common practice to modify linguistic values with [[adjectives]] or [[adverbs]]. For example, we can use the [[hedge (linguistics)|hedges]] ''rather'' and ''somewhat'' to construct the additional values ''rather old'' or ''somewhat young''.<ref>{{cite journal |last1=Zadeh |first1=L. A. |title=The concept of a linguistic variable and its application to approximate reasoning—I |journal=Information Sciences |date=January 1975 |volume=8 |issue=3 |pages=199–249 |doi=10.1016/0020-0255(75)90036-5 }}</ref>