Editing Fuzzy logic (section)

=== Probability ===
Fuzzy logic and probability address different forms of uncertainty. While both fuzzy logic and probability theory can represent degrees of certain kinds of subjective belief, [[fuzzy set theory]] uses the concept of fuzzy set membership, i.e., how much an observation is within a vaguely defined set, and probability theory uses the concept of [[subjective probability]], i.e., frequency of occurrence or likelihood of some event or condition {{clarify|date=April 2019}}. The concept of fuzzy sets was developed in the mid-twentieth century at [[University of California, Berkeley|Berkeley]]<ref>{{cite web |url=https://www2.eecs.berkeley.edu/Faculty/Homepages/zadeh.html |title=Lotfi Zadeh Berkeley |url-status=live |archive-url=https://web.archive.org/web/20170211080227/https://www2.eecs.berkeley.edu/Faculty/Homepages/zadeh.html |archive-date=2017-02-11 }}</ref> as a response to the lack of a probability theory for jointly modelling uncertainty and [[vagueness]].<ref>{{Cite journal |title=Fuzzy Sets |journal=Scholarpedia |volume=1 |issue=10 |pages=2031 |doi=10.4249/scholarpedia.2031 |year=2006 |last1=Mares |first1=Milan |bibcode=2006SchpJ...1.2031M |doi-access=free }}</ref>

[[Bart Kosko]] claims in Fuzziness vs. Probability<ref>{{cite web |last1=Kosko |first1=Bart |author-link1=Bart Kosko |title=Fuzziness vs. Probability |url=http://sipi.usc.edu/~kosko/Fuzziness_Vs_Probability.pdf |archive-url=https://web.archive.org/web/20060902032943/http://sipi.usc.edu/%7Ekosko/Fuzziness_Vs_Probability.pdf |archive-date=2006-09-02 |url-status=live |publisher=University of South California |access-date=9 November 2018 }}</ref> that probability theory is a subtheory of fuzzy logic, as questions of degrees of belief in mutually-exclusive set membership in probability theory can be represented as certain cases of non-mutually-exclusive graded membership in fuzzy theory. In that context, he also derives [[Bayes' theorem]] from the concept of fuzzy subsethood. [[Lotfi A. Zadeh]] argues that fuzzy logic is different in character from probability, and is not a replacement for it. He fuzzified probability to fuzzy probability and also generalized it to [[possibility theory]].<ref>{{cite journal | last1 = Novák | first1 = V | year = 2005 | title = Are fuzzy sets a reasonable tool for modeling vague phenomena? | journal = Fuzzy Sets and Systems | volume = 156 | issue = 3| pages = 341–348 | doi=10.1016/j.fss.2005.05.029}}</ref>

More generally, fuzzy logic is one of many different extensions to classical logic intended to deal with issues of uncertainty outside of the scope of classical logic, the inapplicability of probability theory in many domains, and the paradoxes of [[Dempster–Shafer theory]].