Editing Lotfi A. Zadeh (section)

== Work ==
[[File:Lotfi A. Zadeh stamp 2021.png|thumb|Stamp of Azerbaijan dedicated to the 100th anniversary of Lotfi A. Zadeh]]
According to [[Google Scholar]], as of November 2021, Zadeh's work has been cited at least 269,091 times in scholarly works,<ref>{{cite web |title=Lotfi A. Zadeh |url=https://scholar.google.com/citations?user=S6H-0RAAAAAJ&hl=en  |website=[[Google Scholar]] |access-date=30 November 2021 |archive-url=https://web.archive.org/web/20211130203932/https://scholar.google.com/citations?user=S6H-0RAAAAAJ |archive-date=30 November 2021 |quote=All Citations: 269091}}</ref> with the 1965 ''Fuzzy sets'' paper receiving at least 122,743 citations.<ref name="scholar.google-S6H-0RAAAAAJ:QKtdBID3u5MC">{{cite web |last1=Zadeh |first1=Lotfi |title=Fuzzy Sets |url=https://scholar.google.com/citations?view_op=view_citation&hl=en&user=S6H-0RAAAAAJ&citation_for_view=S6H-0RAAAAAJ:QKtdBID3u5MC |website=[[Google Scholar]] |access-date=30 November 2021 |archive-url=https://web.archive.org/web/20211130203157/https://scholar.google.com/citations?view_op=view_citation&hl=en&user=S6H-0RAAAAAJ&citation_for_view=S6H-0RAAAAAJ%3AQKtdBID3u5MC |archive-date=30 November 2021 |date=1965 |quote=Total citations: Cited by 122743}}</ref>

=== Fuzzy sets and systems ===
Zadeh, in his theory of [[fuzzy set]]s, proposed using a [[membership function]] (with a [[Interval (mathematics)|range]] covering the [[interval (mathematics)|interval]] [0,1]) operating on the [[Domain of a function|domain]] of all possible values. He proposed new operations for the calculus of logic and showed that [[fuzzy logic]] was a generalisation of classical and Boolean [[logic]]. He also proposed [[fuzzy number]]s as a special case of fuzzy sets, as well as the corresponding rules for consistent mathematical operations (fuzzy arithmetic).<ref>[[#McNeil|McNeil & Freiberger]], ''passim''</ref>

=== Fuzzy logic and artificial intelligence ===
Zadeh's research career has had a lasting impact on artificial intelligence (AI). Fuzzy sets and fuzzy logic are both motivated by our understanding of human cognition: that we are comfortable with concepts that have vague boundaries. This is well aligned with the [[Physical symbol system]] assumption in AI (by [[Allen Newell]] and [[Herbert A. Simon]]), inspired by another aspect of human cognition: that humans are comfortable with concepts that are described by symbols.

The concept of a linguistic variable in fuzzy logic connects a symbol that is typically a predicate in classical logic (e.g., "John is Bold", or in [[predicate logic]] – Bold(John)) – to linguistic values (e.g., "John is somewhat bold." or in fuzzy logic – Bold(John)=Somewhat ) – which generalizes the binary value of predicate logic in two ways.
First, the two possible values (True or False) in predicate logic are generalized to a continuum (typically from 0, which corresponds to False, to 1, which corresponds to True). This allows the expression of Bold(John)= 0.5, which indicates that John is midway between being devoid of boldness and being entirely bold.

The second generalization enabled by fuzzy logic is to use a fuzzy set such as "somewhat bold" to describe a person's boldness level in a way that is more natural to human understanding and communication. Without this generalization, we can only describe the value of a person's boldness as a number (e.g., 0.5) or as an interval (e.g., [0.25, 0.75]). With this generalization, one can express the semantic meaning of "somewhat bold" as a fuzzy set in the domain of 0 and 1.

Zadeh was also an active contributor to the AI community, including at the [[Dartmouth Workshop]] that coined the term "artificial intelligence". He was subsequently a frequent contributor to leading AI conferences such as AAAI and IJCAI, as well as other top venues such as AI Magazine.

=== Other contributions ===
Zadeh is credited, along with [[John R. Ragazzini]], in 1952, with having pioneered the development of the [[Z-transform]] method in discrete time [[signal processing]] and analysis. These methods are now standard in [[digital signal processing]], [[digital control]], and other discrete-time systems used in industry and research. He was an editor of the ''International Journal of Computational Cognition''.

Zadeh's work also included [[computing with words and perceptions]]. His later papers include "From Search Engines to Question-Answering Systems"<ref>{{cite book |last=Zadeh |first=Lotfi A. |date=2006 |chapter=From search engines to question answering systems—The problems of world knowledge, relevance, deduction and precisiation |editor-last=Sanchez |editor-first=Elie |title=Fuzzy Logic and the Semantic Web |series=Capturing Intelligence |volume=1 |publisher=Elsevier |pages=[https://archive.org/details/fuzzylogicsemant0000unse/page/163 163–210] |isbn=9780444519481 |oclc=62475292 |doi=10.1016/S1574-9576(06)80011-0 |chapter-url=https://archive.org/details/fuzzylogicsemant0000unse/page/163 |chapter-url-access=registration |citeseerx=10.1.1.89.3883}}</ref> and "Toward a Generalized Theory of Uncertainty (GTU)—An Outline".<ref>{{cite journal |last=Zadeh |first=Lotfi A. |date=June 2005 |title=Toward a generalized theory of uncertainty (GTU)—an outline |journal=[[Information Sciences (journal)|Information Sciences]] |volume=172 |issue=1 |pages=1–40 |doi=10.1016/j.ins.2005.01.017 |citeseerx=10.1.1.95.1834}}</ref>