[FOM] Lofti Zadeh: sad news

[Kreinovich, Vladik]

Lotfi Zadeh, the founder of fuzzy logic, died on September 6, 2017, he was 96.

One of the main motivations for Zadeh's work was to be able to describe imprecise ("fuzzy") expert statements in precise terms.  To capture this imprecision, he proposed to use multi-valued logic - e.g., the [0,1]-based extension of classical 2-valued logic that was proposed in the 1920s by Lukasiewicz.

This idea had many interesting applications, in particular, to consumer products that better reflect our imprecise desires, ranging from fuzzy-controlled trains and elevators to fuzzy-controller rice cookers and video cameras.

For this mailing list, it is interesting to mention that Zadeh and his followers not only used multi-valued logic to describe basic statements, they have also made many efforts to extend fuzzy logic to fuzzy mathematics, i.e., to form a mathematics based on the multi-valued foundations.

This is somewhat similar to intuitionistic set theory and intuitionistic mathematics, where complex logical statements formed from the basic ones like "a in A" are interpreted not in classical logic, but in the intuitionistic one - similarly, in fuzzy mathematics,  such statements are interpreted in terms of the corresponding multi-valued logic.

In many cases, the properties of thus generalized mathematical objects - fuzzy groups, fuzzy linear spaces etc. - easily follow from the similar properties of the usual mathematical objects - but in some cases, this fuzzification led to not-so-trivial mathematical results, with interesting applications.

Requiescat in pace - rest In peace!
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