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Wednesday, December 01, 2021

Lotfi Zadeh and Fuzzy Logic

 I note the post about Lotfi Zaheh and the connection to fuzzy logic, from the Language Log.  Just featured in the Google Doodle.  We used some of his methods to implement 'fuzzy logic' for AI implementations.  Worth reexamining. 

Lofti Zadeh and the Z transform  from Language Log

December 1, 2021 @ 9:32 am · Filed by Mark Liberman under Research tools

The Google Doodle for November 30 featured Lofti Zadeh.

The Doodles page explains that:

Today’s Doodle celebrates world-renowned Azerbaijani-American computer scientist, electrical engineer, and professor, Lotfi Zadeh. On this day in 1964, Zadeh submitted “Fuzzy Sets,” a groundbreaking paper that introduced the world to his innovative mathematical framework called “fuzzy logic.”

You can learn more about this contribution from the Wikipedia page on Fuzzy Mathematics. What I learned, from reading the Other Contributions section of Zadeh's Wikipedia page, was his role in the invention (discovery?) of the z-transform.

In my lecture notes on the z transform, 20-odd years ago, I wrote:

The z transform is unusual, in being named after a letter of the alphabet rather than a famous mathematician. The Fourier transform is named after Baron Jean Baptiste Joseph Fourier (1768-1830); the Walsh-Hadamard transform is named after J.L. Walsh (1895-1973) and Jacques Salomon Hadamard (1865-1963); we haven't discussed the Laplace and Hilbert transforms yet, but we will (at least briefly), and they are named after Pierre-Simon de Laplace (1749-1827) and David Hilbert (1862-1943) respectively.

Laplace transforms have long been used in solving (continuous-time) linear constant-coefficient differential equations.  ..... '

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