Defining Fuzzy Sets

Fuzzy Operations

Fuzzy Decisions

Fuzzy Engineering


History and Objections


History and Objections

    Fuzzy logic was introduced in 1965 by Lofti A Zadeh in his paper "Fuzzy Sets". Zadeh and others continued to develop fuzzy logic at that time. The idea of fuzzy sets and fuzzy logic were not accepted well within academic circles because some of the underlying mathematics had not yet been explored. The applications of fuzzy logic were slow to develop because of this, except in the east. In Japan specifically fuzzy logic was fully accepted and implemented in products simply because fuzzy logic worked, regardless of whether mathematicians agreed or not. The success of many fuzzy logic based products in Japan in the early 80s led to a revival in fuzzy logic in the US in the late 80s. Since that time America has been playing catch up with the east in the area of fuzzy logic.
    Some of the objections that faced fuzzy logic in its early days are shown below. Note that Professor William Kahan is Lofti Zadeh colleague at UC Berkely. Most objections to fuzzy logic have since faded due to the success of fuzzy applications.

    "Fuzzy theory is wrong, wrong, and pernicious. What we need is more logical thinking, not less. The danger of fuzzy logic is that it will encourage the sort of imprecise thinking that has brought us so much trouble. Fuzzy logic is the cocaine of science."

-Professor William Kahan UC Berkeley


    "’Fuzzification’ is a kind of scientific permissiveness. It tends to result in socially appealing slogans unaccompanied by the discipline of hard scientific work and patient observation."

-Professor Rudolf Kalman UFlorida


    "Fuzziness is probability in disguise. I can design a controller with probability that could do the same thing that you could do with fuzzy logic."

-Professor Myron Tribus, on hearing of the fuzzy-logic control of the Sendai subway system IEEE Institute, may 1988.


Fuzzy Logic