Degrees of truth are often confused with probabilities. For example, if a 100-ml glass contains 30 ml of water, then, for two fuzzy sets, Empty and Expert systems principles and programming pdf, one might define the glass as being 0. Another designer might equally well design a set membership function where the glass would be considered full for all values down to 50 ml.
A probabilistic setting would first define a scalar variable for the fullness of the glass, and second, conditional distributions describing the probability that someone would call the glass full given a specific fullness level. While fuzzy logic avoids talking about randomness in this context, this simplification at the same time obscures what is exactly meant by the statement the ‘glass is 0. 0 and 1, and in its linguistic form, imprecise concepts like “slightly”, “quite” and “very”. Specifically, it allows partial membership in a set. It is related to fuzzy sets and possibility theory. It was introduced in 1965 by Lotfi Zadeh at the University of California, Berkeley. Fuzzy logic is controversial in some circles and is rejected by some control engineers and by most statisticians who hold that probability is the only rigorous mathematical description of uncertainty.
Critics also argue that it cannot be a superset of ordinary set theory since membership functions are defined in terms of conventional sets. A basic application might characterize subranges of a continuous variable. For instance, a temperature measurement for anti-lock brakes might have several separate membership functions defining particular temperature ranges needed to control the brakes properly. Each function maps the same temperature value to a truth value in the 0 to 1 range. These truth values can then be used to determine how the brakes should be controlled. A point on that scale has three “truth values” — one for each of the three functions. Fuzzy logic is the same as “imprecise logic”.
The concept of “coldness” cannot be expressed in an equation, because although temperature is a quantity, “coldness” is not. 1 degrees — a concept classical logic cannot easily handle due to the principle of bivalence. The result has no set answer so it is believed to be a ‘fuzzy’ answer. Fuzzy logic is a new way of expressing probability.
Fuzzy logic and probability are different ways of expressing uncertainty. However, many statisticians are persuaded by the work of Bruno de Finetti that only one kind of mathematical uncertainty is needed and thus fuzzy logic is unnecessary. On the other hand, Bart Kosko argues that probability is a subtheory of fuzzy logic, as probability only handles one kind of uncertainty. He also claims to have proven a derivation of Bayes’ theorem from the concept of fuzzy subsethood. Lotfi Zadeh, the creator of fuzzy logic, argues that fuzzy logic is different in character from probability, and is not a replacement for it.