Fuzzy
logic is derived from
Fuzzy set theory dealing with reasoning
that is approximate rather than precisely deduced from classical predicate
logic. It can be thought of as the application side of fuzzy set theory dealing
with well thought out real world expert
values for a complex problem.
Degrees of truth are often confused with probabilities. However, they are
conceptually distinct; fuzzy truth represents
membership in vaguely defined
sets, not likelihood of some event or condition. For example, if a 100-ml glass
contains 30
ml of water, then, for two fuzzy sets, Empty and Full, one might
define the glass as being 0.7 empty and 0.3 full. Note that the concept of
emptiness would be subjective and thus would depend on the
observer or
designer. 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. Note
that the conditioning can be achieved by having a specific observer that
randomly selects the label for the glass, a distribution over deterministic
observers, or both. 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 0.3 full''.
Fuzzy logic allows for set membership values to range (inclusively) between
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.
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