There is a deep-seated tradition in science of employing probability theory, and
only probability theory, to deal with uncertainty and imprecision. The monopoly
of probability theory came to an end when fuzzy logic made its debut. However,
this is by no means a widely accepted view. The belief persists, especially
within the probability community, that probability theory is all that is needed to
deal with uncertainty. To quote a prominent Bayesian, Professor Dennis Lindley,
“The only satisfactory description of uncertainty is probability. By this I mean that
every uncertainty statement must be in the form of a probability; that several uncertainties
must be combined using the rules of probability; and that the calculus of
probabilities is adequate to handle all situations involving uncertainty…probability
is the only sensible description of uncertainty and is adequate for all problems involving
uncertainty. All other methods are inadequate…anything that can be done
with fuzzy logic, belief functions, upper and lower probabilities, or any other alternative
to probability can better be done with probability.” What can be said about
such views is that they reflect unfamiliarity with fuzzy logic. The book “Modeling
Uncertainty with Fuzzy Logic,” co-authored by Dr. A. Celikyilmaz and Professor
I.B. Turksen, may be viewed as a convincing argument to the contrary. In effect,
what this book documents is that in the realm of uncertainty and imprecision fuzzy
logic has much to offer.