Conditional constraints, implication based rules, and possibilistic rule bases: are they any good?

To answer the question imposed in the title right away: Yes,
they are. Conditional constraints, implication based rules, and
possibilistic rule bases are different notions representing the
very same concept. And this concept is as useful and interesting
as the well known and widely used Mamdani approach. So far, real
success in applying fuzzy rule bases is restricted to fuzzy
control and Mamdani inference. We claim that the lack of
applications making use of possibilistic reasoning is mainly due
to a lack of understanding how to deal with rules based on
possibility distributions.

Mamdani inference as used in fuzzy control and possibilistic
reasoning are complementary mechanisms. They are complementary
with respect to the way they deal with incomplete and
inconsistent information. From that point of view, it is not
surprising that using the very same rule base in both settings
does not work. This means, that the standard way of specifying
Mamdani knowledge bases does not help in the possibilistic case.
Based on the assumption that rule based systems are helpful and
manageable as long as rules represent local information we
... mehr
present a new way how to specify possibilistic rule bases. In
order to prove the usefulness of this approach, we show that
there are some major drawbacks and limitations of Mamdani
inference, that are easily solved by correctly applying
possibilistic reasoning.

We do not claim, however, that possibilistic reasoning is the
one and only mechanism to choose. Both mechanisms have their
advantages and drawbacks and it heavily depends on the problem
at hand whether one or the other mechanism should be chosen. In
complex situations we expect a combined mechanism to be useful.