| Technischer Bericht| [1] | Joachim Weisbrod, Martin Spott, Conditional constraints, implication based rules, and possibilistic rule bases: Are they any good?, Oct 2000.
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ZusammenfassungTo 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 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.
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