Computational Intelligence: An Introduction - Computational Intelligence in Time Series Forecasting - page 4

probabilistic uncertainties. To name a few, Bayesian belief networks and
Dempster-Shafer theory belong to this kind of reasoning approach.
At this point a few words of clarification concerning the similarity between the
terms probability and fuzziness could be of use, because it is still controversial.
The reason is that probability theory as a formal framework for reasoning about
uncertainty was “there earlier” than fuzzy reasoning, so that some doubts have
been raised about the fuzzy reasoning: Is it really something new or only a clever
disguise for probability? Bezdek (1992b) denied this. Zadeh (1995) has even seen
probability and fuzzy logic as being complementary, rather than as competitive
approaches. In the meantime, this is actually accepted consensusly within the soft
computing community.
Probabilistic reasoning deals with the evaluation of the outcomes of systems
that are subjects of probabilistic uncertainty. The reasoning helps in evaluating the
relative certainty of occurrence of true or false values in random processes. It relies
on sets described by means of some probability distributions. Therefore,
probabilistic reasoning represents the possible worlds that are the solutions of an
approximate reasoning problem and thus being consistent with the existing
information and knowledge (Ruspini, 1996). Probabilistic reasoning methods are
primarily interested in the likelihood, in the sense of whether a given hypothesis
will be true under given circumstances.
Zadeh (1979) extended the reasoning component of soft computing by
introducing the concepts of
x fuzzy reasoning
x possibilistic reasoning
which belong to the approximated reasoning . According to Zadeh, approximate
reasoning is the reasoning about imprecise propositions , such as the chains of
inferences in fuzzy logic. Similarly, the predicate logic deals with precise
propositions . Therefore, approximate reasoning can be seen as an extension of the
traditional propositional calculus operating with the incomplete truth.
Fuzzy reasoning , with roots in fuzzy set theory, deals with the fuzzy
knowledge as imprecise knowledge. Unlike the probabilistic reasoning, fuzzy
reasoning deals with vagueness rather than with randomness . Fuzzy reasoning is
thus an approximate reasoning (Zadeh, 1979), in the sense that it is neither exact
nor absolutely inexact, but only to a certain degree exact or inexact. Fuzzy
reasoning schemes operate on chains of inferences in fuzzy logic, in a similar way
to predicate logic reasons with precise propositions. That is why approximate
reasoning is understood as an extension of traditional prepositional calculus
dealing with uncertain or imprecise information, primarily with the elements of
fuzzy sets, where an element belongs to a specific set only to some extent of
certainty. The inference by reasoning with such uncertain facts produces new facts,
with the degree of certainty corresponding to the original facts.
Possibilistic reasoning , which also roots in fuzzy set theory (Zadeh, 1965), as
an alternative theory to bivalent logic and the traditional theory of probability,
tends to describe possible worlds in terms of their similarity to other sets of
possible worlds and produces estimates that should be valid in each given case and