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Later, the initial partnership group was extended by adding
x evolutionary computation
x belief theory
x learning theory.
Fuzzy logic, which is the most important part of soft computing, bridges the gap
between the quantitative information ( i.e. the numerical data) and the qualitative
information (or the linguistic statements), which can be jointly processed using
fuzzy computing. In addition, fuzzy logic operates with the concept of IF-THEN
rules in which the antecedents and the consequents are expressed using linguistic
variables. Neural networks, for their part, have the capability of extracting
knowledge from available data, i.e. the capability of learning from examples,
which fuzzy logic systems do not have. This capability is known as the
connectionist learning paradigm.
The process of learning can take place in supervisory mode (when the
backpropagation networks are used) or in unsupervised mode (when the recurrent
networks/Kohonen networks are used). This is due to the computing neuron or
the perceptron (Rosenblatt, 1962), the theoretical background of which was
worked out by Minsky and Papert (1969). It is the multi-layer perceptron
configuration that is capable of emulating human brain behaviour in learning and
cognition . The learning capability of multi-layer perceptrons, as proposed by
Werbos (1974), should be obtained through a process of adaptive training on
examples.
Dubois and Prade (1998) remarked that soft computing, because it was a
collection of various technologies and methodologies with distinct foundations and
distinct scopes, “lumped together” although each of the components has little in
common with the other, could not form a scientific discipline in the traditional
sense of the term. Therefore, they understand the term soft computing more as a
“fashionable name with little actual contents”. This is in fact a hard judgement, in
view of the fact that in the meantime various combinations of the constituent
technologies have been used to build hybrid computational systems, such as neuro-
fuzzy systems , fuzzy-neuro systems , evolutionary neural networks , adaptive
evolutionary systems , and others, that were extensively documented by Bonissone
(1997 and 1999). This issue is the main subject of Part 3 of this topic, where it will
be shown that the individual components of soft computing are not mutually
competitive, but rather are complementary and co-operative . Jang et al . (1997)
considered soft computing from the neuro-fuzzy point of view, rather than from the
fuzzy set theory only, and pointed out that the neuro-fuzzy approach is to be seen
as a technological revolution in modelling and control of dynamic systems, taking
the adaptive network-based fuzzy inference system (ANFIS) as an example .
1.3 Probabilistic Reasoning
As the third principal constituent of soft computing, probabilistic reasoning is a
tool for evaluating the outcome of computations affected by randomness and
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