Abstract: A new approach to promote the generalization ability
of neural networks is presented. It is based on the point of view of
fuzzy theory. This approach is implemented through shrinking or
magnifying the input vector, thereby reducing the difference between
training set and testing set. It is called “shrinking-magnifying
approach" (SMA). At the same time, a new algorithm; α-algorithm is
presented to find out the appropriate shrinking-magnifying-factor
(SMF) α and obtain better generalization ability of neural networks.
Quite a few simulation experiments serve to study the effect of SMA
and α-algorithm. The experiment results are discussed in detail, and
the function principle of SMA is analyzed in theory. The results of
experiments and analyses show that the new approach is not only
simpler and easier, but also is very effective to many neural networks
and many classification problems. In our experiments, the proportions
promoting the generalization ability of neural networks have even
reached 90%.
Abstract: A logic model for analyzing complex systems- stability
is very useful to many areas of sciences. In the real world, we are
enlightened from some natural phenomena such as “biosphere", “food
chain", “ecological balance" etc. By research and practice, and taking
advantage of the orthogonality and symmetry defined by the theory of
multilateral matrices, we put forward a logic analysis model of
stability of complex systems with three relations, and prove it by
means of mathematics. This logic model is usually successful in
analyzing stability of a complex system. The structure of the logic
model is not only clear and simple, but also can be easily used to
research and solve many stability problems of complex systems. As an
application, some examples are given.