  A generalized information formula related to logical probability and fuzzy
set is deduced from the classical information formula. The new information
measure accords with to Popper's criterion for knowledge evolution very much.
In comparison with square error criterion, the information criterion does not
only reflect error of a proposition, but also reflects the particularity of the
event described by the proposition. It gives a proposition with less logical
probability higher evaluation. The paper introduces how to select a prediction
or sentence from many for forecasts and language translations according to the
generalized information criterion. It also introduces the rate fidelity theory,
which comes from the improvement of the rate distortion theory in the classical
information theory by replacing distortion (i.e. average error) criterion with
the generalized mutual information criterion, for data compression and
communication efficiency. Some interesting conclusions are obtained from the
rate-fidelity function in relation to image communication. It also discusses
how to improve Popper's theory.
