Updating Parameters with Fuzzy Entropies

Abstract

The uncertainty of a continuous variable is estimated by the combination of the objective entropy, which is obtained from the statistics of a countable population, and the fuzzy entropy, which is a measure of imprecision estimated from an engineer's experience and knowledge. This is illustrated by using subjective, imprecise, fuzzy information to update the objective parameters of an initial truncated normal distribution by means of combining Shannon's objective information entropy and fuzzy entropies. The entropies are treated as information measures of uncertainty of both the objective and subjective kinds. Three fuzzy entropy functions are presented and their effects on the altered parameters illustrated.