To improve the identification precision of the adaptive system by using multi-valued logic based upon the fuzzy logical function instead of binary theory.

The difference Ej between the outputs of an unknown transmission system 1 and a noncyclic filter 2 to which a reference signal Xj is inputted is inputted to a coefficient update means 4 equipped with coefficient update algorithm and the tap coefficient of the noncyclic filter 2 is updated to learn and identify the noncyclic filter 2. At this time, it is assumed that there is a probability distribution based upon the reference signal Xj as a fuzzy variable, the probability distribution is represented as a membership function and a fuzzy inference mechanism 3 updates the said tap coefficient by inference.