(p, q)-Logical completeness for output-coherent sets of (p, q)-Logical functions and an application of the set to image processing

Abstract We have previously proposed an idea of p -valued input, q -valued output threshold logic to synthesize many-valued, p -valued, logical networks, and derived the condition for ( p , q )-logical completeness for the output-closed set of ( p , q )-logical functions. In this paper, the condition for ( p , q )-logical completeness for the output-coherent set F of ( p , q )-logical functions is described, and the proof is given in almost the same way as for the output-closed set. The output-coherent set F is applied to image processing. That is, a restoration scheme is described for images to which normal random noise is added.