Mathematical models of optical methods in data processing

Approximations of geometrical and Fourier optics are considered in the fram ework of the triangular norms technique. For each of the approximations, op erators of subsets relations are defined. It is shown that the approximatio n of the geometrical optics generates a probabilistic many-valued logic and the approximation of the Fourier optics generates a fuzzy-valued logic. Fo r the approximation of the Fourier optics, an operator of implication is de fined that makes it possible to implement the inference rule "generalized m odus ponens." Some experimental results are given.