About the Spectrum of the Eigenvalues of Color Operators in a Theory of Canonically Conjugate Fuzzy Subsets

Abstract

In the present work is considered an approach, according to which canonically conjugate colors in the theory of fuzzy sets are related to the properties of information functions and non-commutative linear operators in Gilbert’s space: each information state corresponds to the estimation of compatibility function, every color – to the operator.It is supposed that color, as some property (attribute), characterizing a condition of a system, can receive different values called by eigenvalues of this color. The cases of discrete and continuous spectrum of eigenvalues of color are considered. The example of calculation of conditional computable values of color is given.