On the Relationship between the Average Characteristics of the Input and Output Fuzzy Signals of a Linear Dynamic System

This paper considers the problem of transforming a fuzzy signal by a linear dynamic system described by a linear differential equation of high order with variable real coefficients, a fuzzy-valued inhomogeneity, and fuzzy initial conditions. By assumption, certain numerical average characteristics of the fuzzy-valued input signal (fuzzy means and fuzzy half-ranges) are known. Based on these characteristics and system parameters, the corresponding numerical average characteristics of the fuzzy signal at the output are established. Methods of fuzzy mathematics and the theory of ordinary differential equations are used. As an application, the model of a series resonant radio circuit with a fuzzy-valued input signal is considered.