Fuzzy-Random Processes with Orthogonal and Independent Increments

In this paper, random processes with fuzzy states and continuous time are investigated. The main attention is paid to the class of fuzzy random processes with orthogonal and independent increments. The characteristic properties of the variances and covariance functions of such processes are established. Gaussian and Wiener fuzzy random processes, which are analogs of the corresponding real random processes, are considered. The obtained results are based on the properties of fuzzy random variables and the classical results of the theory of real random processes with orthogonal and independent increments. Examples characterize the possibility of applying the developed theory to fuzzy-random processes of a triangular type.