Future states forecasting under uncertainty by using non-deterministic conditional relations

A problem of extrapolation of a large class of processes and of their future states forecasting based on their occurrence in the past is considered. Discrete-time discrete-value processes are presented as instances of relations subjected to the general extended algebra of relations rules. The notions of relative relations, parametric relations and non-deterministic relations have been introduced. For extrapolated process states assessment relative credibility levels of process trajectories are used. The variants of direct one-step, indirect one-step and direct multi-step process extrapolation are described and illustrated by numerical examples. Basic notions of extended algebra of relations are given in the Appendix.