An identification model for a fuzzy time based stationary discrete process

A new approach of fuzzy processes, the source of which are expert knowledge reflections on the states on Stationary Discrete Extremal Fuzzy Dynamic  System (SDEFDS) in extremal fuzzy time intervals, are considered.  A fuzzy-integral representation of a stationary discrete   extremal fuzzy process is given.A method and an algorithm  for identifying the transition operator of SDEFDS are developed.  The SDEFDS transition operator is restored by means of  expert knowledge reflections on the states of SDEFDS. The regularization condition for obtaining of the quasi-optimal estimator of the transition operator is represented by the theorem. The corresponding calculating algorithm is provided. The results obtained are illustrated by an example in the case of a finite set of SDEFDS states.

Keywords:

Sugeno's type extremal fuzzy measures and integrals , extremal fuzzy time intervals , SDEFDS , identification of the SDEFDS integral model