A Fuzzy Identification Problem for the Stationary Discrete Extremal Fuzzy Dynamic System

This work deals with the problem of the Stationary Discrete Extremal Fuzzy Dynamic System (SDEFDS) identification and briefly discusses the results developed by G. Sirbiladze [10]–[17]. Applying the results of [10] and [11], the fuzzy process with possibilistic uncertainty, the source of which is expert knowledge reflections, is constructed [12]. The dynamics of SDEFDS is described. Based on the fuzzy-integral model, methods and algorithms are developed for identifying the transition operator of the stationary discrete extremal fuzzy dynamic system. The SDEFDS transition operator is restored by means of expert data with possibilistic uncertainty, the source of which is expert knowledge reflections on the states of SDEFDS in the extremal fuzzy time intervals [13]. The regularization condition for obtaining a quasi-optimal estimator of the transition operator is represented by the theorems. The corresponding calculating algorithm is provided. The results obtained are illustrated by the example in the case of a finite set of SDEFDS states. Key–Words: Fuzzy extremal processes, SDEFDS, Identification of the SDEFDS model, Solution regularization principles