Parameter Identification of Fuzzy Autoregressive Models

Abstract In this paper, a method for identifying vague parameters is presented, where the underlying system is described by the “fuzzy autoregressive model” which is a class of fuzzy stochastic models proposed by the authors First, considering that the vagueness exists only in unknown system parameters, a fuzzy autoregressive model is proposed as the model of systems whose remarkable features lie on the simultaneous existence of its vagueness and randomness. Secondly, extending the identification method for ordinary autoregressive models to fuzzy one, the identification procedure for vague unknown parameters is proposed. Furthermore, introducing the fuzzy metric, asymptotic properties of proposed estimators are investigated mathematically. Finally, for the purpose of better understanding, digital simulation studies are developed.