Identification of vaguely dependent parameters for a class of fuzzy stochastic systems

A method for identifying vaguely dependent unknown parameters is presented, where the underlying system has properties of both fuzziness and randomness. The authors describe boundaries of level sets of unknown fuzzy parameters by the functions of levels with unknown but non-fuzzy coefficients. First. considering that the fuzziness exists only in unknown system parameters, the reasonable definition of fuzzy stochastic systems (FSSs) is stated. Second, the identification procedure for fuzzy unknown parameters is proposed by extending the moment method for non-fuzzy random data. when the system is described by the class of FSSs called fuzzy moving average models having vaguely dependent system parameters. By introducing fuzzy metrics, asymptotic of fuzzy estimators are investigated mathematically. Digital simulation studies are described.<>