Signal parameter estimation when the parameters are fuzzy variables

We present a methodology for estimation of the fuzzy parameters of a stochastic signal. The proposed approach minimizes a fuzzy average decision error probability by a proper choice of decision regions. We use a scalar index, called the total distance criterion (TDC) ranking index, in order to rank the fuzzy average decision error probabilities of different decision rules. We identify, the optimal decision rule which minimizes the TDC index of the fuzzy average decision error probability. As an example we apply the general approach proposed here to the classification of the fuzzy mean of a Gaussian random variable. The optimal decision regions are specified explicitly and closed form probability expressions are given for arbitrary symmetric membership functions.