Multiple fuzzy hypotheses testing

In many parameteric statistical decision problems, one has to make a decision in the presence of some uncertainties about the parameters in the statistical model of the observed random variables. Examples include estimation of signal parameters in additive noise of unknown power and detection of a signal of unknown amplitude. We present a methodology to test multiple hypotheses on the distribution of a random variable when the hypotheses are parameterized by fuzzy variables. The proposed approach has a Bayesian favor in the sense that the objective is to minimize 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 derive 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