Extension of fuzzy hypothesis testing with hybrid data

Abstract The problem of binary hypothesis testing, where the available data under both hypotheses is a superposition of a random and a fuzzy component, is addressed. A rule that compares two fuzzy likelihood functions is used in the decision making process. This rule is proved to result from the application of a fuzzified version of the Bayes criterion. In order that a crisp decision is ultimately obtained, use is made of a criterion for ordering fuzzy sets over the real line which was developed elsewhere by the author. A specific case which assumes normally distributed random component of the data is considered. Probability of error performance curves for fuzzy hypothesis testing are plotted and compared with the curves that correspond to the minimax probability of error criterion and the generalized likelihood ratio test when non-fuzzy hypothesis testing is concerned.