ON DISCRIMINATION OF FUZZY STATES IN PROBABILITY SPACE

This paper deals with the discrimination problem of the states which involve two types of uncertainty: “randomness” and “fuzziness.” This problem is very important in the fields of soft science such as management science, sociology, eta, since the object of discrimination involves these types of uncertainty. In this paper, we propose a discrimination system of fuzzy states on a probability space and derive the decision rule which minimizes the average of error probability of discrimination. In our formulation of the discrimination system there exists the case that a large number of observations does not necessarily make the average of error probability small, so that an index for decision of an upper limit of number of observations is also derived.