THE FUZZY DECISION PROBLEM: AN APPROACH TO THE PROBLEM OF TESTING STATISTICAL HYPOTHESES WITH FUZZY INFORMATION M.R. Casals, M.A. Gil and P. Gil ABSTRACT: Departamento de Matemáticas Universidad de Ov i e do Oviedo, SPA 1 N This paper is devoted to the problem of testing statistical hypoth- eses about an experiment, when the available information from its sampling is 11 vague 11 • When the information supplied by the experimental sampling is exact, the problem of testing statistical hypotheses about the experiment can be regarded as a particular statistical decision problem. In addition, decision procedures may be used in problems of testing hypotheses. In a similar manner, the problem of testing statistical hypothese about an experiment when the available sample information is vague, is approached in this paper as a particular fuzzy decision problem (as defined by H. Tanaka, T. Okuda and K. Asai). This approach assumes that the previous information about the experiment can be expressed by means of certain conditional probabilistic information, whereas the present information about it can be expressed by means of fuzzy information. The preceding framework allows us to extend the notion of risk function and sorne nonfuzzy decision procedures to the fuzzy case, and particularize them to the problem of testing. Finally, several illustrative examples are presented. Keywords: fuzzy infor1ation, fuzzy infor1ation syste1, fuzzy rando1 sa1ple, fuzzy test function, risk function, prior risk, posterior risk, Bayes fuzzy test, 1ini1ax fuzzy test. l. APPROACHING THE PROBLEM OF TESTING STATISTICAL HYPOTHESES AS A STATISTICAL PROBLEM. To test a statistical hypothesis is to perform an experiment concern- ing this hypothesis and, on the basis of the outcome of the experiment,