Fundamentals and Bayesian analyses of decision problems with fuzzy-valued utilities

A manageable model to deal with general single-stage statistical decision problems with fuzzy-valued consequences is presented. The model is based on the notion of fuzzy random variable, as defined by Puri and Ralescu, and also on a crisp ranking method for fuzzy numbers introduced by Campos and Gonzalez. Fundamentals of the fuzzy utility function representing the preference pattern of the decision maker are established to guarantee the existence of this function by means of an axiomatic development. Bayesian analyses of these statistical decision problems in normal and extensive forms are formalized, and conditions for the equivalence of these analyses are given. Finally, an example illustrating the Bayesian analysis is considered. (C) 1996 Elsevier Science Inc.