Comparison of experiments in statistical decision problems with fuzzy utilities

The choice of an optimal action in a decision-making problem involving fuzzy utilities has been reduced in most previous studies to modeling the fuzzy utilities and the expected fuzzy utility and selecting a technique for ranking fuzzy numbers that fits the situation. A new element is incorporated in the decision problem, namely, the sample information supplied by a random experiment associated with the decision problem. This element, along with the use of fuzzy random variables to model fuzzy utilities and an appropriate fuzzy preference relation, makes it possible to extend, in the Bayesian framework, the concept of expected value of sample information (or gain in expected fuzzy utility due to knowledge of sample information). A criterion for comparing random experiments associated with the problem is established, and some properties confirming its suitability are analyzed. An example illustrates the application of the procedure. The criterion is contrasted with the pattern criterion based on Blackwell's concept of statistical `sufficiency'