Evidential theoretic revision of beliefs under a mixed strategy for safety-control of a large-complex plant

This paper discusses how beliefs of a decision maker can be revised for the safety control of a large-complex plant via Dempster-Shafer theory. In this paper, we examine the following two methods for belief revision: (i) combination rules for basic probability assignments, and (ii) updating rules based on the conditioning of belief functions. We give, for each case, an optimal rule for minimizing the expected loss caused by actions of a decision maker who adopts a mixed strategy for safety control, where the decision maker's safety-control is probabilistic over policies of the safety-preservation type and the fault-warning type. We clarify the following two points: (1) An optimal rule of combination cannot be determined until the exact time moment of combining information, because the optimality depends on a mixed strategy adopted by the decision maker and information items obtained to be combined. (2) An optimal rule of updating can be specified in advance, irrespective of a decision maker's mixed strategy or information items to be obtained. These two points show an essential difference between the combination rules and the updating rules: The optimal combination rule has a dynamic nature, while the optimal updating rule has a static aspect. (author)