Easy and optimal queries to reduce set uncertainty

Abstract : In this paper, we address the problem of optimally querying a single expert to reduce set (interval) uncertainty. We propose optimal querying strategies for two particular query formats (local bound and pair wise comparisons) based on two main selection criteria (the minimax and the Bayesian rules). We study the computational aspects of the optimal solution in the general case and for the specific functions of practical interest (monotonic and multi-linear). The use of the proposed approach is illustrated through numerical simulations on a common estimation problem in reliability analysis.