Reduction of uncertainty using sensitivity analysis methods for infinite random sets of indexable type

In this paper we deal with the question “which is the best way to spend our resources in order to decrease the width of the interval [Bel(F),Pl(F)] in Dempster–Shafer evidence theory?”. A solution based on sensitivity analysis techniques using the Hartley-like measure of nonspecificity is proposed. This technique is a generalization of an approach introduced by Ferson and Tucker [S. Ferson, W.T. Tucker, Sensitivity in risk analysis with uncertain numbers, Report SAND2006-2801, Sandia National Laboratories, Albuquerque, NM, July 2006. ; S. Ferson, W.T. Tucker, Sensitivity analysis using probability bounding, Reliability Engineering and System Safety 91 (10–11) (2006) 1435–1442], which does not require the calculation of the probability box associated to the output Dempster–Shafer structure after the application of the extension principle for random sets. The proposed technique is computationally much more efficient than the one of Ferson and Tucker by several orders of magnitude. Finally, the extension principle of Dubois and Prade [D. Dubois, H. Prade, Random sets and fuzzy interval analysis, Fuzzy Sets and Systems 42 (1) (1991) 87–101] is generalized for infinite random sets of indexable type.