BELIEF FUNCTIONS INDUCED BY MULTIMODAL PROBABILITY DENSITY FUNCTIONS, AN APPLICATION TO THE SEARCH AND RESCUE PROBLEM

In this paper, we propose a new method to generate acontinuous belief functions from a multimodal probability distributionfunction defined over a continuous domain. We generalize Smets’ ap-proach in the sense that focal elements of the resulting continuous belieffunction can be disjoint sets of the extended real space of dimension n.We then derive the continuous belief function from multimodal prob-ability density functions using the least commitment principle. Weillustrate the approach on two examples of probability density func-tions (unimodal and multimodal). On a case study of Search AndRescue (SAR), we extend the traditional probabilistic framework ofsearch theory to continuous belief functions theory. We propose a newoptimization criterion to allocate the search effort as well as a newrule to update the information about the lost object location in thislatter framework. We finally compare the allocation of the search ef-fort using this alternative uncertainty representation to the traditionalprobabilistic representation