In this paper, we propose a new method to generate a continuousbelief functions from a multimodal probability distribution function definedover a continuous domain. We generalize Smets' approach in the sense thatfocal elements of the resulting continuous belief function can be disjoint setsof the extended real space of dimension n. We then derive the continuousbelief function from multimodal probability density functions using the leastcommitment principle. We illustrate the approach on two examples of probabilitydensity functions (unimodal and multimodal). On a case study of Search AndRescue (SAR), we extend the traditional probabilistic framework of search theoryto continuous belief functions theory. We propose a new optimization criterionto allocate the search effort as well as a new rule to update the informationabout the lost object location in this latter framework. We finally compare theallocation of the search effort using this alternative uncertaintyrepresentation to the traditional probabilistic representation.

In this paper we consider two optimization problems and two game problems. In each problem, a particle is hidden on the real line (sometimes randomly, and sometimes by an antagonistic hider), and a seeker, starting at the origin, wishes to find the particle with minimal expected cost. We consider a fairly wide class of cost functions depending upon the position of the particle and the time used to discover it. For the games we obtain the values and (∊-) optimal strategies. For the optimization problems we obtain qualitative features of (∊-) optimal searches.

We will consider the optimal search for a target whose motion is a Markov process. The classical detection law leads to the use of multiplicative functionals and the search is equivalent to the termination of the Markov process with a termination density. A general condition for the optimality is derived and for Markov processes in n-dimensional Euclidean space with continuous transition functions we derive a simple necessary condition which generalizes the result of Hellman (1972).