Evidence theory has been primarily used in the past to model imperfect information, and it is a powerful tool for reasoning under uncertainty. It appeared as an alternative to probability theory and is now considered a generalization of it. In this paper we first introduce an object identification problem and then present two approaches to solve it: a probabilistic approach and the Dempster- Shafer approach. We also present the limitations of Dempster's rule of combination when conflictual pieces of information are combined and we present alternatives rules proposed in the literature to overcome this problem. We propose a class of adaptive combination rules obtained by mixing the basic conjunctive and disjunctive combination rules. The symmetric adaptive combination rule is finally considered and we compare it with the other existing rules.