The problem of merging multiple sources of information is central in many information processing areas such as databases integrating problems, multiple criteria decision making, etc. To solve this problem, two kinds of approaches have been proposed. The first category of approaches merges the different bases into a unique consistent base, and the second category, such as argumentation, accepts inconsistency and copes with it. It is well known that priorities are crucial to solve conflicts. Recently, powerful approaches have been proposed to merge multiple sources information where priorities are either explicitly or implicitly associated to information [L. Cholvy, Reasoning about merging information, Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 3, 1998, pp. 233-263; S. Konieczny, R. Pino Perez, On the logic of merging, in: Proceedings of the 6th International Conference on Principles of Knowledge Representation and Reasoning (KR'98), Trento, 1998, pp. 488-498; J. Lin, Integration of weighted knowledge bases, Artificial Intelligence 83 (1996) 363-378; J. Lin, A. Mendelzon, Merging databases under constraints, International Journal of Cooperative Information Systems 7(1) (1998) 55-76; N. Rescher, R. Manor, On inference from inconsistent premises, Theory and Decision I (1970) 179-219; P.Z. Revesz, On the semantics of theory change: arbitration between old and new information, in: 12th ACM SIGACT-SIGMOD-SIGART Symposium oil Principles of Databases, 1993, pp. 71-92; S. Benferhat, D. Dubois, S. Kaci, H. Prade, Possibilistic merging and