Problems of Dealing with Conflicts in the Combination of Beliefs

In many areas, humans have to act on the basis of uncertain contradictory information. Evident examples of this are passing sentence based on contradictory evidences and making important political, economic and other decisions under available contradictory information about circumstances and consequences of such decisions. Ignoring the existing contradictive information may considerably increase the risk of unsuccessful decisions and activities. Due to that, methods of combination of contradictive initial information are of great scientific and practical interest. This paper examines the conceptual foundations of the theory of evidence, transferable belief model of Ph.Smets and the Dezert-Smarandache theory. Most of the attention is focused on problems of dealing with conflicting belief masses. These problems are fundamental in the combination of beliefs obtained on the basis of independent groups of evidence. Different rules of belief combination propose essentially different logical validations for solving such problems. In this sense there is no absolutely best rule of belief combination. Each rule possesses both advantages and shortcomings. The paper pays much attention to the consideration and analysis of specific rules for conflict redistribution, PCR3 – PCR5, lately proposed by Dezert and Smarandache. A brief comparative analysis of the merits and demerits of these rules is provided. In conclusion, the conceptual validity of approaches to the redistribution of conflicting belief masses to the subsets involved in the conflict is analysed