A Study On Conditional Event Algebras And Their Computation Of Probabilities

Data fusion has been a hot topic of many researchers from a variety of disciplines as sciences and technologies are developed rapidly, and novel theories and new methods are proposed continuously. In contrast, the study for conditional event algebras (CEA), which has less achievement, is slowly in progress as a classical theory of information fusion. It is obviously that the reasons are mathematical abstract and understanding difficulties of CEA. Meanwhile, it is relative to applications since the computation involved with CEA is rather burden and there are almost not simple algorithms and complete inference rules, which restricts the development of CEA-based information fusion methods. Recently, many researchers have given CEA increasing concerns and think that CEA as an algebraic system will be a prospective direction in information fusion and can automatically perform fusion by computers.This paper aims at analyzing and establishing a computational method of probabilities involved with CEA on the basis of systematic studies for CEA theories and three usual CEA models. Our main works are briefly as follows:Firstly, we introduce the background, concepts and theoretical basics of data fusion as well as treatment models and structures of data fusion in general sense. At the same time, implementation techniques and current situations are given and the theoretical position and application values of CEA in data fusion are pointed out.Secondly, the fundamental concepts about CEA are rigorously introduced from a mathematical sense. Three usual CEA models and their relationship and differences are discussed by the two viewpoints of probability theory and mathematical logic. Their logical operation rules and computation of probabilities are discussed also.Finally, a computational method of involved probabilities in CEA is proposed by using Moore machines and Markov chains models. Several examples are been performed according to mathematical software and they can confirm the feasibility and effectiveness of the proposed method.