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Three key aspects of the problem of fusion of information include, in order of implementation: (1) grouping of relative consistent information; (2) proper fusing of information within each group; and (3) deducing for decision making. All of these aspects may be implemented by classical statistical hypotheses testing, estimation, and deduction techniques, but in a restricted way due to a number of difficulties arising in modeling of information which have long been ignored or treated in an ad hoc manner. This applies to linguistic-based information, as well as to certain types of probabilistic-based information, such as the evaluation of inference rules via conditional probabilities and modeling of expert opinion as forced weighted linear functions of probabilities. Each of the above information models can be shown to be in the form of a function of probabilities. This paper emphasizes basic motivations for use of two new mathematical tools-conditional and relational event algebra-to address a wide variety of such data fusion problems, yet staying within the context of ordinary probability theory.