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The mathematical theory of evidence is a generalization of the Bayesian theory of probability. It is one of the primary tools for knowledge representation and uncertainty and probabilistic reasoning and has found many applications. Using this theory to solve a specific problem is critically dependent on the availability of a mass function (or basic belief assignment). In this paper, we consider the important problem of how to systematically derive mass functions from the common multivariate data spaces and also the ensuing problem of how to compute the various forms of belief function efficiently. We also consider how such a systematic approach can be used in practical pattern recognition problems. More specifically, we propose a novel method in which a mass function can be systematically derived from multivariate data and present new methods that exploit the algebraic structure of a multivariate data space to compute various belief functions including the belief, plausibility, and commonality functions in polynomial-time. We further consider the use of commonality as an equality check. We also develop a plausibility-based classifier. Experiments show that the equality checker and the classifier are comparable to state-of-the-art algorithms.