A unified framework for evidential reasoning
Abstract
A unified framework for evidential reasoning is proposed. In this framework, uncertainties are represented by intervals and modeled by belief functions. The procedure for belief conjunction is proposed. The belief combination and belief propagation are shown to be special cases of belief conjunction. By properly representing evidence in the common framework, belief combination is shown to be the belief conjunction procedure plus the normalization process. When evidence are independent, the belief combination procedure is equivalent to Dempster's rule of combination. The result of the belief propagation procedure is shown to be an interpolation between total ignorance and the uncertainty associated with the rule. The belief propagation procedure is shown to be associative but not commutative. The associativity of belief propagation implies the existence of chaining syllogism. The evidential framework is extended to handle dependent evidence. An ad-hoc interpolative procedure for belief conjunction and belief combination of dependent evidence with degree of dependency $\rho$ is proposed. Three types of structural dependencies are discussed. (1) All nodes in the inference network are OR nodes. (2) All nodes are AND nodes. (3) Mixture of AND/OR nodes. A modification to Dempster's rule is proposed to ovecome the counter-intuitive results due to the normalization process. A new interpretation for the rules in the framework is proposed. It is shown that this interpretation yields tighter intervals for belief propagation procedure while maintaining the interpolative property. This interpretation is extended to fuzzy sets and approximate reasoning. It is shown that the proposed belief propagation procedure is a further generalization of Zadeh's generalized modus ponens. Some aspects of the complexity issue in the belief function approach are discussed. It is shown that, when the hypotheses space is hierarchically structured, then any basic probability assignment function whose focal elements are nodes in the hierarchy is a separable belief function. Furthermore, this separable belief function can be decomposed into simple support functions in polynomial time.
Degree
Ph.D.
Advisors
Kashyap, Purdue University.
Subject Area
Electrical engineering
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