A logic-based analysis of Dempster-Shafer theory

AbstractDempster-Shafer (DS) theory is formulated in terms of propositional logic, using the implicit notion of provability underlying DS theory. Dempster-Shafer theory can be modeled in terms of propositional logic by the tuple (Σ, ϱ), where Σ is a set of propositional clauses and ϱ is an assignment of mass to each clause Σi ϵ Σ. It is shown that the disjunction of minimal support clauses for a clause Σi with respect to a set Σ of propositional clauses, ξ(Σi, Σ), when represented in terms of symbols for the ϱi 's, corresponds to a symbolic representation of the Dempster-Shafer belief function for δi. The combination of Belief functions using Dempster's rule of combination corresponds to a combination of the corresponding support clauses. The disjointness of the Boolean formulas representing DS Belief functions is shown to be necessary. Methods of computing disjoint formulas using network reliability techniques are discussed.In addition, the computational complexity of deriving DS Belief functions, including that of the logic-based methods which are the focus of this paper, is explored. Because of intractability even for moderately sized problem instances, efficient approximation methods are proposed for such computations. Finally, implementations of DS theory based on domain restrictions of DS theory, hypertree embeddings, and the ATMS, are examined

A method of classification for multisource data in remote sensing based on interval-valued probabilities

An axiomatic approach to intervalued (IV) probabilities is presented, where the IV probability is defined by a pair of set-theoretic functions which satisfy some pre-specified axioms. On the basis of this approach representation of statistical evidence and combination of multiple bodies of evidence are emphasized. Although IV probabilities provide an innovative means for the representation and combination of evidential information, they make the decision process rather complicated. It entails more intelligent strategies for making decisions. The development of decision rules over IV probabilities is discussed from the viewpoint of statistical pattern recognition. The proposed method, so called evidential reasoning method, is applied to the ground-cover classification of a multisource data set consisting of Multispectral Scanner (MSS) data, Synthetic Aperture Radar (SAR) data, and digital terrain data such as elevation, slope, and aspect. By treating the data sources separately, the method is able to capture both parametric and nonparametric information and to combine them. Then the method is applied to two separate cases of classifying multiband data obtained by a single sensor. In each case a set of multiple sources is obtained by dividing the dimensionally huge data into smaller and more manageable pieces based on the global statistical correlation information. By a divide-and-combine process, the method is able to utilize more features than the conventional maximum likelihood method

ARTIFICIAL INTELLIGENCE DIALECTS OF THE BAYESIAN BELIEF REVISION LANGUAGE

Rule-based expert systems must deal with uncertain data, subjective expert opinions, and inaccurate decision rules. Computer scientists and psychologists have proposed and implemented a number of belief languages widely used in applied systems, and their normative validity is clearly an important question, both on practical as well on theoretical grounds. Several well-know belief languages are reviewed, and both previous work and new insights into their Bayesian interpretations are presented. In particular, the authors focus on three alternative belief-update models the certainty factors calculus, Dempster-Shafer simple support functions, and the descriptive contrast/inertia model. Important "dialectsâ of these languages are shown to be isomorphic to each other and to a special case of Bayesian inference. Parts of this analysis were carried out by other authors; these results were extended and consolidated using an analytic technique designed to study the kinship of belief languages in general.Information Systems Working Papers Serie

Rejoinder to comments on “reasoning with belief functions: An analysis of compatibility”

AbstractAn earlier position paper has examined the applicability of belief-functions methodology in three reasoning tasks: (1) representation of incomplete knowledge, (2) belief-updating, and (3) evidence pooling. My conclusions were that the use of belief functions encounters basic difficulties along all three tasks, and that extensive experimental and theoretical studies should be undertaken before belief functions could be applied safely. This article responds to the discussion, in this issue, of my conclusions and the degree to which they affect the applicability of belief functions in automated reasoning tasks

ARTIFICIAL INTELLIGENCE DIALECTS OF THE BAYESIAN BELIEF REVISION LANGUAGE

Rule-based expert systems must deal with uncertain data, subjective expert opinions, and inaccurate decision rules. Computer scientists and psychologists have proposed and implemented a number of belief languages widely used in applied systems, and their normative validity is clearly an important question, both on practical as well on theoretical grounds. Several well-know belief languages are reviewed, and both previous work and new insights into their Bayesian interpretations are presented. In particular, the authors focus on three alternative belief-update models the certainty factors calculus, Dempster-Shafer simple support functions, and the descriptive contrast/inertia model. Important "dialectsâ of these languages are shown to be isomorphic to each other and to a special case of Bayesian inference. Parts of this analysis were carried out by other authors; these results were extended and consolidated using an analytic technique designed to study the kinship of belief languages in general.Information Systems Working Papers Serie

Applications of Belief Functions in Business Decisions: A Review

This is the author's final draft. The publisher's official version is available from: .In this paper, we review recent applications of Dempster-Shafer theory (DST) of belief functions to auditing and business decision-making. We show how DST can better map uncertainties in the application domains than Bayesian theory of probabilities. We review the applications in auditing around three practical problems that challenge the effective application of DST, namely, hierarchical evidence, versatile evidence, and statistical evidence. We review the applications in other business decisions in two loose categories: judgment under ambiguity and business model combination. Finally, we show how the theory of linear belief functions, a new extension of DST, can provide an alternative solution to a wide range of business problems