Valuation-based system (VBS) provides a general framework for representing knowledge and drawing inferences under uncertainty. Recent studies have shown that the semantics of VBS can represent and solve Bayesian decision problems (Shenoy, 1991a). The purpose of this paper is to propose a decision calculus for Dempster-Shafer (D-S) theory in the framework of VBS. The proposed calculus uses a weighting factor whose role is similar to the probabilistic interpretation of an assumption that disambiguates decision problems represented with belief functions (Strat 1990). It will be shown that with the presented calculus, if the decision problems are represented in the valuation network properly, we can solve the problems by using fusion algorithm (Shenoy 1991a). It will also be shown the presented decision calculus can be reduced to the calculus for Bayesian probability theory when probabilities, instead of belief functions, are given.

Current Bayesian net representations do not consider structure in the domain and include all variables in a homogeneous network. At any time, a human reasoner in a large domain may direct his attention to only one of a number of natural subdomains, i.e., there is ?localization' of queries and evidence. In such a case, propagating evidence through a homogeneous network is inefficient since the entire network has to be updated each time. This paper presents multiply sectioned Bayesian networks that enable a (localization preserving) representation of natural subdomains by separate Bayesian subnets. The subnets are transformed into a set of permanent junction trees such that evidential reasoning takes place at only one of them at a time. Probabilities obtained are identical to those that would be obtained from the homogeneous network. We discuss attention shift to a different junction tree and propagation of previously acquired evidence. Although the overall system can be large, computational requirements are governed by the size of only one junction tree.

In this paper, a unified framework for representing uncertain information based on the notion of an interval structure is proposed. It is shown that the lower and upper approximations of the rough-set model, the lower and upper bounds of incidence calculus, and the belief and plausibility functions all obey the axioms of an interval structure. An interval structure can be used to synthesize the decision rules provided by the experts. An efficient algorithm to find the desirable set of rules is developed from a set of sound and complete inference axioms.

Jeffrey's rule has been generalized by Wagner to the case in which new evidence bounds the possible revisions of a prior probability below by a Dempsterian lower probability. Classical probability kinematics arises within this generalization as the special case in which the evidentiary focal elements of the bounding lower probability are pairwise disjoint. We discuss a twofold extension of this generalization, first allowing the lower bound to be any two-monotone capacity and then allowing the prior to be a lower envelope.

In a previous paper [Pearl and Verma, 1991] we presented an algorithm for extracting causal influences from independence information, where a causal influence was defined as the existence of a directed arc in all minimal causal models consistent with the data. In this paper we address the question of deciding whether there exists a causal model that explains ALL the observed dependencies and independencies. Formally, given a list M of conditional independence statements, it is required to decide whether there exists a directed acyclic graph (dag) D that is perfectly consistent with M, namely, every statement in M, and no other, is reflected via dseparation in D. We present and analyze an effective algorithm that tests for the existence of such a day, and produces one, if it exists.

The DUCK-calculus presented here is a recent approach to cope with probabilistic uncertainty in a sound and efficient way. Uncertain rules with bounds for probabilities and explicit conditional independences can be maintained incrementally. The basic inference mechanism relies on local bounds propagation, implementable by deductive databases with a bottom-up fixpoint evaluation. In situations, where no precise bounds are deducible, it can be combined with simple operations research techniques on a local scope. In particular, we provide new precise analytical bounds for probabilistic entailment.

This paper discusses a target tracking problem in which no dynamic mathematical model is explicitly assumed. A nonlinear filter based on the fuzzy If-then rules is developed. A comparison with a Kalman filter is made, and empirical results show that the performance of the fuzzy filter is better. Intensive simulations suggest that theoretical justification of the empirical results is possible.

Bayesian networks have been used extensively in diagnostic tasks such as medicine, where they represent the dependency relations between a set of symptoms and a set of diseases. A criticism of this type of knowledge representation is that it is restricted to this kind of task, and that it cannot cope with the knowledge required in other artificial intelligence applications. For example, in computer vision, we require the ability to model complex knowledge, including temporal and relational factors. In this paper we extend Bayesian networks to model relational and temporal knowledge for high-level vision. These extended networks have a simple structure which permits us to propagate probability efficiently. We have applied them to the domain of endoscopy, illustrating how the general modelling principles can be used in specific cases.

The general use of subjective probabilities to model belief has been justified using many axiomatic schemes. For example, ?consistent betting behavior' arguments are well-known. To those not already convinced of the unique fitness and generality of probability models, such justifications are often unconvincing. The present paper explores another rationale for probability models. ?Qualitative probability,' which is known to provide stringent constraints on belief representation schemes, is derived from five simple assumptions about relationships among beliefs. While counterparts of familiar rationality concepts such as transitivity, dominance, and consistency are used, the betting context is avoided. The gap between qualitative probability and probability proper can be bridged by any of several additional assumptions. The discussion here relies on results common in the recent AI literature, introducing a sixth simple assumption. The narrative emphasizes models based on unique complete orderings, but the rationale extends easily to motivate set-valued representations of partial orderings as well.

Within the transferable belief model, positive basic belief masses can be allocated to the empty set, leading to unnormalized belief functions. The nature of these unnormalized beliefs is analyzed.