1,369 research outputs found
An Introduction to Evidential Reasoning for Decision Making under Uncertainty: Bayesian and Belief Functions Perspectives
The main purpose of this article is to introduce the evidential reasoning approach, a research
methodology, for decision making under uncertainty. Bayesian framework and Dempster-Shafer
theory of belief functions are used to model uncertainties in the decision problem. We first
introduce the basics of the DS theory and then discuss the evidential reasoning approach and
related concepts. Next, we demonstrate how specific decision models can be developed from the basic evidential diagrams under the two frameworks. It is interesting to note that it is quite
efficient to develop Bayesian models of the decision problems using the evidential reasoning
approach compared to using the ladder diagram approach as used in the auditing literature. In
addition, we compare the decision models developed in this paper with similar models developed in the literature
A theory of Gaussian belief functions
AbstractA Gaussian belief function can be intuitively described as a Gaussian distribution over a hyperplane, whose parallel subhyperplanes are the focal elements. This paper elaborates on the idea of Dempster and Shafer and formally represents a Gaussian belief function as a wide-sense inner product and a linear functional over a variable space, and as their duals over a hyperplane in a sample space. By adapting Dempster's rule to the continuous case, it derives a rule of combination and proves its equivalence to its geometric description by Dempster. It illustrates by examples how mixed knowledge involving linear equations, multivariate Gaussian distributions, and partial ignorance can be represented and combined as Gaussian belief functions
An introduction to DSmT
The management and combination of uncertain, imprecise, fuzzy and even
paradoxical or high conflicting sources of information has always been, and
still remains today, of primal importance for the development of reliable
modern information systems involving artificial reasoning. In this
introduction, we present a survey of our recent theory of plausible and
paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT), developed for
dealing with imprecise, uncertain and conflicting sources of information. We
focus our presentation on the foundations of DSmT and on its most important
rules of combination, rather than on browsing specific applications of DSmT
available in literature. Several simple examples are given throughout this
presentation to show the efficiency and the generality of this new approach
Probability Transform Based on the Ordered Weighted Averaging and Entropy Difference
Dempster-Shafer evidence theory can handle imprecise and unknown information, which has attracted many people. In most cases, the mass function can be translated into the probability, which is useful to expand the applications of the D-S evidence theory. However, how to reasonably transfer the mass function to the probability distribution is still an open issue. Hence, the paper proposed a new probability transform method based on the ordered weighted averaging and entropy difference. The new method calculates weights by ordered weighted averaging, and adds entropy difference as one of the measurement indicators. Then achieved the transformation of the minimum entropy difference by adjusting the parameter r of the weight function. Finally, some numerical examples are given to prove that new method is more reasonable and effective
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