Dempster-Shafer Theory of Belief Functions: A Language for Managing Uncertainties in the Real-World Problems (original) (raw)
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International Journal of Accounting Information Systems, 2011
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.
Modeling decision in the dempster-shafer belief structure uncertainty
2009
A general model for decision problems is presented by a basic probability assignment of a body of evidence, which gives the information on distribution of states, situations or factors in the form of Dempster-Shafer belief structure. The rule for decision making is constructed from two steps by means of a composition of two functions -Dempster's lower and upper expected values. Shapley information entropy decreasing principal is received for the information inclusion relation constructed in the framework of the Dempster-Shafer belief structure.
On the mathematical theory of evidence and Dempster's rule of combination
In this paper we present an analysis of the use of Dempster's rule of combination, its consistency with the probability calculus and its usefulness for combining sources of evidence expressed by belief functions in the framework of the Mathematical Theory of Evidence, known also as Dempster-Shafer Theory (DST), or as the classical theory of belief functions.
2013
This is the author's final draft. The publisher's official version is available electronically from:<http://onlinelibrary.wiley. com/journal/10.1111/%28ISSN%291835-2561>.The main purpose of this paper is to introduce the Dempster-Shafer theory (“DS” theory) of belief functions for managing uncertainties, specifically in the auditing and information systems domains. We illustrate the use of DS theory by deriving a fraud risk assessment formula for a simplified version of a model developed by Srivastava, Mock, and Turner (2007). In our formulation, fraud risk is the normalized product of four risks: risk that management has incentives to commit fraud, risk that management has opportunities to commit fraud, risk that management has an attitude to rationalize committing fraud, and the risk that auditor’s special procedures will fail to detect fraud. We demonstrate how to use such a model to plan for a financial audit where management fraud risk is assessed to be high. In a...
Dempster–Shafer belief structures for decision making under uncertainty
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We discuss the need for tools for representing various types of uncertain information in decision-making. We introduce the Dempster-Shafer belief structure and discuss how it provides a formal mathematical framework for representing various types of uncertain information. We provide some fundamental ideas and mechanisms related to these structures. We then investigate their role in the important task of decision-making under uncertainty.
An extended framework for evidential reasoning systems
[1990] Proceedings of the 2nd International IEEE Conference on Tools for Artificial Intelligence, 1990
reasoning is a body of techniques that supports automated reasoning from evidence. It is based upon the Dempster-Shafer theory of belief functions. Both the formal basis and a framework for the implementation of automated reasoning systems based upon these techniques are presented. The formal and practical approaches are divided into four parts (1) specifying a set of distinct propositional spaces, each of which delimits a set of possible world situations (2) specifying the interrelationships among these propositional spaces representing bodies of evidence as belief distributions over these propositional spaces and (4) establishing paths for the bodies of evidence to move through these propositional spaces by means of evidential operations, eventually converging on spaces where the target questions can be answered. AUTOMATED REASONING / 90 1 Figure 8: Data from ANALYSISl. AUTOMATED REASONING / 903
Dempster-Shafer Belief Function - A New Interpretation
ArXiv, 2017
We develop our interpretation of the joint belief distribution and of evidential updating that matches the following basic requirements: * there must exist an efficient method for reasoning within this framework * there must exist a clear correspondence between the contents of the knowledge base and the real world * there must be a clear correspondence between the reasoning method and some real world process * there must exist a clear correspondence between the results of the reasoning process and the results of the real world process corresponding to the reasoning process.
Applications of Belief Functions in Business Decisions: A Review
2003
In this paper, we review recent applications of the 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 revie w 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. Key words. Dempster-Shafer theory of belief functions, linear belief functions, audit decision, hierarchical evidence, versatile evidence, statistical evidence, judgment under ambiguity
Combining belief functions taking into consideration error in judgement
International Journal of General Systems, 2020
Dempster-Shafer (D-S) evidence theory is very efficient and widely used mathematical tool for uncertain and imprecise information fusion for decision making. D-S rule is criticised by many researchers as it gives illogical and counterintuitive results especially when the series of evidence provided by various experts are in a high degree of conflict. Various attempts have been made and several alternatives proposed to this rule. In this paper, a new alternative is proposed which considers the possibility of an error made by experts while providing evidence, calculates the error and incorporates in the revised masses. The validity and efficiency of the proposed approach have been demonstrated with numerous examples and the results are compared with already existing methods. Highlights • An alternative method is proposed to handle the conflicting evidence. • An Error In Judgement while gathering evidence is considered and incorporated before combining evidence. • The method is simple and gives better and reasonable results than other previous methods when evidence conflicts ARTICLE HISTORY