Classic Works of the Dempster-Shafer Theory of Belief Functions: An Introduction

2008 ◽  
pp. 1-34 ◽  
Author(s):  
Liping Liu ◽  
Ronald R. Yager
Keyword(s):  
Belief Functions ◽  
Dempster Shafer Theory ◽  
Theory Of Belief Functions ◽  
Shafer Theory

Belief Function Approach to Evidential Reasoning in Causal Maps

2005 ◽  
pp. 109-141
Author(s):  
Rajendra P. Srivastava ◽  
Mari W. Buche ◽  
Tom L. Roberts
Keyword(s):  
Job Satisfaction ◽  
Information Technology ◽  
Belief Function ◽  
Evidential Reasoning ◽  
Belief Functions ◽  
Causal Maps ◽  
Dempster Shafer Theory ◽  
Evidential Reasoning Approach ◽  
Theory Of Belief Functions ◽  
Shafer Theory

The purpose of this chapter is to demonstrate the use of the evidential reasoning approach under the Dempster-Shafer (D-S) theory of belief functions to analyze revealed causal maps (RCM). The participants from information technology (IT) organizations provided the concepts to describe the target phenomenon of Job Satisfaction. They also identified the associations between the concepts. This chapter discusses the steps necessary to transform a causal map into an evidential diagram. The evidential diagram can then be analyzed using belief functions technique with survey data, thereby extending the research from a discovery and explanation stage to testing and prediction. An example is provided to demonstrate these steps. This chapter also provides the basics of Dempster-Shafer theory of belief functions and a step-by-step description of the propagation process of beliefs in tree-like evidential diagrams.

Risk and Reliability Formulas for Systems Security under Dempster-Shafer Theory of Belief Functions

2008 ◽  
Vol 5 (1) ◽  
pp. 189-219 ◽  
Author(s):  
Rajendra P. Srivastava ◽  
Chan Li
Keyword(s):  
Network Model ◽  
Analytical Formula ◽  
Sensitivity Analyses ◽  
Belief Functions ◽  
Security Risk ◽  
Tree Model ◽  
Dempster Shafer Theory ◽  
Systems Security ◽  
Theory Of Belief Functions ◽  
Shafer Theory

ABSTRACT: This paper develops comprehensive formulas for assessing the risk and reliability of “Systems Security” under the Dempster-Shafer theory of belief functions, using the Trust Services framework as proposed by the American Institute of Certified Public Accountants (AICPA) and Canadian Institute of Chartered Accountants (CICA). In addition, we discuss how these formulas can be used for planning and evaluation of “Systems Security” risk under the SysTrust services. The analytical formulas are derived for a tree-structured evidential diagram which is constructed by converting the exact network-structured evidential diagram. The use of an analytical formula eliminates the computational complexities of propagating beliefs in a network and allows the assurance provider to use a simple spreadsheet to combine evidence. We provide theoretical justification and perform sensitivity analyses to show that the analytical formula based on a tree-type evidential diagram is a good approximation of the exact network model under realistic situations. However, as shown theoretically and also through the sensitivity analysis, the analytical formula provides significantly different results when input beliefs are significantly negative. It should be noted that the analytical formula based on the tree model provides a more conservative assessment of information systems risk than the exact network model.

scholarly journals Probability Estimation in the Framework of Intuitionistic Fuzzy Evidence Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Yafei Song ◽  
Xiaodan Wang
Keyword(s):  
Evidence Theory ◽  
Estimation Method ◽  
Probability Estimation ◽  
Belief Functions ◽  
Intuitionistic Fuzzy ◽  
Dempster Shafer Theory ◽  
Fuzzy Environment ◽  
Shafer Theory ◽  
Theory Of Evidence ◽  
Interval Valued

Intuitionistic fuzzy (IF) evidence theory, as an extension of Dempster-Shafer theory of evidence to the intuitionistic fuzzy environment, is exploited to process imprecise and vague information. Since its inception, much interest has been concentrated on IF evidence theory. Many works on the belief functions in IF information systems have appeared. Although belief functions on the IF sets can deal with uncertainty and vagueness well, it is not convenient for decision making. This paper addresses the issue of probability estimation in the framework of IF evidence theory with the hope of making rational decision. Background knowledge about evidence theory, fuzzy set, and IF set is firstly reviewed, followed by introduction of IF evidence theory. Axiomatic properties of probability distribution are then proposed to assist our interpretation. Finally, probability estimations based on fuzzy and IF belief functions together with their proofs are presented. It is verified that the probability estimation method based on IF belief functions is also potentially applicable to classical evidence theory and fuzzy evidence theory. Moreover, IF belief functions can be combined in a convenient way once they are transformed to interval-valued possibilities.

A NON-SPECIFICITY MEASURE FOR CONVEX SETS OF PROBABILITY DISTRIBUTIONS

2000 ◽  
Vol 08 (03) ◽  
pp. 357-367 ◽  
Author(s):  
JOAQUIN ABELLAN ◽  
SERAFIN MORAL
Keyword(s):  
Convex Sets ◽  
Probability Distributions ◽  
Belief Functions ◽  
Dempster Shafer Theory ◽  
Shafer Theory ◽  
Theory Of Evidence ◽  
Specificity Measure ◽  
Lack Of Knowledge

In belief functions, there are two types of uncertainty which are due to lack of knowledge: randomness and non-specificity. In this paper, we present a non-specificity measure for convex sets of probability distributions that generalizes Dubois and Prade's non-specificity measure in the Dempster-Shafer theory of evidence.

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