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.

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.

scholarly journals Plato's Cave in the Dempster-Shafer land--the Link between Pignistic and Plausibility Transformations

2017 ◽  
Author(s):  
Chunlai Zhou ◽  
Biao Qin ◽  
Xiaoyong Du
Keyword(s):  
Statistical Inference ◽  
Belief Function ◽  
Belief Functions ◽  
Reasoning Under Uncertainty ◽  
Function Model ◽  
Probability Functions ◽  
Degree Of Belief ◽  
Dempster Shafer Theory ◽  
Shafer Theory ◽  
Theory Of Evidence

In reasoning under uncertainty in AI, there are (at least) two useful and different ways of understanding beliefs: the first is as absolute belief or degree of belief in propositions and the second is as belief update or measure of change in belief. Pignistic and plausibility transformations are two well-known probability transformations that map belief functions to probability functions in the Dempster-Shafer theory of evidence. In this paper, we establish the link between pignistic and plausibility transformations by devising a belief-update framework for belief functions where plausibility transformation works on belief update while pignistic transformation operates on absolute belief. In this framework, we define a new belief-update operator connecting the two transformations, and interpret the framework in a belief-function model of parametric statistical inference. As a metaphor, these two transformations projecting the belief-update framework for belief functions to that for probabilities are likened to the fire projecting reality into shadows on the wall in Plato's cave.

Using Dempster-Shafer Theory in Data Mining

2011 ◽  
pp. 1166-1170
Author(s):  
Malcolm J. Beynon
Keyword(s):  
Data Mining ◽  
Mathematical Theory ◽  
Evidential Reasoning ◽  
Belief Functions ◽  
Partial Knowledge ◽  
Dempster Shafer Theory ◽  
Upper And Lower Probabilities ◽  
Shafer Theory ◽  
Theory Of Evidence

The origins of Dempster-Shafer theory (DST) go back to the work by Dempster (1967) who developed a system of upper and lower probabilities. Following this, his student Shafer (1976), in his book “A Mathematical Theory of Evidence” added to Dempster’s work, including a more thorough explanation of belief functions. In summary, it is a methodology for evidential reasoning, manipulating uncertainty and capable of representing partial knowledge (Haenni & Lehmann, 2002; Kulasekere, Premaratne, Dewasurendra, Shyu, & Bauer, 2004; Scotney & McClean, 2003).

MODELLING DEPENDENCE IN DEMPSTER-SHAFER THEORY

2007 ◽  
Vol 15 (01) ◽  
pp. 93-114 ◽  
Author(s):  
PAUL-ANDRE MONNEY ◽  
MOSES CHAN
Keyword(s):  
General Framework ◽  
Probability Distributions ◽  
Joint Probability ◽  
Belief Functions ◽  
Dempster Shafer Theory ◽  
Compact Representations ◽  
Probabilistic Dependence ◽  
Joint Probability Distributions ◽  
Shafer Theory

Belief functions can only be combined by Dempster's rule when they are based on independent items of evidence. This paper proposes a method for handling the case where there is some probabilistic dependence among the items of evidence. The method relies on compact representations of joint probability distributions on the assumption variables associated with the belief functions. These distributions are then used to compute degrees of support of hypotheses of interest. It is shown that the theory of hints is the appropriate general framework for this method.

scholarly journals A MODIFIED D NUMBERS METHODOLOGY FOR ENVIRONMENTAL IMPACT ASSESSMENT

2017 ◽  
Vol 24 (2) ◽  
pp. 653-669 ◽  
Author(s):  
Ningkui WANG ◽  
Daijun WEI
Keyword(s):  
Environmental Impact ◽  
Impact Assessment ◽  
Environmental Impact Assessment ◽  
Previous Method ◽  
Combination Process ◽  
Dempster Shafer Theory ◽  
Shafer Theory ◽  
Theory Of Evidence ◽  
D Numbers ◽  
Commutative Property

Environmental impact assessment (EIA) is usually evaluated by many factors influenced by various kinds of uncertainty or fuzziness. As a result, the key issues of EIA problem are to rep­resent and deal with the uncertain or fuzzy information. D numbers theory, as the extension of Dempster-Shafer theory of evidence, is a desirable tool that can express uncertainty and fuzziness, both complete and incomplete, quantitative or qualitative. However, some shortcomings do exist in D numbers combination process, the commutative property is not well considered when multiple D numbers are combined. Though some attempts have made to solve this problem, the previous method is not appropriate and convenience as more information about the given evaluations rep­resented by D numbers are needed. In this paper, a data-driven D numbers combination rule is proposed, commutative property is well considered in the proposed method. In the combination process, there does not require any new information except the original D numbers. An illustrative example is provided to demonstrate the effectiveness of the method.

Knowledge reduction in random information systems via Dempster–Shafer theory of evidence

2005 ◽  
Vol 174 (3-4) ◽  
pp. 143-164 ◽  
Author(s):  
Wei-Zhi Wu ◽  
Mei Zhang ◽  
Huai-Zu Li ◽  
Ju-Sheng Mi
Keyword(s):  
Information Systems ◽  
Knowledge Reduction ◽  
Dempster Shafer Theory ◽  
Shafer Theory ◽  
Theory Of Evidence
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