Specifying and Storing Valuations: Belief Functions and Probabilities

2022 ◽  
pp. 125-143
Author(s):  
Russell G. Almond
Keyword(s):  
Belief Functions

Extended two-dimensional belief function based on divergence measurement

2020 ◽  
pp. 1-8
Author(s):  
Jianping Fan ◽  
Jing Wang ◽  
Meiqin Wu
Keyword(s):  
Belief Function ◽  
Distribution Functions ◽  
Divergence Measure ◽  
Uncertain Information ◽  
Belief Functions ◽  
Two Dimensional ◽  
Probability Distribution Functions ◽  
Basic Probability ◽  
The Difference ◽  
Supporting Degree

The two-dimensional belief function (TDBF = (mA, mB)) uses a pair of ordered basic probability distribution functions to describe and process uncertain information. Among them, mB includes support degree, non-support degree and reliability unmeasured degree of mA. So it is more abundant and reasonable than the traditional discount coefficient and expresses the evaluation value of experts. However, only considering that the expert’s assessment is single and one-sided, we also need to consider the influence between the belief function itself. The difference in belief function can measure the difference between two belief functions, based on which the supporting degree, non-supporting degree and unmeasured degree of reliability of the evidence are calculated. Based on the divergence measure of belief function, this paper proposes an extended two-dimensional belief function, which can solve some evidence conflict problems and is more objective and better solve a class of problems that TDBF cannot handle. Finally, numerical examples illustrate its effectiveness and rationality.

Econometric Forecasting Using Linear Regression and Belief Functions

2014 ◽  
pp. 304-312 ◽  
Author(s):  
Orakanya Kanjanatarakul ◽  
Philai Lertpongpiroon ◽  
Sombat Singkharat ◽  
Songsak Sriboonchitta
Keyword(s):  
Linear Regression ◽  
Belief Functions

scholarly journals Features modeling with an α-stable distribution: Application to pattern recognition based on continuous belief functions

2013 ◽  
Vol 14 (4) ◽  
pp. 504-520 ◽  
Author(s):  
Anthony Fiche ◽  
Jean-Christophe Cexus ◽  
Arnaud Martin ◽  
Ali Khenchaf
Keyword(s):  
Pattern Recognition ◽  
Stable Distribution ◽  
Belief Functions

Mathematical Alternatives to Standard Probability that Provide Selectable Degrees of Precision

2017 ◽  
Author(s):  
Terrence Fine
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Models ◽  
Theory Of Measurement ◽  
Belief Functions ◽  
Standard Practice ◽  
Mathematical Probability ◽  
Comparative Probability ◽  
The Relationship ◽  
Standard Probability

This chapter challenges the nearly universal reliance upon standard mathematical probability for mathematical modeling of chance and uncertain phenomena, and offers four alternatives. In standard practice, precise assignments are made inappropriately, even to the occurrences of events that may be unobservable in principle. Four familiar examples of chance or uncertain phenomena are discussed, about which this is true. The theory of measurement provides an understanding of the relationship between the accuracy of information and the precision with which the phenomenon under examination should be modeled mathematically. The model of modal or classificatory probability offers the least precision. Comparative probability, plausibility/belief functions and upper/lower probabilities are carefully considered. The selectable precision of these alternative mathematical models of chance and uncertainty makes for an improved range of levels of accuracy in modeling the empirical domain phenomena of chance, uncertainty, and indeterminacy. Knowledge of such models encourages further thought in this direction.

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