Basic Belief Functions

2022 ◽  
pp. 71-102
Author(s):  
Russell G. Almond
Keyword(s):  
Basic Belief ◽  
Belief Functions

scholarly journals Belief AHP Method — AHP Method with the Belief Function Framework

2016 ◽  
Vol 15 (03) ◽  
pp. 553-573 ◽  
Author(s):  
Amel Ennaceur ◽  
Zied Elouedi ◽  
Eric Lefevre
Keyword(s):  
Life Cycle Assessment ◽  
Belief Function ◽  
Basic Belief ◽  
Belief Functions ◽  
Ahp Method ◽  
Analytic Hierarchy ◽  
Life Phase ◽  
Application Problem ◽  
Belief Model ◽  
Hierarchy Process

In this paper, the analytic hierarchy process (AHP) method is extended to an uncertain environment where the uncertainty is represented by belief functions as interpreted in the transferable belief model (TBM). Our proposed approach, called belief AHP, is developed to help the decision maker to determine what the best alternatives are, considering multiple conflicting criteria where both alternatives and criteria may be soiled with imperfection. The Belief AHP method aims at comparing subsets of criteria and groups of alternatives in order to reduce the pair-wise comparisons number. Furthermore, to handle uncertainty that may appear in the comparison procedure, we use basic belief assignments (BBA) instead of exact ratios to elicitate expert preferences. Finally, to illustrate the feasibility of our approach and to judge its performances, we have applied our proposed method on a real application problem: we have considered the polyvinyl chloride (PVC) life cycle assessment especially the end of life phase.

Basic Belief Functions

1995 ◽  
pp. 71-102
Author(s):  
Russell G. Almond
Keyword(s):  
Basic Belief ◽  
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

scholarly journals A Thermal Infrared and Visible Images Fusion Based Approach for Multitarget Detection under Complex Environment

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Xinnan Fan ◽  
Pengfei Shi ◽  
Jianjun Ni ◽  
Min Li
Keyword(s):  
Thermal Infrared ◽  
Basic Belief ◽  
Measured Signal ◽  
Complex Environment ◽  
Distance Distribution Function ◽  
Detection Approach ◽  
Efficiency And Effectiveness ◽  
Visible Images ◽  
Belief Theory ◽  
Update Process

Multitarget detection under complex environment is a challenging task, where the measured signal will be submerged by noise. D-S belief theory is an effective approach in dealing with Multitarget detection. However, there are some limitations of the general D-S belief theory under complex environment. For example, the basic belief assignment is difficult to establish, and the subjective factors will influence the update process of evidence. In this paper, a new Multitarget detection approach based on thermal infrared and visible images fusion is proposed. To easily characterize the defected heterogeneous image, a basic belief assignment based on the distance distribution function of heterogeneous characteristics is presented. Furthermore, to improve the discrimination and effectiveness of the Multitarget detection, a concept of comprehensive credibility is introduced into the proposed approach and a new update rule of evidence is designed. Finally, some experiments are carried out and the experimental results show the efficiency and effectiveness of the proposed approach in the Multitarget detection task.

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