New Methods of Transforming Belief Functions to Pignistic Probability Functions in Evidence Theory

2009 ◽  
Author(s):  
Wei Pan ◽  
Hongji Yang
Keyword(s):  
Evidence Theory ◽  
Belief Functions ◽  
Probability Functions ◽  
New Methods

Estimating Measurement Error Based on Evidence Theory

2012 ◽  
Vol 548 ◽  
pp. 839-842
Author(s):  
Ming Zhu Xiao
Keyword(s):  
Measurement Error ◽  
General Framework ◽  
Probability Distributions ◽  
Evidence Theory ◽  
Belief Functions ◽  
Random Set ◽  
Estimation Process

Measurement error is traditionally represented with probability distributions. Although probabilistic representations of measurement error have been successfully employed in many analyses, such representations have been criticized for requiring more refined knowledge with respect to the existing error than that is really present. As a result, this paper proposes a general framework and process for estimating the measurement error based on evidence theory. In this research cumulative belief functions (CBFs) and cumulative plausibility functions (CPFs) are used to estimate measurement error. The estimation includes two steps:(1) modeling the parameters by means of a random set, and discrediting the random set to focal elements in finite numbers; (2)summarizing the propagation error. An example is demonstrated the estimation process.

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.

Evidence Theory of One-Dimensional Compression KNN Classification Method

2010 ◽  
Vol 143-144 ◽  
pp. 1337-1341
Author(s):  
Wei Feng Yan ◽  
Gen Xiu Wu ◽  
Can Ze Li ◽  
Li Zhou
Keyword(s):  
Euclidean Distance ◽  
Evidence Theory ◽  
Numerical Data ◽  
Calculation Methods ◽  
Data Set ◽  
One Dimensional ◽  
Actual Distance ◽  
Distance Calculation ◽  
New Methods ◽  
Knn Classification

As only using Euclidean distance KNN algorithm has its limits, many researchers use other distance calculation methods as the replacement it to improve the accuracy of Data Classification. While combining the DS evidence theory with a series of KNN algorithm which discussed in this paper, we found that every algorithm has their merits. All of them ignore the analysis of the data set, through deeply analysis we found that the actual distance is determined by the larger value when two attribute values are in great difference. Therefore, what we do next is to compress the large-dimensional numerical data values. By this way, the accuracy of KNN, VSMKNN, KERKNN algorithm are obviously improved after experiment and then these new methods are called CDSKNN, CDSVSMKNN, CDSKERKNN.

Evidence Theory Representations for Properties Associated with Weak Link/strong Link Systems, Part 2: Failure Time and Failure Temperature

2021 ◽  
Author(s):  
Jon C. Helton ◽  
Dusty M. Brooks ◽  
John L. Darby
Keyword(s):  
Failure Time ◽  
Weak Link ◽  
Evidence Theory ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Belief Functions ◽  
Strong Link ◽  
Cumulative Distribution Functions ◽  
Failure Temperature

Abstract The use of evidence theory and associated cumulative plausibility functions (CPFs), cumulative belief functions (CBFs), cumulative distribution functions (CDFs), complementary cumulative plausibility functions (CCPFs), complementary cumulative belief functions (CCBFs), and complementary cumulative distribution functions (CCDFs) in the analysis of loss of assured safety (LOAS) for weak link (WL)/strong link (SL) systems is introduced and illustrated. Article content includes cumulative and complementary cumulative belief, plausibility and probability for (i) time at which LOAS occurs for a 1 WL/2 SL system, (ii) time at which a 2 link system fails, (iii) temperature at which a 2 link system fails, and (iv) temperature at which LOAS occurs for a 1 WL/ 2 SL system. The presented results can be generalized to systems with more than 1 WL and 2 SLs.

scholarly journals Computational procedures of the evidence theory for interval and fuzzy assignments of the basic probability masses for focal elements

2019 ◽  
Vol 22 ◽  
pp. 47-51
Author(s):  
Oleg Uzhga-Rebrov ◽  
Ekaterina Karaseva ◽  
Vasily V. Karasev
Keyword(s):  
Possible Worlds ◽  
Evidence Theory ◽  
Belief Functions ◽  
Specific Kind ◽  
Basic Probability ◽  
Computational Procedures ◽  
Theory Uncertainty ◽  
Similar Elements ◽  
Calculation Procedures

The evidence theory is ascribed to a specific kind of uncertainty. In this theory, uncertainty refers to the fact that the element of our interest (the true world) may be included in subsets of other similar elements (possible worlds). In the original evidence theory, the estimates of the basic probability masses for the focal elements are given in an unambiguous form. In practice, to obtain such estimates is often difficult or even impossible. In such a situation, the relevant estimates are given in the interval or fuzzy form. The goal of the paper is to present and analyse the calculation procedures for determination of the belief functions and plausibility functions in the evidence theory for cases when the initial estimates are given in the interval or fuzzy form.

New Methods of Evidence Conflict Measurement Based on Conjunctive Combination Rule

2012 ◽  
Vol 256-259 ◽  
pp. 2877-2885
Author(s):  
Jing Zhu ◽  
Chen Xi Wang ◽  
Li Fang Hu ◽  
Yi Cheng Zheng
Keyword(s):  
Evidence Theory ◽  
Measurement Methods ◽  
Project Implementation ◽  
Combination Rule ◽  
New Methods ◽  
Effective Combination ◽  
Operational Problem ◽  
Moderate Complexity ◽  
Logic Reasoning

In the effective combination of conflicting evidences using the Dempster-Shafer evidence theory, the first step is to reasonably measure the conflict between evidences, but there are limitations in the existing conflict measurement methods. Two new conflict measurement methods based on conjunctive combination rule are put forword, which overcome the limitations of the existing measurement methods. They have four satisfactory properties. Firstly, new methods can measure the total conflict between any pieces of evidence simultaneously, which can satisfy the interchangeability and combinability. Secondly, they overcome the operational problem of the existing binary conflict measurement methods. Thirdly, they are more suitable for people's intuitive logic reasoning. Another, their moderate complexity are easy for project implementation. So new methods have better comprehensive effect under different evidence conditions.

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