Entropic methodology for entanglement measures

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Dempster‐Shafer is widely used to address the problems of uncertainty. One assumption mentioned in this theory is that the distribution of information should be independent. In practice, the requirement cannot be fulfilled. One of the efficient methods to deal with dependent evidence is to calculate the correlation discounting. However, existing coefficient can only be applied to show the direct relation between evidence A and B but do not take the indirect relationship into consideration. To address this issue, in this paper, a new method to combine dependent evidence based on decision‐making trial and evaluation laboratory is presented, not only considering the relation between evidence A and B and the relation between evidence B and C, but also considering the transitive influence between evidence A and C. Finally, the experiments on some benchmark data sets are illustrated to show the efficiency of the proposed method.

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Dependent evidence combination based on decision‐making trial and evaluation laboratory method

Deng

2019

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“…Uncertainty exists everywhere in the real application . Among the existing methods to deal with uncertainty, evidence theory is efficient to model epistemic uncertainty.…”

Section: Preliminariesmentioning

confidence: 99%

TDBF: Two‐dimensional belief function

Deng

2019

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How to efficiently handle uncertain information is still an open issue. In this paper, a new method to deal with uncertain information, named as two-dimensional belief function (TDBF), is presented. A TDBF has two components, T = (m m , A B ), both m A and m B are classical belief functions, while m B is a measure of reliable of m A . The definition of TDBF and the discounting algorithm are proposed. Compared with the classical discounting model, the proposed TDBF is more flexible and reasonable. Numerical examples are used to show the efficiency and application of the proposed method. K E Y W O R D S belief function, conflict management, Dempster-Shafer evidence theory, information fusion, two-dimensional belief function, Z-numbers 1 | INTRODUCTIONIt is inevitable to deal with uncertain information in real word. 1-3 There are many articles that take advantage of uncertain information processing problems. 4 To address this issue, many methods have been proposed, such as probability theory, 5 Dempster-Shafer evidence theory, 6,7 fuzzy sets, 8-10 rough sets, 11 Z-numbers, 12 R-numbers, 13,14 and D numbers. [15][16][17][18][19][20] Among these methods, Dempster-Shafer evidence theory 6,7 is one of the most widely used math tools in many engineering applications such as pattern recognition 21,22 and decision-making. 23 Evidence theory has many advantages to handle uncertain information. [24][25][26] For example, the belief function is more flexible to model uncertainty compared with probability distribution. In addition, Dempster's combination rule can combine evidence from different sources without prior information. 27,28 However, it should be pointed out that illogical results may be obtained by classical Dempster combination rule when collected evidence highly conflicts each other. [29][30][31][32][33] Z-numbers is proposed by Zadeh. 12 A Z-number has two components, Z = (A, B). The first component, A, is a restriction (constraint) on the values which a real-valued uncertain variable, X, is allowed to take. The second component, B, is a measure of reliability (certainty) of the first component. 12 Similarly, in evidence theory, discounting coefficient is a measure of sensor report's reliability, for example, discounting factors based on dissimilarity measure, 34 dynamic discounting rates. 35 Nevertheless, the simple value is not enough and reasonable to express the experts evaluation under uncertain situation. To solve this problem, a new math model named as two-dimensional belief function (TDBF) is proposed in this paper.A TDBF is an ordered pair of basic probability assignments (BPAs) denoted as T = (m m , A B ). The first component m A is a classical BPA, which usually is collected from the sensors. The second component m B is a measure of reliability for the first component, which can be collected by the experts. The frame of discernment of m B set Y N Θ = { , }, where "Y" denotes "positive" and "N" denotes "negative." The power set of Y N Θ = { , } consists of two singletons {Y} and {N}, an universal Θ and t...

“…It is known to all that entropy is a measure of uncertainty associated with the information. [34][35][36] The more the uncertainty, the more the entropy; the smaller the entropy, the more the information contained in the probability distribution. 37,38 From the definition of Gini entropy, it is obvious that to magnify the value of G p ( ) i , the bigger the value of ∑ ∥ ∥ p i n i =1 2 , the better.…”

Section: Infromation Qualitymentioning

confidence: 99%

Aggregation of uncertainty data based on ordered weighting aggregation and generalized information quality

Xiao

2019

It is necessary to take the information quality into consideration in information fusion. However, existing information quality has a limitation due to the ignorance of the credibility of information source. In this paper, the generalized information quality (GIQ) been proposed considering the association among the collected sensor reports, first. Then, the ordered weighting aggregation (OWA) operator of probability distribution based on the GIQ is presented. Numerical example and real application in fault diagnosis are used to illustrate the efficiency of the proposed method. The proposed GIQ and OWA algorithm has the advantage in fault tolerance and reduce the impact of conflict data in data fusion process, due to the consideration of the credibility of each sensor report. The proposed method has the promising aspects in uncertainty data aggregation.