Combination of Evidential Sensor Reports with Distance Function and Belief Entropy in Fault Diagnosis

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...

Section: Preliminariesmentioning

confidence: 99%

TDBF: Two‐dimensional belief function

2019

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“…Such measures alleviate the conflict between the bodies of evidence to a certain extent, but at the same time, it is difficult for the new rules to maintain the original properties of the D‐S combination rules. (b) Keep the classic combination rules unchanged, and preprocess conflict data before combination . Haenni believes that the modification of the data model is in engineering, mathematics and philosophically more reasonable.…”

Section: Introductionmentioning

confidence: 99%

An association coefficient of a belief function and its application in a target recognition system

Pan

2019

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The conflict problem in D-S evidence theory has attracted the attention of many scholars. Conflict coefficients are proposed to describe conflicts between bodies of evidence. The association coefficient as the opposite of the conflict coefficient is also used to measure the conflict. The larger the association coefficient, the smaller the conflict degree, and the higher the similarity between the evidence bodies, and vice versa.In this paper, the degree of association is defined by Deng Entropy, and a new association coefficient is proposed based on the basic inequality. The nature of the new association coefficient and conflict coefficients is explored using examples. Finally, the association coefficient combined with the D-S combination rule is applied to the target recognition system, and accurate results are obtained.association coefficient, conflict coefficients, conflict problem, Deng entropy, D-S evidence theory, target recognition system | INTRODUCTIONThe D-S evidence theory was first proposed by Dempster 1 in 1967 and later developed by his student Shafer 2 in 1976 as an imprecise reasoning theory, which is widely promoted. [3][4][5][6] The theory was first applied to expert systems, 7-9 and it was gradually applied in the fields of information fusion, 10-12 intelligence analysis, 9,13-16 evidential reasoning, [17][18][19] and multiattribute decision analysis. [20][21][22][23][24] As an indeterminate reasoning method which satisfies the conditions weaker than Bayesian probability theory; it has the ability to directly express "uncertainty" 25 and "don't know." 26 Therefore, the D-S evidence theory is flexible and convenient for describing uncertainties. However, D-S evidence theory has produced counterintuitive results in the fusion of a highly conflicting example proposed by Zadeh. 27 Therefore, the issue of conflict between bodies of evidence has attracted more and more researchers so far. [28][29][30][31][32] Domestic and foreign scholars have proposed a large number of improved methods, which can be divided into two major categories: (a) modification of the combination rules of the classical D-S evidence theory to achieve the redistribution of conflicts in the case of evidence conflicts. [33][34][35][36] Such measures alleviate the conflict between the bodies of evidence to a certain extent, but at the same time, it is difficult for the new rules to maintain the original properties of the D-S combination rules. (b) Keep the classic combination rules unchanged, and preprocess conflict data before combination. [37][38][39][40][41][42] Haenni 43 believes that the modification of the data model is in engineering, mathematics and philosophically more reasonable. However, regardless of the type of method used to deal with conflicts between evidence, the conflict coefficient is an extremely important parameter. Therefore, the most critical step before choosing the right combination of evidence is the measure of evidence conflict.To measure the conflict between evidence bodies, many researchers have proposed...

“…Dealing with uncertainty information plays an important role in real applications . Many math tools, such as fuzzy sets, rough sets, Z‐numbers, belief structures, D numbers entropy function, and evidence theory, are presented to handle different types of uncertainty information. Among these tools, probability is heavily studied and is widely used in many applications, including decision making, estimation, and uncertain measurement …”

Section: Introductionmentioning

confidence: 99%

A new soft likelihood function based on power ordered weighted average operator

Song

2019

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The likelihood function is widely used in data processing but the classical likelihood function is too strict to deal with data with extreme values in real applications.To address this issue, a soft likelihood function based on power ordered weighted average (POWA) operator for probability distribution is proposed. Compared with the existing soft likelihood functions, one of the main features of the proposed likelihood function is that the weighted mean is displayed by the geometric mean of the weighted probability products. As a result, the effect on final result caused by extreme data can be efficiently decreased. Numerical examples are used to illustrate the efficiency of the proposed soft likelihood function. K E Y W O R D S geometric mean, likelihood function, OWA operator, POWA operator, soft likelihood function | INTRODUCTIONDealing with uncertainty information plays an important role in real applications. 1-3 Many math tools, such as fuzzy sets, 4-6 rough sets, 7 Z-numbers, 8-11 belief structures, 12-14 D numbers 15-17 entropy function, 18,19 and evidence theory, 20-22 are presented to handle different types of uncertainty information. Among these tools, probability is heavily studied and is widely used in many applications, including decision making, 23-26 estimation, 27,28 and uncertain measurement. [29][30][31][32] One of the most used models in probability is the likelihood function, which is used when data are available to describe plausibility of a parameter value. [33][34][35] However, it is very strict in real applications since the original likelihood function made up with the probability product is too strict to show the compatibility probabilities for the different pieces of evidence since any piece of probabilities, which are low-value would greatly reduce the likelihood function.How to cite this article: Song Y, Deng Y. A new soft likelihood function based on power ordered weighted average operator. Int J Intell