A New Method to Determine Generalized Basic Probability Assignment in the Open World

Sun, Ruiyan; Deng, Yong

doi:10.1109/access.2019.2911626

Cited by 36 publications

(31 citation statements)

References 57 publications

(36 reference statements)

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“…Definition A BPA function

m

is a mapping of

2^{Θ}

to a probability interval

[0, 1]

, formally defined by

m : 2^{normalΘ} \to [0, 1],

which satisfies the following conditions:

m (\emptyset) = 0 \sum_{A \in 2^{normalΘ}} m (A) = 1, 0 \leq m (A) \leq 1, A \in 2^{normalΘ} .

The mass

m (A)

represents how strongly the evidence supports

A

. One assumption of evidence theory is the close world, which means the mass function of empty set is zero . In addition, due to the fact that the BPA is the most important concept of evidence theory, many operations such as belief structure, correlation, negation, entropy, and divergence are developed.…”

Section: Preliminariesmentioning

confidence: 99%

TDBF: Two‐dimensional belief function

Deng

2019

Int J Intell Syst

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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...

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“…Definition A BPA function

m

is a mapping of

2^{Θ}

to a probability interval

[0, 1]

, formally defined by

m : 2^{normalΘ} \to [0, 1],

which satisfies the following conditions:

m (\emptyset) = 0 \sum_{A \in 2^{normalΘ}} m (A) = 1, 0 \leq m (A) \leq 1, A \in 2^{normalΘ} .

The mass

m (A)

represents how strongly the evidence supports

A

Section: Preliminariesmentioning

confidence: 99%

TDBF: Two‐dimensional belief function

Deng

2019

Int J Intell Syst

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“…Here we assume that quantifier Q x On the basis of Equation (18), the aggregation result G j of IVEDF j ( ) i at each satisfaction level based on the quantifier-based OWA operator can be calculated. The specific calculation process is shown as follows: After the normalization process, G j  for each satisfaction level can be obtained as Then, the aggregated criteria satisfaction v  can be obtained based on Equation (19).̃̃̃ṽ with the same process shown above. Then, the IREV for A 2 can be obtained, which is 2.2266.…”

Section: Application Analysismentioning

confidence: 99%

“…Multicriteria decision‐making (MCDM) is an important part of modern decision‐making science, which is also widely used in many fields, such as supplier selection, medical diagnosis, sensor fusion, uncertainty modeling, risk analysis, reliability, and so forth . Many effective techniques have been used in solving MCDM problems, such as intuitionistic fuzzy sets, soft sets, evidence theory, evidential reasoning, D number, and Z number . With the development of information science, these problems have attracted many researchers …”

Section: Introductionmentioning

confidence: 99%

An interval‐valued exceedance method in MCDM with uncertain satisfactions

Liu

Xiao

2019

Int J Intell Syst

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Multicriteria decision‐making problems have been applied to many applications for its practicality. Nevertheless, when the evaluated satisfactions are more complex, such as interval‐valued distributions, how to reasonably obtain the aggregation results of alternatives is still an open issue. In this paper, an interval‐valued exceedance method is proposed to solve such a question based on the Golden Rule representative value and probabilistic exceedance method. Due to good performance of expressing uncertain information, the Golden Rule representative value method is used to order interval‐valued satisfactions after an effective normalization process. In addition, a quantifier‐based ordered weighted averaging operator is also introduced to consider the preferences of decision makers. A realistic application of supplier selection is shown to illustrate the practicality of the proposed method.

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“…28 In the present work, a new method for evaluating nuclear safeguards is proposed. The method is based on Dempster-Shafer theory of evidence, which has been widely invoked to handle uncertain information, such as fault diagnosis, [29][30][31][32] human reliability analysis, 33 pattern recognition, [34][35][36][37] uncertainty modeling, [38][39][40] evidential reasoning, 41,42 decision making, 43 and environmental assessment. 44,45 In this article, first, according to the belief degrees of linguistic evaluation values given by IAEA experts and weights of IAEA experts about indicators, we obtain the basic probability assignment (BPA) of each indicator.…”

Section: Introductionmentioning

confidence: 99%

An evidential evaluation of nuclear safeguards

Gao

Deng

2019

International Journal of Distributed Sensor Networks

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Nuclear safeguards evaluation is a complicated issue with many missing values and uncertainties. By invoking Dempster-Shafer theory of evidence, the missing values are assigned to a subset of a set of multiple objects, at the same time, by combining different evaluation values, and the effect of uncertainty will be decreased. In this way, both the missing values and uncertainties are considered in the final evaluations. This method has been used in considering the International Atomic Energy Agency experts' evaluation for nuclear safeguards. The result shows that (s 2 , 0.1897) is the biggest belief degree.

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A New Method to Determine Generalized Basic Probability Assignment in the Open World

Cited by 36 publications

References 57 publications

TDBF: Two‐dimensional belief function

TDBF: Two‐dimensional belief function

An interval‐valued exceedance method in MCDM with uncertain satisfactions

An evidential evaluation of nuclear safeguards

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