TDBF: Two‐dimensional belief function

Li, Yangxue; Deng, Yong

doi:10.1002/int.22135

Cited by 46 publications

(19 citation statements)

References 66 publications

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“…The theory was first applied to expert systems, and it was gradually applied in the fields of information fusion, intelligence analysis, evidential reasoning, and multiattribute decision analysis . As an indeterminate reasoning method which satisfies the conditions weaker than Bayesian probability theory; it has the ability to directly express “uncertainty” and “don't know.” 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 .…”

Section: Introductionmentioning

confidence: 99%

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

Pan

Deng

2019

Int J Intell Syst

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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...

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Section: Introductionmentioning

confidence: 99%

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

Pan

Deng

2019

Int J Intell Syst

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“…Uncertainty is very important in many fields, which has attracted many researchers' attention . There are various models to handle uncertainty, including fuzzy sets, rough sets, Z numbers, D numbers, R numbers, intuitionistic evidence sets (IES), Two Dimension Belief Function (TDBF) and Dempster‐Shafer (D‐S) evidence theory and so on . D‐S evidence theory attract more and more attention due to it needs weaker condition than the Bayesian probability .…”

Section: Introductionmentioning

confidence: 99%

Quantum model of mass function

Gao

Deng

2019

Int J Intell Syst

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Dempster-Shafer (D-S) evidence theory has been used in many fields due to the flexibility and effectiveness in modelling uncertainties, which is the extension of classical probability. Uncertainty principle is one of the most important principles in quantum theory, which has been used in many fields. How to set the connection between quantum theory and D-S evidence theory is also an open issue. Hence, the paper proposed the quantum model of mass function to consider the quantum theory and D-S evidence theory. In the proposed quantum method, quantum mass function uses euler formula to represent. The paper also discusses some operations based on the quantum model of the mass function. Moreover, the paper also discusses the relationship between quantum mass function and classical mass function by using some numerical examples. Classical mass function is a special case when there is no interference in quantum mass function. Similar to the other quantum models, this study provides a more wide application in quantum information. K E Y W O R D S basic probability assignment, belief function, Dempster-Shafer evidence theory, mass function, quantum theory

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“…Since Zadeh's paradox 15 was proposed, the means of overcoming the shortcomings of Dempster's rule and integrating conflicting sources of evidence effectively has become a crucial research field in DST. Quite a few novel or alternative combination rules have been developed to improve the performance of Dempster's rule, such as the conjunctive rule, [16][17][18] disjunctive rule, [19][20][21] cautious conjunctive rule, 22,23 and the bold disjunctive rule. [24][25][26][27][28][29][30] To correct the deviation of the fusion rules, many studies have been carried out, and there are two main popular ideas.…”

Section: Introductionmentioning

confidence: 99%

Evidence combination using OWA‐based soft likelihood functions

2019

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Dempster's combination rule has been widely regarded and applied since it is an effective and rigorous method of synthesizing multisource information with its special information representation (ie, mass function or basic probability assignment). However, it has also been criticized and debated upon regarding some of its unreasonable behaviors and restrictive requirements, such as the counterintuitive results in some cases. To address these issues from different perspectives, in this study, an alternative fusion rule is developed under the framework of Dempster‐Shafer evidence theory. A novel evidence combination rule called CR‐SLF is proposed based on soft likelihood functions (SLF) considering the ordered weighted average aggregation operator. Some illustrative examples are shown, and the corresponding analyses demonstrate the good performance of CR‐SLF to fuse multisource evidence. To extend CR‐SLF further, the reliability of multisource evidence is considered from two aspects, subsequently two reliability‐based combination rules are presented, including the discount‐based rule and the SLF improvement‐based rule. The simulation results show that the reliability‐based CR‐SLF has a better fusion effect than the rule without considering the reliability.

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TDBF: Two‐dimensional belief function

Cited by 46 publications

References 66 publications

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

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

Quantum model of mass function

Evidence combination using OWA‐based soft likelihood functions

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