Belief Interval-Based Distance Measures in the Theory of Belief Functions

Han, Deqiang; Dezert, Jean; Yang, Yi

doi:10.1109/tsmc.2016.2628879

Cited by 102 publications

(29 citation statements)

References 37 publications

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“…The theory of evidence was first proposed by Dempster in 1967 [6], an inaccurate reasoning theory developed by his student Shafer in 1976 [8]. After that, D-S evidence theory has obtained plenty of achievement in different fields, e.g., quantum-like bayesian networks [33], information aggregation [34]- [36], failure mode and effects analysis [37], data classification [38], [39], decision making and reasoning [40]- [46],etc.…”

Section: A Basic Concept Of D-s Evidence Theorymentioning

confidence: 99%

A New Synthesis Combination Rule Based on Evidential Correlation Coefficient

2020

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Dempster-Shafer evidence theory has been widely applied to solving data fusion problems. However, it is still an open issue about how to combine the evidences effectively when the high conflict evidences are collected. Many scholars have made improvements to solve this problem, but there are new problems such as violation of the theoretical attributes of D-S combination rules and limitations of application scope of improvement methods. Considering these shortcomings, a new evidence synthesis formula based on correlation coefficient of belief functions is proposed in this paper. Our contribution is that the proposed formula can solve the highly conflict issues mentioned above effectively. Moreover, the various types of evidences collected can be well combined. One of the advantages of the proposed model is that conflict coefficient K r is the coefficient of the fusion formula which represents the degree of conflict about evidences. So the fusion process is more flexible and useful. Several examples and comparative experimental simulation are used to illustrate the effectiveness of the proposed methodology.

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Section: A Basic Concept Of D-s Evidence Theorymentioning

confidence: 99%

A New Synthesis Combination Rule Based on Evidential Correlation Coefficient

2020

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“…DST is commonly applied to the expression and processing of uncertain information . The classical combination rule of Dempster has been improved by using soft likelihood functions .…”

Section: Environmental Impact Assessment Using the Approaches In Dstmentioning

confidence: 99%

“…DST is commonly applied to the expression and processing of uncertain information. 46,47 The classical combination rule of Dempster has been improved by using soft likelihood functions. 23 To verify the presented rule, the approaches are developed in DST for solving environmental impact assessment problem.…”

Section: Environmental Impact Assessment Using the Approaches In Dstmentioning

confidence: 99%

On combination rule in Dempster–Shafer theory using OWA‐based soft likelihood functions and its applications in environmental impact assessment

Fei

2019

Int J Intell Syst

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Dempster–Shafer theory (DST) was presented as an effective mathematical tool to represent uncertainty. Its significant innovation is to allow the allocation of the belief of mass to sets or intervals, and it becomes a valuable method in the field of decision making and evaluation when accurate information is not available or when knowledge is expressed subjectively by humans. A crucial research issue in DST is the combination of multi‐sources of evidence. In this paper, a novel combination rule for Dempster–Shafer structures is developed based on ordered weighted average (OWA)‐based soft likelihood functions proposed by Yager. First, the belief intervals, including the belief measures and plausibility measures, of all the hypotheses in the frame of discernment (FOD) are calculated. Second, the representative value of belief interval is defined based on golden rule introduced by Yager. Third, the soft likelihood value of each hypothesis is calculated based on the proposed OWA‐based soft likelihood function for belief interval, which can be considered as the combined evidence. The final evaluation results can be employed for practical applications, such as decision making and evaluation. In addition, the improved evidence combination rule is presented which takes into account the weight of evidence. Several illustrative examples are conducted to manifest the use of the developed methods. Finally, an application for environmental impact assessment is given to demonstrate the usefulness of the developed combination rule in DST.

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“…According to previous studies of evidence theory, considering optimal management of conflicts may improve the accuracy performance at the decision-making level in data science applications [38][39][40]. Therefore, how to measure the conflict of multiple pieces of evidence has attracted considerable research attention in recent years [41][42][43], and many related definitions have been presented [44] which can be used for fuzzy system-based industrial application areas. Although the outcomes of current conflict management methods are acceptable in DSE theory, we assume there still remains room for improving decision-making performance at the decision level in terms of the measure and management of conflicts.…”

Section: Introductionmentioning

confidence: 99%

A Novel Conflict Measurement in Decision-Making and Its Application in Fault Diagnosis

Xiao

Cao

Jolfaei

2021

IEEE Trans. Fuzzy Syst.

143

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Dempster-Shafer evidence (DSE) theory, which allows combining pieces of evidence from different data sources to derive a degree of belief function that is a type of fuzzy measure, is a general framework for reasoning with uncertainty. In this framework, how to optimally manage the conflicts of multiple pieces of evidence in DSE remains an open issue to support decision making. The existing conflict measurement approaches can achieve acceptable outcomes but do not fully consider the optimization at the decision-making level using the novel measurement of conflicts. In this paper, we proposed a novel evidential correlation coefficient (ECC) for belief functions by measuring the conflict between two pieces of evidence in decision making. Then, we investigated the properties of our proposed evidential correlation and conflict coefficients, which are all proven to satisfy the desirable properties for conflict measurement, including nonnegativity, symmetry, boundedness, extreme consistency, and insensitivity to refinement. We also presented several examples and comparisons to demonstrate the superiority of our proposed ECC method. Finally, we applied the proposed ECC in a decision-making application of motor rotor fault diagnosis, which verified the practicability and effectiveness of our proposed novel measurement.

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Belief Interval-Based Distance Measures in the Theory of Belief Functions

Cited by 102 publications

References 37 publications

A New Synthesis Combination Rule Based on Evidential Correlation Coefficient

A New Synthesis Combination Rule Based on Evidential Correlation Coefficient

On combination rule in Dempster–Shafer theory using OWA‐based soft likelihood functions and its applications in environmental impact assessment

A Novel Conflict Measurement in Decision-Making and Its Application in Fault Diagnosis

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