Maximal confidence intervals of the interval-valued belief structure and applications

Su, Zhi‐gang; Wang, Peihong; Yu, Xiangbin; Zhen-zhong, LU

doi:10.1016/j.ins.2011.01.004

Cited by 12 publications

(6 citation statements)

References 88 publications

(69 reference statements)

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“…In the IIB, t t ={1,0}, it means that m 1:t = m 1:t-1 according to the extended linear updating rule in Eqs. (15) and (16). Since m 1:1 = m ,1 , the updated result at each step is always taken as m ,1 , therefore, the IIB is quite insensitive to the change of the incoming diagnosis evidence.…”

Section: Methodsmentioning

confidence: 99%

“…The first point above is concerned with the representation of uncertainty. In recent years, intervalvalued belief structures (IBSs) have attracted considerable attention for its effectiveness of modeling and combining uncertain information by using interval form of belief masses [15][16][17] . Compared with single-valued BBA, IBS can describe fault information in a more elaborate way and caters for human's general understandings to uncertainty.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Interval-valued Evidence Updating with Reliability and Sensitivity Analysis for Fault Diagnosis

Xu¹,

Zhang²,

Xu³

et al. 2016

IJCIS

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Information fusion methods based on Dempster-Shafer evidence theory (DST) have been widely used in fault diagnosis. In DST-based methods, the monitoring information collected from sensors is modeled as multiple pieces of diagnosis evidence in the form of basic belief assignment (BBA), and Dempster's rule is then used to combine these BBAs to obtain the fused BBA for diagnosis decision making. However, the belief structure with crisp singlevalued belief degrees in BBA may be too coarse to truthfully represent detailed fault information. Moreover, Dempster's rule only uses a static combination process, which is unsuitable for dynamically fusing information collected at different time steps. In order to address these issues, the paper proposes a dynamic diagnosis method based on interval-valued evidential updating. First of all, the diagnosis evidence is constructed as an interval-valued belief structure (IBS), which provides a more informative scheme than BBA to model fault information. Secondly, the proposed evidential updating strategy can generate updated IBS as global diagnosis evidence by updating the previous evidence with the new incoming evidence recursively. Thirdly, the reliability and sensitivity indices are designed to evaluate and compare the performance of the proposed updating strategy with other commonly used strategies. Finally, the effectiveness of the proposed evidential updating strategy is demonstrated through some typical fault experiments of a machine rotor.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interval-valued Evidence Updating with Reliability and Sensitivity Analysis for Fault Diagnosis

Xu¹,

Zhang²,

Xu³

et al. 2016

IJCIS

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show abstract

“…Generally speaking, Equation 11. cannot be applied to cases in which different forms of independence hold between the parameters; other formula have been proposed to address these different situations [10], [46], [40]. In particular, when the experts are asked to provide all the otherwise where the symbol '\' indicates the set of all elements belonging to the set on the left but not to that on the right.…”

Section: Uncertainty Propagationmentioning

confidence: 99%

“…On the other side, there are other techniques such as DSTE and Possibility Theory (see [5]- [8], [13]- [16], [18], [21], [23], [38], [40], [45], [46], for detailed surveys and comparisons) which are emerging to be more appropriate in describing epistemic uncertainty, though they have never been adopted in Markov models (as pointed out in [37]) nor in other models of the degradation mechanisms ( [4]). …”

Section: Introductionmentioning

confidence: 99%

Maintenance policy performance assessment in presence of imprecision based on Dempster–Shafer Theory of Evidence

Baraldi

Compare

Zio

2013

Information Sciences

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To cite this version:Piero Baraldi, Michele Compare, Enrico Zio. Maintenance policy performance assessment in presence of imprecision based on Dempster-Shafer Theory of Evidence. Information Sciences, Elsevier, 2013, 245, pp.112 -131 Abstract: The aim of this work is to assess the performance of a maintenance policy when a stochastic model of the life of the component of interest is known, but relies on parameters that are imprecisely known, and only through information elicited from experts. The case in which the information used to feed the model comes from a single expert has been investigated by the authors in a previous work. This paper deals with the different situation in which a number of experts are involved in the elicitation of the uncertain parameters; in particular, each expert provides an interval he/she believes containing the unknown value of the parameter which he/she is knowledgeable about. The different type of available information calls for the development of a different method to represent and propagate the associated uncertainty. Resorting to Probability theory to address this issue is questionable. Then, a technique based on the Dempster-Shafer Theory of Evidence (DSTE) is embraced in this work, which allows facing a practical case study concerning the check valve of a turbo-pump lubricating system in a Nuclear Power Plant. The output of such method consists of couples of Lower and Upper cumulative distributions describing the uncertainty in the maintenance performance indicators of interest (i.e., unavailability and costs), which accounts for both the aleatory and epistemic contributions.

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“…Since its proposal, many researchers have contributed to the interval‐valued belief structure. Fu and Yang, Su et al provided a series of combination rules of interval‐valued belief structures. Wang et al and Zhang et al investigated the evidential reasoning under interval‐valued belief structures.…”

Section: Introductionmentioning

confidence: 99%

Belief intervals aggregation

Sun¹,

Guan²,

Xiao³

et al. 2018

Int. J. Intell. Syst.

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The combination rule is the core of Dempster-Shafer theory (DST), and there is no uniform aggregation rule adapting to all conditions. The construction of such a ruleis still an open and hot topic. In this article, we focus on this point. We focus on the belief interval, which is made up of belief function and plausibility function, in the form of [belief function, plausibility function], instead of basic belief assignment, to represent the DST. We aim at exploring a belief interval combination rule as the combination rule of DST. To do this, we contrast the belief interval with the intuitionistic fuzzy sets and construct the belief interval combination rule based on the intuitionistic fuzzy weighted averaging (IFWA) operator, which opens the door for DST combination rules to the aggregation operator perspective. Further, we find that directly using the IFWA operator as the belief interval combination rule poses three problems: the "'one' veto problem," converge easily close to [1,1] and the belief function from the belief interval combination rule is not normalized. To solve these problems, we add a normalization process in the belief interval combination rule to modify it, which can address all these three problems well.We also set up a series of examples to illustrate the belief interval combination rule, including a multisensor fusion scenario to compare it with some of the existing rules, which shows its superiorities in better stability and lower operational load. K E Y W O R D S aggregation operator, belief functions, belief intervals, combination rule, plausibility function Int J Intell Syst. 2018;2425-2447.wileyonlinelibrary.com/journal/int

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Maximal confidence intervals of the interval-valued belief structure and applications

Cited by 12 publications

References 88 publications

Interval-valued Evidence Updating with Reliability and Sensitivity Analysis for Fault Diagnosis

Interval-valued Evidence Updating with Reliability and Sensitivity Analysis for Fault Diagnosis

Maintenance policy performance assessment in presence of imprecision based on Dempster–Shafer Theory of Evidence

Belief intervals aggregation

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