On the fusion of imprecise uncertainty measures using belief structures

Yager, Ronald R.

doi:10.1016/j.ins.2011.02.010

Cited by 50 publications

(20 citation statements)

References 28 publications

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“…In this context, a nonprobabilistic uncertainty representation method, the Belief Function Theory (BFT) [14,35], has been adopted for uncertainty representation given its capability of representing very limited knowledge [5,17,41]. If we consider, for example, an extreme case, in which the only information available on the equipment RUL is that it will fail in the time interval as it has been shown in [46], this assignment causes the paradox that it assigns a precise probability value to an event such as "RUL in the interval…”

Section: Direct Rul Prediction: Similarity-based Rul Predictionmentioning

confidence: 99%

“…Thus, in order to perform the aggregation, we resort to the extension of the BFT to the continuous real axis  [35], which allows transforming the belief functions into belief densities. Then, using the least commitment principle, the RUL pdf predicted by the GPR method is transformed into a belief density function and, finally, the Dempster's rule of combination is applied to aggregate the BBAs provided by the similarity-based approach and the GPR method [2,32,46]. The remaining part of the paper is organized as follows: in Section 2, we briefly state the prognostic problem of interest; Section 3 describes the method for performing RUL predictions based on GPR; in Section 4, the methodology for providing prediction intervals for the RUL value based on the SBR method in the framework of BFT is described; in Section 5 a BFT-based technique for aggregating the outcomes of the GPR and SBR approaches is proposed; Section 6 presents the results of the numerical application of these methods to the prediction of the RUL for clogging filters; finally, in Section 7 we state our conclusions and suggest some potential future works.…”

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confidence: 99%

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A belief function theory based approach to combining different representation of uncertainty in prognostics

Baraldi

Mangili

Zio

2015

Information Sciences

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In this work, we consider two prognostic approaches for the prediction of the remaining useful life (RUL) of degrading equipment. The first approach is based on Gaussian Process Regression (GPR) and provides the probability distribution of the equipment RUL; the second approach adopts a Similarity-Based Regression (SBR) method for the RUL prediction and belief function theory for modeling the uncertainty on the prediction. The performance of the two approaches is comparable and we propose a method for combining their outcomes in an ensemble. The least commitment principle is adopted to transform the RUL probability density function supplied by the GPR method into a belief density function. Then, the Dempster's rule is used to aggregate the belief assignments provided by the GPR and the SBR approaches. The ensemble method is applied to the problem of predicting the RUL of filters used to clean the sea water entering the condenser of the boiling water reactor (BWR) in a Swedish nuclear power plant. The results by the ensemble method are shown to be more satisfactory than that provided by the individual GPR and SBR approaches from the point of view of the representation of the uncertainty in the RUL prediction.

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Section: Direct Rul Prediction: Similarity-based Rul Predictionmentioning

confidence: 99%

mentioning

confidence: 99%

A belief function theory based approach to combining different representation of uncertainty in prognostics

Baraldi

Mangili

Zio

2015

Information Sciences

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“…Concretely, in a GDM problem, we have a set of options to solve the problem and a set of experts, who are usually required to provide their preferences for the options by means of a particular preference format. At this time, the preference information provided by decision makers can be expressed in multiple formats, such as utility values, multiplicative preference relations, fuzzy preference relations, linguistic variables, interval numbers, and preference rankings or ranking ordinals (Chiclana et al 2013;Ma 2010;Wang et al 2005;Guo and Wang 2012;Yager 2011;Angiz et al 2012;Frini et al 2012;Lodwick and Jamison 2008;Tavares 2012).…”

Section: Introductionmentioning

confidence: 99%

“…However, the approaches of González-Pachón et al (2003), González-Pachón and Romero (2001, 2011), Wang et al (2005, and Fan et al (2010) are based on total order or partial order preference, and do not consider lattice-ordered preference or the DM's behavior.…”

Section: Introductionmentioning

confidence: 99%

Lattice Order Group Decision Making with Interval Probability Based on Prospect Theory

Guo

Peng

2014

Group Decis Negot

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A random lattice order decision analysis method is proposed based on an interval probability distribution preference vector by way of entropy theory, focusing on a decision preference system in which preference relation probability is described by interval values and the decision maker's behavior is also considered. The preference characterization of decision makers is extended from four varieties of relations to seven varieties of preference relations. In addition to the concept, property, and operation rules of interval probability, the concept of interval-valued distribution preference vectors and the relative entropy on the lattice-ordered preference system are given. Then, the interval probability can be more precisely determined, and the weighting interval probability is transformed into the interval probability weight. The ER nonlinear optimization model based on preference entropy is established, individual preferences are aggregated by applying the priority rule and the intersection rule, and the specific steps of decision making are given. Finally, the feasibility and effectiveness of the approach proposed in this paper are illustrated with a numerical example.

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“…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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On the fusion of imprecise uncertainty measures using belief structures

Cited by 50 publications

References 28 publications

A belief function theory based approach to combining different representation of uncertainty in prognostics

A belief function theory based approach to combining different representation of uncertainty in prognostics

Lattice Order Group Decision Making with Interval Probability Based on Prospect Theory

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

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