A 2-D Metrology-Sound Probability–Possibility Transformation

Ferrero, Alessandro; Prioli, Marco; Salicone, Simona; Vantaggi, Barbara

doi:10.1109/tim.2013.2246910

Cited by 17 publications

(26 citation statements)

References 26 publications

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“…In this framework, the possibility is viewed as the upper envelope of the family of probability measures (Jacquin, 2010;Ferrero et al, 2013;Betrie et al, 2014). There are two important considerations for this transformation, first it guarantees that something must be possible before it is probable; hence, the degree of possibility cannot be less than the degree or probability -this is known as the consistency principle (Zadeh, 1965).…”

Section: Probability-possibility Transformationsmentioning

confidence: 99%

Dissolved oxygen prediction using a possibility theory based fuzzy neural network

Khan

Valeo

2016

Hydrol. Earth Syst. Sci.

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Abstract.A new fuzzy neural network method to predict minimum dissolved oxygen (DO) concentration in a highly urbanised riverine environment (in Calgary, Canada) is proposed. The method uses abiotic factors (non-living, physical and chemical attributes) as inputs to the model, since the physical mechanisms governing DO in the river are largely unknown. A new two-step method to construct fuzzy numbers using observations is proposed. Then an existing fuzzy neural network is modified to account for fuzzy number inputs and also uses possibility theory based intervals to train the network. Results demonstrate that the method is particularly well suited to predicting low DO events in the Bow River. Model performance is compared with a fuzzy neural network with crisp inputs, as well as with a traditional neural network. Model output and a defuzzification technique are used to estimate the risk of low DO so that water resource managers can implement strategies to prevent the occurrence of low DO.

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Section: Probability-possibility Transformationsmentioning

confidence: 99%

Dissolved oxygen prediction using a possibility theory based fuzzy neural network

Khan

Valeo

2016

Hydrol. Earth Syst. Sci.

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“…can be considered as a generalization of the probabilistic concept of confidence intervals and a credibility that an element x belongs to them can be associated to each interval, in the range [0,1] [6,8]. In particular, the credibility value is given, for each α-cut at level α, by 1 − α [7].…”

Section: Overview Of the Rfv Approachmentioning

confidence: 99%

“…In this case, the samples of v are directly obtained and they provide an estimate of the PDF of v. In Sec. 4.3, this PDF will be transformed into an equivalent PD [8] that will be compared with the ones obtained following the RFV approach.…”

Section: Gum Approachmentioning

confidence: 99%

Possibility and probability: application examples and comparison of two different approaches to uncertainty evaluation

Ferrero¹,

Pou²,

Prioli³

et al. 2015

17th International Congress of Metrology

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Abstract. This paper proposes two interesting applications of the approach to uncertainty evaluation and representation in terms of Random-Fuzzy Variables. One covers the expression of the calibration uncertainty of gauge blocks, and one considers unknown temperature variations, with respect to temperature at calibration time, in expressing a voltmeter uncertainty. Both considered examples show that the proposed approach is more effective than the traditional GUM approach.

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“…In particular, while the internal PD is generally built directly in terms of a possibility distribution, the random PD is often induced by a probability distribution function (pdf). This can be obtained by applying suitable probabilitypossibility transformations to the pdf representing the random phenomena [16,17].…”

Section: Rfv Approachmentioning

confidence: 99%

“…Therefore, the random PDs of U i and U o are assumed to be induced by normal probability distributions [13,16,17] whose 99% confidence interval ±3σ is given by the experimental interval ±2 digits.…”

Section: Uncertainty Evaluationmentioning

confidence: 99%

Uncertainty evaluation by means of joint possibility distributions

Ferrero

Prioli

Salicone

2013

16th International Congress of Metrology

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Abstract. The recent theories of evidence and possibility represent an interesting generalization of the wellknow probability theory. Therefore, they appear to be a promising mathematical framework for the expression of uncertainty in measurement, capable of overcoming the limitations of the presently followed probability approach when uncompensated systematic effects are present. This paper proposes an example of uncertainty evaluation framed within these new theories and an experimental validation that shows the correctness and effectiveness of the proposed approach.

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A 2-D Metrology-Sound Probability–Possibility Transformation

Cited by 17 publications

References 26 publications

Dissolved oxygen prediction using a possibility theory based fuzzy neural network

Dissolved oxygen prediction using a possibility theory based fuzzy neural network

Possibility and probability: application examples and comparison of two different approaches to uncertainty evaluation

Uncertainty evaluation by means of joint possibility distributions

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