Fuzzy approach to the theory of measurement inexactness

Urbański, Michał; Wa̧sowski, J.

doi:10.1016/s0263-2241(03)00021-6

Cited by 83 publications

(38 citation statements)

References 8 publications

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“…This is clearly shown by Figs. 5,6,7,8, that confirm also, in the limited number of considered multimeters, the uniform probability assumption.…”

Section: Discussionsupporting

confidence: 75%

“…The theory of evidence [3], which encompasses probability as a particular case, and the theory of possibility (that is another particular case of evidence) have been considered by several researchers [4][5][6][7] as a promising mathematical tool to overcome the limitations of the GUM probabilistic approach. Several interesting applications are already available [8][9][10][11][12], thus proving the interest toward this more general approach and its capability of providing an effective representation of measurement results together with their uncertainty.…”

Section: Introductionmentioning

confidence: 99%

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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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“…This is clearly shown by Figs. 5,6,7,8, that confirm also, in the limited number of considered multimeters, the uniform probability assumption.…”

Section: Discussionsupporting

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Uncertainty evaluation by means of joint possibility distributions

Ferrero

Prioli

Salicone

2013

16th International Congress of Metrology

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“…That is, different t-norms induce different T-independence operations. An increasing number of studies have been done in the domain of T-independent (also called ''T-related'' in the literature) fuzzy variables or fuzzy numbers (see [13,[16][17][18][19][20]), for it provides a wider range of options for arithmetic operator selection towards a variety of applications, e.g., image processing [21,22], fuzzy logic [23], and measurement theory [24,25].…”

Section: Introductionmentioning

confidence: 99%

Modeling renewal processes in fuzzy decision system

Wang

Liu

2015

Applied Mathematical Modelling

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a b s t r a c tUnder expected value of fuzzy variable and continuous Archimedean triangular norms, this paper discusses a renewal process and a renewal reward process for T-independent L-R fuzzy variables in fuzzy decision systems. First, a renewal process with T-independent L-R fuzzy interarrival times is discussed, some limit theorems on renewal variable, average renewal time, and long-term renewal rate in (fuzzy) measure are obtained, and a fuzzy elementary renewal theorem is proved for the limit of the long-term expected renewal rate. Second, a renewal reward process with T-independent L-R fuzzy interarrival times and rewards is discussed, a limit theorem on reward rate in (fuzzy) measure is derived, and a fuzzy renewal reward theorem is proved for the limit value of expected reward rate. Finally, the comparison with stochastic counterparts shows an interesting and reasonable homology in convergence mode and limit value between the results obtained in fuzzy renewal processes and the corresponding results in stochastic renewal processes, though they build on two essentially different mathematical cornerstones, possibility theory and probability theory, respectively.

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“…For this reason, the possibility theory has been recently investigated as a more general tool than probability to express measurement results together with the related measurement uncertainty [2,4,5], and Random-Fuzzy Variables (RFVs) have been defined [6,7] as a promising tool for representing and combining measurement results and related uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Combination of measurement uncertainty contributions via the generalized Dombi operator

Ferrero¹,

Prioli²,

Salicone³

et al. 2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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Possibility is considered as a promising mathematical tool to represent that particular case of incomplete information given by a measurement result. A measurement result can be affected by systematic and random effects. The combination of random contributions in the possibility theory returns only approximated results, and it is important to identify an optimal combination method to obtain acceptable uncertainty evaluations. This paper considers the generalized Dombi operator as a promising tool to obtain satisfying results.

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Fuzzy approach to the theory of measurement inexactness

Cited by 83 publications

References 8 publications

Uncertainty evaluation by means of joint possibility distributions

Uncertainty evaluation by means of joint possibility distributions

Modeling renewal processes in fuzzy decision system

Combination of measurement uncertainty contributions via the generalized Dombi operator

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