By Simona Salicone
The expression of uncertainty in dimension is a difficult element for researchers and engineers operating in instrumentation and size since it consists of actual, mathematical and philosophical matters. This challenge is intensified through the restrictions of the probabilistic method utilized by the present typical (GUM). this article is the 1st to make complete use of the mathematical thought of proof to specific the uncertainty in measurements. It offers an summary of the present common, then pinpoints and constructively resolves its boundaries via its new angle. The textual content offers a number of instruments for comparing uncertainty, starting with the probabilistic method and concluding with the expression of uncertainty utilizing random-fuzzy variables. The exposition is pushed by means of a variety of examples. The publication is designed for fast use and alertness in examine and laboratory paintings. necessities for college kids comprise classes in information and size technological know-how. except a lecture room environment, this ebook can be utilized through practitioners in quite a few fields (including utilized arithmetic, utilized chance, electric and laptop engineering, and experimental physics), and via such associations because the IEEE, ISA, and nationwide Institute of criteria and know-how.
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Additional resources for Measurement Uncertainty: An Approach Via the Mathematical Theory of Evidence
As an example, the square root of a fuzzy variable can be defined as follows. α Let A be a fuzzy variable, defined by its α-cuts Aα = [aα 1 , a2 ], and let √ us consider the square root C = A. 5 shows an example. It is important to underline that, in some particular applications, it could be also necessary to perform a square root of a fuzzy variable that falls across the zero value. In fact, when the measurement uncertainty of a value near zero is considered, the correspondent confidence interval (and the correspondent fuzzy variable too) contains the zero value.
8), the following characteristics of basic probability assignments can be drawn: • it is not required that m(X) = 1; • it is not required that m(A) ≤ m(B) when A ⊆ B; • there is no relationship between m(A) and m(A). 9) B| B⊆A It can be proved that the total belief t(A) committed to A is a belief function; that is, it satisfies Eqs. 4). Proof : 1. If A = ∅, then by taking into account Eq. 7): m(B) = m(∅) = 0 t(∅) = B| B⊆∅ and Eq. 2) is satisfied. 1 Basic definitions 2. If A = X, then by taking into account Eq.
This implies that Bel(A) cannot be low unless Bel(A) is high; that is, failure to believe A needs ¯ Therefore, within the Bayesian theory, complete ignorance is believing in A. expressed as follows: 1 Bel(A) = Bel(A) = 2 ¯ that is, with an equal degree of belief for both A and A. Although this solution seems to be plausible in case only two possibilities ¯ it is totally useless in representing ignorance are considered, that is (A, A), when the set of possibilities contains more than two elements, as demonstrated by the following example.
Measurement Uncertainty: An Approach Via the Mathematical Theory of Evidence by Simona Salicone