Measuring Uncertainty within the Theory of Evidence (Springer Series in Measurement Science and Technology)

a probable knowledge could be obtained, probability being, at that time, the attribute assigned to opinions (inductive knowledge), and, lastly, the one where knowledge was impossible. In the 18 th century, Lambert makes a distinction between random probabilities that can be objectively known (either a priori, as in the game theory, or a posteriori from experience) and subjective probabilities obtained from an inference based on effects or circumstances. In the 20 th century, Kolmogorov introduced an axiomatic probability formulation, but it is the development of artificial intelligence that caused a new interest in the mathematical modeling of human reasoning and led to a more subjective approach to probability. Starting from the 1960s, theories have been proposed that are not directly related to probability any longer: Zadeh introduced the fuzzy sets and the theory of possibilities, and Shafer developed the theory of evidence. The probability theory allows one to draw conclusions between certainty and impossibility. Therefore, the probabilistic point of view finds its limits when it is requested to model human reasoning, when decisions are taken on the basis of data that may be uncertain, partial, not totally reliable, and conflicting and when constraints and objectives may be imprecise. The possibility theory, for instance, allows one to distinguish between indetermination (related to the truth of a statement) and imprecision (related to the nature of a statement), while probability does not allow this.Uncertainty evaluation has been a well-known topic of metrology for a long time. Nonetheless, it is not yet totally mastered by metrologists, who have often a limited, sometimes wrong knowledge of the mathematical tools that can suitably analyze and exploit the core of their job: the quantative representation of information. The work of Simona Salicone and Marco Prioli, which introduces the different concepts and their applications progressively, is an excellent remedy for this matter of fact. By showing how the theory of the credibility functions, which encompass probability, leads to improve the effectiveness of uncertainty calculation, they open new perspectives to metrology and its practice. We hence wish success to this remarkable work that opens, in a relevant way, the science of measurement to new theories and exciting perspectives of renewal of the metrologist tasks.Statistician, "This monograph considers the evaluation and expression of measurement uncertainty within the mathematical framework of the Theory of Evidence. With a new perspective on the metrology science, the text paves the way for innovative applications in a wide range of areas. Building on Simona Salicone’s Measurement Uncertainty: An Approach via the Mathematical Theory of Evidence, the material covers further developments of the Random Fuzzy Variable (RFV) approach to uncertainty and provides a more robust mathematical and metrological background to the combination of measurement results that leads to a more effective RFV combination method. While the first part of the book introduces measurement uncertainty, the Theory of Evidence, and fuzzy sets, the following parts bring together these concepts and derive an effective methodology for the evaluation and expression of measurement uncertainty. A supplementary downloadable program allows the readers to interact with the proposed approach by generating and combining RFVs through custom measurement functions. With numerous examples of applications, this book provides a comprehensive treatment of the RFV approach to uncertainty that is suitable for any graduate student or researcher with interests in the measurement field." -- Prové de l'editor