Measuring Uncertainty within the Theory of Evidence

Covering the developments of the Random Fuzzy Variable (RFV) approach to uncertainty, this monograph provides a more robust mathematical and metrological background to the combination of measurement results when they are expressed in terms of RFVs. While previous books derive the rules for the combination of the RFVs through a simplified and intuitive approach, this book derives new rules in a strictly mathematical way, resulting in a more effective RFV combination method. New perspectives to metrology and its practice are introduced, opening the science of measurement to new theories and exciting perspectives of metrologist tasks. Building on Simona Salicone's book Measurement Uncertainty: An Approach via the Mathematical Theory of Evidence , this book deals with the theory of evidence and measurement uncertainty through new topics and a new proposed approach. Two parts of the book offer a background of the theory of measurements and the uncertainty measurement as well as an in-depth discussion on the theory of fuzzy sets. The book's concluding section shows how the theory of measurements can be mathematically framed within the theory of evidence and how the possibility distributions can be suitably used to represent measurement results. With numerous examples and a supplementary downloadable program that adds to the text, this book provides a comprehensive treatment of the material perfect for any graduate student or researcher interested in the field.