G. Shafer [A mathematical theory of evidence. Princeton Univ. Press (1976; Zbl 0359.62002)] elaborated the mathematical theory of evidence . The book under review is the first to make full use of this theory to express the uncertainty in measurements. The text presents various tools for evaluating uncertainty, beginning with the probabilistic approach and concluding with an expression of uncertainty using random-fuzzy variables (RFVs). The last chapter deals with decision-making rules for the comparison of two RFVs. Several methods available in the literature are presented and discussed, and then a new method is proposed which is quantifying the grade of belief associated with the selected statements.
The exposition is driven by numerous examples. The book is designed for immediate use and applications in research and laboratory work in various fields, including applied probability, electrical and computer engineering, and experimental physics. Prerequisites for students include courses in statistics and measurement science.
Contents: Chap. 1. Uncertainty in measurement; Chap. 2. Fuzzy variables and measurement uncertainty; Chap. 3. The theory of evidence; Chap. 4. Random-fuzzy variables; Chap. 5. Construction of random fuzzy variables; Chap. 6. Fuzzy operators; Chap. 7. The mathematics of random fuzzy variables; Chap. 8. Representation of random-fuzzy variables; Chap. 9. Decision-making rules with random-fuzzy variables.