Introduction: Toward an Alternative Representation of the Measurement Results

Abstract

In the previous parts of the book, different matters are considered. In Part I, the concept of measurement uncertainty is introduced and discussed. Then, different mathematical methods to deal with measurement uncertainty and measurement results are presented, and a simple preliminary example to compare these methods is given. In Part II, the mathematical Theory of Evidence is in depth presented. In particular the possibility distribution functions are defined, as well as all operators to combine PDs, compare PDs, and build a joint PD. In Part III, the fuzzy set theory is briefly recalled. In particular, the fuzzy numbers and fuzzy numbers of type 2 are defined, as well as their membership functions and α-cuts. Then, it is shown how the membership function of a fuzzy number and the membership functions of some subclasses of the fuzzy numbers of type 2, included the RFVs , are possibility distribution functions.