ABSTRACT
Data and information collected about a system require synthesis for the purpose of achieving an analytical goal or a mission. Engineers and scientists are always interested in understanding and predicting system behavior (or performance) for the purpose of making appropriate decisions. The behavior or performance of the system can only be assessed according to available information, thereby involving some uncertainty, and to the best of their knowledge, that involves some aspects of ignorance. This synthesis requires the employment of fundamental measures to assess these uncertainties and ignorance types. Various measures, including probability measures as special and commonly used measures, are introduced in this chapter, building on data-encoding and information expression methods, i.e., formalized languages, presented in Chapter 2. The identification (or selection) of appropriate measures for uncertainty-based synthesis of information requires the definition of an analytical goal that can be used as a basis for recognizing ignorance types most relevant to the system under consideration, developing universal spaces and appropriate structures, and selecting and using appropriate measures.
