Label Semantics Theory

As we have discussed in Chapter 1, modeling real world problems typically involves processing two distinct types of uncertainty. These are, firstly, uncertainty arising from a lack of knowledge relating to concepts which, in the sense of classical logic, may be well defined and, secondly, uncertainty due to inherent vagueness in concepts themselves. Traditionally, these two types of uncertainties are modeled in terms of probability theory and fuzzy set theory, respectively, though, Zadeh recently pointed out that all the approaches for uncertainty modeling can be unified into a general theory of uncertainty (GTU)^[1]. The first type of uncertainty has been a focus of Bayesian probabilistic models^[2]. The most recent advancement in machine learning has been about using using hierarchical Bayesian generative models to describe data.