Representations of Uncertainty in Artificial Intelligence: Probability and Possibility

Abstract

Due to its major focus on knowledge representation and reasoning, artificial intelligence was bound to deal with various frameworks for the handling of uncertainty: probability theory, but more recent approaches as well: possibility theory, evidence theory, and imprecise probabilities. The aim of this chapter is to provide an introductive survey that lays bare specific features of two basic frameworks for representing uncertainty: probability theory and possibility theory, while highlighting the main issues that the task of representing uncertainty is faced with. This purpose also provides the opportunity to position related topics, such as rough sets and fuzzy sets, respectively motivated by the need to account for the granularity of representations as induced by the choice of a language, and the gradual nature of natural language predicates. Moreover, this overview includes concise presentations of yet other theoretical representation frameworks such as formal concept analysis, conditional events and ranking functions, and also possibilistic logic, in connection with the uncertainty frameworks addressed here. The next chapter in this volume is devoted to more complex frameworks: belief functions and imprecise probabilities.

Imprecise Data and Their Impact on Translational Research in Medicine

“…CDSS suggest to algorithmically treat problems characterized by high levels of imprecision, and this may indicate a potential role for soft computing and fuzzy logic methods, which may solve complexities too difficult to model at the mathematical level by leveraging the uncertainty [ (14,15) among other authors] and approximation [see the seminal work of (16)]. These methods can also be combined with probabilistic reasoning thus forming a relevant base for the field of approximate reasoning as a strategy to manage the imprecision of knowledge in inference tasks [see for instance (17)].…”

A new evidential K-nearest neighbor rule based on contextual discounting with partially supervised learning

“…In the general partially supervised case, the discounting operation (23) can be replaced by contextual discounting. Using (10), the evidence from the j-th neighbor with label m j and situated at distance d j then becomes…”

“…The evidential K-nearest neighbor (EKNN) classifier [6] is a distance-based classification algorithm based on the Dempster-Shafer (DS) theory of evidence [5,30,10]. Since its introduction in 1995, it has been used extensively (see, e.g., [3], [15], [31], [37]) and several variants have been developed [1], [18], [17], [20], [21], [22], [26], [36], [38].…”

Evidence-based recommender system and experimental validation for high-entropy alloys

“…Subsequently, we use the evidence theory [16][17][18][19][20] to model and combine evidence on the similarity between the intended element combinations. The combined similarity evidence is then used to generate evidence for hypothesizing whether the substituted alloys are HEAs.…”