It is shown in this paper how the emergence of fuzzy set theory and the theory of monotone
measures considerably expanded the framework for formalizing uncertainty and suggested …

This paper presents a summary of Peter Walley's theory of coherent lower previsions. We
introduce three representations of coherent assessments: coherent lower and upper …

Set functions are mappings that assign to subsets of a universal set a real number and
appear in many fields of mathematics (pure and applied) and computer sciences …

859 theory lies at the crossroads between fuzzy sets, probability, and nonmonotonic
reasoning. Possibility theory is closely related to fuzzy sets if one considers that a possibility …

A classical measure is essentially a set function satisfying nonnegativity and countable
additivity axioms. However, the additivity axiom of classical measure theory has been …

Some information and knowledge are usually represented by human language like “about
100km”,“approximately 39° C”,“roughly 80kg”,“low speed”,“middle age”, and “big size”. How …

Generalized Measure Theory examines the relatively new mathematical area of generalized
measure theory. The exposition unfolds systematically, beginning with preliminaries and …

This presents a range of theories about uncertainty, all of them mathematical and allowing
quantitative treatment. A definition of uncertainty is automatically associated with one of …

Information is precious. It reduces our uncertainty in making decisions. Knowledge about the
outcome of an uncertain event gives the possessor an advantage. It changes the course of …

There has been a long-lasting misunderstanding in the literature of artificial intelligence and
uncertainty modeling, regarding the role of fuzzy set theory and many-valued logics. The …