Abstract
This article proposes a new formal definition of an interval valued probability measure (IVPM) based on a measure theoretic foundation, and shows that various uncertainties that occur in data associated in mathematical analyses, for example, in optimization under uncertainty models, can be unified and formulated within this one common IVPM framework facilitating the solution of many mathematical problems. This article develops a theory, we call generalized uncertainty theory, that will be characterized by the generation of upper and lower bounding functions enclosing all distributions that are possible from the given partial information.
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