## Ciclo de Seminários de Sistemas Dinâmicos

**Palestrante:** Professor Weldon A. Lodwick, University of Colorado at Denver

**Título:** Interval-Valued Probability Measures: A Formal Method for Consolidating the Languages of Information: Deficinecy - Foundations

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This presentation proposes a new formal definition of an interval valued

probability measure (IVPM) [8], based on a measure theoretic foundation,

and shows that various theories of generalized uncertainty that occur in

the data associated in mathematical analyses, in particular optimization

models, can be formulated in this one common framework. Many

problems of applied mathematics are inherently uncertain and one of the

most common forms of uncertainty is lack of or partial information. Our

method of analyzing uncertainty from the basis of measure theory, allows

problems with many different types of uncertainty to be solved within one

theory of uncertainty and we are able to construct bounds from

uncertainty information. Uncertainty as developed herein is distinct from

fuzzy set theory. This presentation centers on the creation of a theory

associated with what we call generalized uncertainty that is tied to the

generation of upper and lower bounding functions.

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