On Modeling of Uncertainty Measures and Observed Processes

This paper is about a short survey of some basic uncertainty measures in systems analysis arising from coarse data, together with new modeling results on upper semicontinuous random processes, viewed as random fuzzy sets. Specifically, we present the most general mathematical framework for analyzing coarse data, such as random fuzzy data, which arise often in information systems. Our approach is based upon the theory of continuous lattices. This probabilistic analysis is also useful for investigating upper semicontinuous random functions in stochastic optimization problems.

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