The Use of Interval-Valued Probability Measures in Optimization Under Uncertainty for Problems Containing a Mixture of Fuzzy, Possibilisitic, and Interval Uncertainty

Authors:
Weldon A. Lodwick;K. David Jamison
Affiliations:
Department of Mathematics, University of Colorado at Denver,;Department of Mathematics, University of Colorado at Denver,
Venue:
IFSA '07 Proceedings of the 12th international Fuzzy Systems Association world congress on Foundations of Fuzzy Logic and Soft Computing
Year:
2007

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Abstract

A simple definition of interval-valued probability measure is given and its implications examined. Properties are discussed which allow for the analysis of mixtures of fuzzy, possibilistic, probabilistic, cloud, and interval uncertainty utilizing interval-valued probability theory. It is shown how these properties allow for optimization under uncertainty where the uncertainty is mixed (fuzzy, possibilitic, probabilistic, clouds, and interval ). An example of this type of optimization is given illustrating the usefulness and power of the concepts.