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.
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References
Jamison, K.D., Lodwick, W.A.: The Construction of Consistent Possibility and Necessity Measures. Fuzzy Sets and Systems 132, 1–10 (2002)
Jamison, K.D., Lodwick, W.A.: Interval-valued probability in the analysis of problems that contain a mixture of fuzzy, possibilistic and interval uncertainty. Submitted to International Journal of Approximate Reasoning (2006)
Kolmogorov, A.N.: Confidence limits for an unknown distribution function. Annuals of Mathematics Statistics 12, 461–463 (1941)
Kolmogorov, A.N., Fomin, S.V.: Introductory Real Analysis. Dover Publications, Inc., New York (1975)
Lodwick, W.A., Jamison, K.D.: Estimating and Validating the Cumulative Distribution of a Function of Random Variables: Toward the Development of Distribution Arithmetic. Reliable Computing 9, 127–141 (2003)
Lodwick, W.A., Jamison, K.D.: Interval-valued probability in the analysis of problems that contain a mixture of fuzzy, possibilistic and interval uncertainty (paper 327137). In: Demirli, K., Akgunduz, A. (eds.) Conference of the North American Fuzzy Information Processing Society, Montréal, Canada, June 3-6 (2006)
Moore, R.E.: Methods and Applications of Interval Analysis. SIAM, Philadelphia (1979)
Neumaier, A.: Clouds, fuzzy sets and probability intervals. Reliable Computing 10(4), 249–272 (2004)
Neumaier, A.: On the Structure of Clouds. Submitted (2005), downloadable http://www.mat.univie.ac.at/~neum/papers.html
Wang, Z., Klir, G.J.: Fuzzy Measure Theory. Plenum Press, New York (1992)
Weichselberger, K.: The theory of interval-probability as a unifying concept for uncertainty. International Journal of Approximate Reasoning 24, 149–170 (2000)
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Lodwick, W.A., Jamison, K.D. (2007). The Use of Interval-Valued Probability Measures in Optimization Under Uncertainty for Problems Containing a Mixture of Fuzzy, Possibilisitic, and Interval Uncertainty. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds) Foundations of Fuzzy Logic and Soft Computing. IFSA 2007. Lecture Notes in Computer Science(), vol 4529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72950-1_36
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DOI: https://doi.org/10.1007/978-3-540-72950-1_36
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