Summary |
This volume is a collection of papers presented at the international conference on Nonlinear Mathematics for Uncertainty and Its Applications (NL-MUA2011), held at Beijing University of Technology during the week of September 7-9,2011.
Over the last fifty years there have been many attempts in extending the theory of classical probability and statistical models to the generalized one which can cope with problems of inference and decision making when the model-related information is scarce, vague, ambiguous, or incomplete. Such attempts include the study of nonadditive measures and their integrals, imprecise probabilities and random sets, and their applications in information sciences, economics, finance, insurance, engineering and social sciences.
Possibility measures, belief functions, Choquet capacities, and fuzzy measures are all nonadditive measures, and their related integrals are nonlinear. Imprecise probability allows us to measure chance and uncertainty with a family of classical probability measures. Their lower and upper expectations or previsions are nonlinear again. Theory of random sets and related subjects extend the horizon of classical probability and statistics to set-valued and fuzzy set-valued cases.
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