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This volume is a collection of papers presented at the
international conference on Nonlinear Mathematics for Uncertainty
and Its Applications (NLMUA2011), held at Beijing University of
Technology during the week of September 7--9, 2011. The conference
brought together leading researchers and practitioners involved
with all aspects of nonlinear mathematics for uncertainty and its
applications. 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. The book presents
topics including nonadditive measures and nonlinear integrals,
Choquet, Sugeno and other types of integrals, possibility theory,
Dempster-Shafer theory, random sets, fuzzy random sets and related
statistics, set-valued and fuzzy stochastic processes, imprecise
probability theory and related statistical models, fuzzy
mathematics, nonlinear functional analysis, information theory,
mathematical finance and risk managements, decision making under
various types of uncertainty, and others.
This volume is a collection of papers presented at the
international conference on Nonlinear Mathematics for Uncertainty
and Its Applications (NLMUA2011), held at Beijing University of
Technology during the week of September 7--9, 2011. The conference
brought together leading researchers and practitioners involved
with all aspects of nonlinear mathematics for uncertainty and its
applications. 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. The book presents
topics including nonadditive measures and nonlinear integrals,
Choquet, Sugeno and other types of integrals, possibility theory,
Dempster-Shafer theory, random sets, fuzzy random sets and related
statistics, set-valued and fuzzy stochastic processes, imprecise
probability theory and related statistical models, fuzzy
mathematics, nonlinear functional analysis, information theory,
mathematical finance and risk managements, decision making under
various types of uncertainty, and others.
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