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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.

Probabilities --- Uncertainty --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Computer Science --- Mathematical models --- Artificial intelligence. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Engineering. --- Applied mathematics. --- Engineering mathematics. --- Computational intelligence. --- Computational Intelligence. --- Artificial Intelligence (incl. Robotics). --- Applications of Mathematics. --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Engineering --- Engineering analysis --- Mathematical analysis --- Construction --- Industrial arts --- Technology --- Mathematics. --- Artificial Intelligence. --- Math --- Science

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Mathematics --- Engineering sciences. Technology --- Artificial intelligence. Robotics. Simulation. Graphics --- analyse (wiskunde) --- toegepaste wiskunde --- ingenieurswetenschappen --- robots

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This edited volume is the proceedings of the 2006 International Conference on Soft Methods in Probability and Statistics (SMPS 2006) hosted by the Artificial Intelligence Group at the University of Bristol, between 5-7 September 2006. This is the third of a series of biennial conferences organized in 2002 by the Systems Research Institute from the Polish Academy of Sciences in Warsaw, and in 2004 by the Department of Statistics and Operational Research at the University of Oviedo in Spain. These conferences provide a forum for discussion and research into the fusion of soft methods with probability and statistics, with the ultimate goal of integrated uncertainty modelling in complex systems involving human factors. In addition to probabilistic factors such as measurement error and other random effects, the modelling process often requires us to make qualitative and subject judgments that cannot easily be translated into precise probability values. Such judgments give rise to a number of different types of uncertainty including; fuzziness if they are based on linguistic information; epistemic uncertainty when their reliability is in question; ignorance when they are insufficient to identify or restrict key modelling parameters; imprecision when parameters and probability distributions can only be estimated within certain bounds. Statistical theory has not traditionally been concerned with modelling uncertainty arising in this manner but soft methods, a range of powerful techniques developed within AI, attempt to address those problems where the encoding of subjective information is unavoidable. These are mathematically sound uncertainty modelling methodologies which are complementary to conventional statistics and probability theory. Therefore, a more realistic modelling process providing decision makers with an accurate reflection of the true current state of our knowledge (and ignorance) requires an integrated framework incorporating both probability theory, statistics and soft methods. This fusion motivates innovative research at the interface between computer science (AI), mathematics and systems engineering.

Mathematics --- Engineering sciences. Technology --- Artificial intelligence. Robotics. Simulation. Graphics --- analyse (wiskunde) --- toegepaste wiskunde --- ingenieurswetenschappen --- robots