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Nonlinear Mathematics for Uncertainty and its Applications

  • Conference proceedings
  • © 2011

Overview

Editors:
  1. Shoumei Li

    1. College of Applied Sciences, Beijing University of Technology, Chaoyang District, P.R. China

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  2. Xia Wang

    1. College of Applied Sciences, Beijing University of Technology, Chaoyang District, P.R. China

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  3. Yoshiaki Okazaki

    1. Department of Systems Design and Informatics, Kyushu Institute of Technology, lizuka, Japan

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  4. Jun Kawabe

    1. Department of Mathematics, Shinshu University, Nagano, Japan

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  5. Toshiaki Murofushi

    1. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama, Japan

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  6. Li Guan

    1. College of Applied Sciences, Beijing University of Technology, Chaoyang District, P.R. China

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  • Recent research on Nonlinear Mathematics and Uncertainty Scientific outcome of the conference "Non-Linear Mathematics
  • Uncertaity and Applications" held Sep. 7-9, 2011 in Bejing, China
  • Written by leading experts in the field

Part of the book series: Advances in Intelligent and Soft Computing (AINSC, volume 100)

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Table of contents (85 papers)

  1. Front Matter

    Download chapter PDF

  2. Ordinal Preference Models Based on S-Integrals and Their Verification

    • Michio Sugeno
    Pages 1-18

  3. Strong Laws of Large Numbers for Bernoulli Experiments under Ambiguity

    • Zengjing Chen, Panyu Wu
    Pages 19-30

  4. Comparative Risk Aversion for g-Expected Utility Maximizers

    • Guangyan Jia, Jianming Xia
    Pages 31-34

  5. Riesz Type Integral Representations for Comonotonically Additive Functionals

    • Jun Kawabe
    Pages 35-42

  6. Pseudo-concave Integrals

    • Radko Mesiar, Jun Li, Endre Pap
    Pages 43-49

  7. On Spaces of Bochner and Pettis Integrable Functions and Their Set-Valued Counterparts

    • Coenraad C. A. Labuschagne, Valeria Marraffa
    Pages 51-59

  8. Upper Derivatives of Set Functions Represented as the Choquet Indefinite Integral

    • Shinsuke Nakamura, Toshiyuki Takasawa, Toshiaki Murofushi
    Pages 61-68

  9. On Regularity for Non-additive Measure

    • Toshikazu Watanabe, Tamaki Tanaka
    Pages 69-75

  10. Autocontinuity from below of Set Functions and Convergence in Measure

    • Jun Li, Masami Yasuda, Ling Zhou
    Pages 77-83

  11. On Lusin’s Theorem for Non-additive Measure

    • Tamaki Tanaka, Toshikazu Watanabe
    Pages 85-92

  12. Multiple-Output Choquet Integral Models and Their Applications in Classification Methods

    • Eiichiro Takahagi
    Pages 93-100

  13. On Convergence Theorems of Set-Valued Choquet Integrals

    • Hongxia Wang, Shoumei Li
    Pages 101-108

  14. On Nonlinear Correlation of Random Elements

    • Hung T. Nguyen
    Pages 109-115

  15. On Fuzzy Stochastic Integral Equations—A Martingale Problem Approach

    • Mariusz Michta
    Pages 117-124

  16. Set-Valued Stochastic Integrals with Respect to Poisson Processes in a Banach Space

    • Jinping Zhang, Itaru Mitoma
    Pages 125-134

  17. The Convergence Theorems of Set-Valued Pramart in a Banach Space

    • Li Guan, Shoumei Li
    Pages 135-142

  18. Fuzzy Stochastic Integral Equations Driven by Martingales

    • Marek T. Malinowski, Mariusz Michta
    Pages 143-150

  19. Moderate Deviations of Random Sets and Random Upper Semicontinuous Functions

    • Xia Wang
    Pages 151-159

  20. Solution of Random Fuzzy Differential Equation

    • Jungang Li, Jinting Wang
    Pages 161-168
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Keywords

About this book

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.

Editors and Affiliations

  • College of Applied Sciences, Beijing University of Technology, Chaoyang District, P.R. China

    Shoumei Li, Xia Wang, Li Guan

  • Department of Systems Design and Informatics, Kyushu Institute of Technology, lizuka, Japan

    Yoshiaki Okazaki

  • Department of Mathematics, Shinshu University, Nagano, Japan

    Jun Kawabe

  • Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama, Japan

    Toshiaki Murofushi

Bibliographic Information

  • Book Title: Nonlinear Mathematics for Uncertainty and its Applications

  • Editors: Shoumei Li, Xia Wang, Yoshiaki Okazaki, Jun Kawabe, Toshiaki Murofushi, Li Guan

  • Series Title: Advances in Intelligent and Soft Computing

  • DOI: https://doi.org/10.1007/978-3-642-22833-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer Berlin Heidelberg 2011

  • Hardcover ISBN: 978-3-642-22832-2Published: 21 July 2011

  • Softcover ISBN: 978-3-662-52038-3Published: 23 August 2016

  • eBook ISBN: 978-3-642-22833-9Published: 21 July 2011

  • Series ISSN: 1867-5662

  • Series E-ISSN: 1867-5670

  • Edition Number: 1

  • Number of Pages: XVII, 709

  • Topics: Computational Intelligence, Artificial Intelligence, Applications of Mathematics

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