Li S., Wang X., Okazaki Y., Kawabe J., Murofushi T., Guan L. (eds.) Nonlinear Mathematics for Uncertainty and its Applications

Berlin: Springer, 2011. — 707 p.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.Ordinal Preference Models Based on S-Integrals and Their Verification
Strong Laws of Large Numbers for Bernoulli Experiments under Ambiguity
Comparative Risk Aversion for g -Expected Utility Maximizers
Riesz Type Integral Representations for Comonotonically Additive Functionals
Pseudo-concave Integrals
On Spaces of Bochner and Pettis Integrable Functions and Their Set-Valued Counterparts
Upper Derivatives of Set Functions Represented as the Choquet Indefinite Integral
On Regularity for Non-additive Measure
Autocontinuity from below of Set Functions and Convergence in Measure
On Lusin’s Theorem for Non-additive Measure
Multiple-Output Choquet Integral Models and Their Applications in Classification Methods
On Convergence Theorems of Set-Valued Choquet Integrals
On Nonlinear Correlation of Random Elements
On Fuzzy Stochastic Integral Equations—A Martingale Problem Approach
Set-Valued Stochastic Integrals with Respect to Poisson Processes in a Banach Space
The Convergence Theorems of Set-Valued Pramart in a Banach Space
Fuzzy Stochastic Integral Equations Driven by Martingales
Moderate Deviations of Random Sets and Random Upper Semicontinuous Functions
Solution of Random Fuzzy Differential Equation
Completely Monotone Outer Approximations of Lower Probabilities on Finite Possibility Spaces
Belief Networks and Local Computations
Some New Entropies on the Interval-Valued Fuzzy Set
Bottleneck Combinatorial Optimization Problems with Fuzzy Scenarios
About the Probability-Field-Intersections of Weichselberger and a Simple Conclusion from Least Favorable Pairs
Using Imprecise and Uncertain Information to Enhance the Diagnosis of a Railway Device
Pricing CDS with Jump-Diffusion Risk in the Intensity-Based Model
Pricing Convertible Bonds Using the CGMY Model
The Dividend Problems for Compound Binomial Model with Stochastic Return on Investments
Pricing Formulas of Compound Options under the Fractional Brownian Motion
Influence of Risk Incentive by Limited Dividend Provision
An Application of the Forward Integral to an Insider’s Optimal Portfolio with the Dividend
The Nonlinear Terminal-Boundary Problems for Barrier Options
European Option Pricing with Ambiguous Return Rate and Volatility
Knightian Uncertainty Based Option Pricing with Jump Volatility
Conditional Ruin Probability with a Markov Regime Switching Model
A Property of Two-Parameter Generalized Transition Function
The Extinction of a Branching Process in a Varying or Random Environment
Metric Adjusted Skew Information and Metric Adjusted Correlation Measure
Integral-Based Modifications of OWA-Operators
Fuzzy Similarity Measure Model for Trees with Duplicated Attributes
Linking Developmental Propensity Score to Fuzzy Sets: A New Perspective, Applications and Generalizations
Chaos in a Fractional-Order Dynamical Model of Love and Its Control
The Semantics of wlp and slp of Fuzzy Imperative Programming Languages
Public-Key Cryptosystem Based on n -th Residuosity of n = p 2 q
Shrinking Projection Method for a Family of Quasinonexpansive Mappings with a Sequence of Subsets of an Index Set
Note on Generalized Convex Spaces
Halpern’s Iteration for a Sequence of Quasinonexpansive Type Mappings
Convergence of Iterative Methods for an Infinite Family of Pseudo-contractions
Existence of Fixed Points of Nonspreading Mappings with Bregman Distances
The ( h , ϕ )–Generalized Second-Order Directional Derivative in Banach Space
Estimation of Bessel Operator Inversion by Shearlet
Globally Convergent Inexact Smoothing Newton Method for SOCCP
Existence of Positive Solution for the Cauchy Problem for an Ordinary Differential Equation
Stability of a Two Epidemics Model
The Impulsive Synchronization for m-Dimensional Reaction-Diffusion System
A New Numerical Method for Solving Convection-Diffusion Equations
Pullback Attractor for Non-autonomous P-Laplacian Equation in Unbounded Domain
Monte-Carlo Simulation of Error Sort Model
A Fuzzy Estimation of Fuzzy Parameters with Rational Number Cuts
Regularized REML for Estimation in Heteroscedastic Regression Models
Testing of Relative Difference under Inverse Sampling
Adaptive Elastic-Net for General Single-Index Regression Models
Some Remark about Consistency Problem of Parameter Estimation
Variable Selection for Semiparametric Isotonic Regression Models
Study of Prognostic Factor Based on Factor Analysis and Clustering Method
Applying Factor Analysis to Water Quality Assessment: A Study Case of Wenyu River
On the Profit Manipulations of Chinese Listed Companies
Fuzzy Portfolio Optimization Model with Fuzzy Numbers
Soft Computing Techniques and Its Application in the Intelligent Capital Compensation
Geometric Weighting Method and Its Application on Load Dispatch in Electric Power Market
Application of Cross-Correlation in Velocity Measurement of Rainwater in Pipe
A Decision-Making Model of Adopting New Technology by Enterprises in Industrial Clusters under the Condition of Interaction
Study of Newsboy Problem with Fuzzy Probability Distribution
Blogger’s Interest Mining Based on Chinese Text Classification
Characterization of Generalized Necessity Functions in Łukasiewicz Logic
On Generating Functions of Two-Dimensional T-Norms
Approximating a Fuzzy Vector Given Its Finite Set of Alpha-Cuts
A New Fuzzy Linear Programming Model and Its Applications
Interval Relaxation Method for Linear Complementarity Problem
The Representation Theorem on the Category of FTML( $\mathcal{L}$ )
L -Fuzzy Subalgebras and L -Fuzzy Filters of R 0 -Algebras
Completely Compact Elements and Atoms of Rough Sets.
Weak Approximable Concepts and Completely Algebraic Lattices
Ideal-Convergence in Quantales
On the Factorization Theorem of a Monotone Morphism in a Topos
Error Report