Fuzzy Optimization Problems with Critical Value-at-Risk Criteria

Authors:
Yan-Kui Liu;Zhi-Qiang Liu;Ying Liu
Affiliations:
College of Mathematics & Computer Science, Hebei University, Baoding 071002, Hebei, China and School of Creative Media, City University of Hong Kong, Hong Kong, China;School of Creative Media, City University of Hong Kong, Hong Kong, China;College of Mathematics & Computer Science, Hebei University, Baoding 071002, Hebei, China
Venue:
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Part II--Advances in Neural Networks
Year:
2007

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Abstract

Based on value-at-risk (VaR) criteria, this paper presents a new class of two-stage fuzzy programming models. Because the fuzzy optimization problems often include fuzzy variables defined through continuous possibility distribution functions, they are inherently infinite- dimensional optimization problems that can rarely be solved directly. Thus, algorithms to solve such optimization problems must rely on intelligent computing as well as approximating schemes, which result in approximating finite-dimensional optimization problems. Motivated by this fact, we suggest an approximation method to evaluate critical VaR objective functions, and discuss the convergence of the approximation approach. Furthermore, we design a hybrid algorithm (HA) based on the approximation method, neural network (NN) and genetic algorithm (GA) to solve the proposed optimization problem, and provide a numerical example to test the effectiveness of the HA.