On the specificity of a possibility distribution
Fuzzy Sets and Systems
Information Sciences: an International Journal
On fuzzy-set interpretation of possibility theory
Fuzzy Sets and Systems
Swarm intelligence
Theory and Practice of Uncertain Programming
Theory and Practice of Uncertain Programming
Fuzzy Mathematical Programming: Methods and Applications
Fuzzy Mathematical Programming: Methods and Applications
Fuzzy programming with recourse
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Measurability criteria for fuzzy random vectors
Fuzzy Optimization and Decision Making
A survey of credibility theory
Fuzzy Optimization and Decision Making
An effective co-evolutionary particle swarm optimization for constrained engineering design problems
Engineering Applications of Artificial Intelligence
The expected value of a function of a fuzzy variable with a continuous membership function
Computers & Mathematics with Applications
Risk curve and fuzzy portfolio selection
Computers & Mathematics with Applications
Fuzzy multilevel programming with a hybrid intelligent algorithm
Computers & Mathematics with Applications
An application of swarm optimization to nonlinear programming
Computers & Mathematics with Applications
Expected value of fuzzy variable and fuzzy expected value models
IEEE Transactions on Fuzzy Systems
Convergent results about the use of fuzzy simulation in fuzzy optimization problems
IEEE Transactions on Fuzzy Systems
Two-stage location-allocation problem with credibility objective
FSKD'09 Proceedings of the 6th international conference on Fuzzy systems and knowledge discovery - Volume 4
Hybrid pattern search and simulated annealing for fuzzy production planning problems
Computers & Mathematics with Applications
Optimizing single-source capacitated FLP in fuzzy decision systems
ICSI'11 Proceedings of the Second international conference on Advances in swarm intelligence - Volume Part I
Survey: Facility location dynamics: An overview of classifications and applications
Computers and Industrial Engineering
On the correlations between fuzzy variables
ICSI'10 Proceedings of the First international conference on Advances in Swarm Intelligence - Volume Part II
A class of fuzzy portfolio optimization problems: E-S models
ICSI'10 Proceedings of the First international conference on Advances in Swarm Intelligence - Volume Part II
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This paper presents a class of two-stage fuzzy programming with minimum-risk criteria in the sense of Value-at-Risk (VaR). Since the proposed two-stage fuzzy minimum-risk problem (FMRP) often includes fuzzy variable coefficients defined through possibility distributions with infinite supports, it is inherently an infinite-dimensional optimization problem that can rarely be solved directly. Thus, algorithm procedures for solving such an optimization problem must rely on soft computing and approximation schemes, which result in a finite-dimensional optimization problem. In this paper, we develop an approximation method to compute the objective function of the two-stage FMRP, and discuss the convergent results about the use of the approximation method in FMRP, including the convergence of the objective value, optimal value, and the optimal solutions. To apply the convergent results about the approximation method, we consider a two-stage fuzzy facility location-allocation (FLA) problem with VaR objective, and solve the problem indirectly by solving its approximating problem. Since the approximating fuzzy FLA problem is neither linear nor convex, conventional optimization algorithms cannot be used to solve it. In this paper, we design a hybrid particle swarm optimization (PSO) algorithm to solve the approximating fuzzy FLA problem. One numerical example with five facilities and ten customers is also presented to demonstrate the effectiveness of the designed algorithm.