The Application of Fuzzy Random Theory in Facility Location Problem 

Author  DaiXiaoDong 
Tutor  LiuYanKui 
School  Hebei University 
Course  Applied Mathematics 
Keywords  Mean chance theory Fuzzy random programming Approximation method Facility Location Problem PSO algorithm 
CLC  O211.6 
Type  Master's thesis 
Year  2009 
Downloads  33 
Quotes  0 
First, this thesis discusses the models of convergence concepts for sequences of random fuzzy variables in random fuzzy theory, and deals with the interconnections among convergence almost uniform, convergence almost sure, and convergence in chance. In the establishment of mathematical model, this thesis buids a class of twostage fuzzy random minimum risk problem (FRMRP), proposes an approximation method to the FRMRP, and deals with the convergence of the approximation method about the objective function. In the model application, this thesis applies the FRMRP to the facility location problem, and design a hybrid particle swarm optimizer (PSO) algorithm based on the approximation method to solve the fuzzy random facility location problem.The major work of this thesis include the following three aspects:(1)The modes of convergence for sequence of random fuzzy variables are defined, including uniform convergence, convergence almost uniform, convergence almost sure, convergence in chance, and convergence in distribution. The relations among the convergences are also discussed;(2)We build a class of twostage FRMRP with mean chance objective function, give its approximation method, and discuss the convergence of the approximation method about the objective function;(3)We apply the twostage fuzzy random minimum risk problem to the facility location problem, and design a hybrid PSO algorithm based on approximation to solve it. One numerical example is also presented to show the effectiveness of designed algorithm.