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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
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Abstract


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 two-stage fuzzy random minimum risk problem (FRMRP), proposes an approxima-tion 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 two-stage 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 two-stage fuzzy random minimum risk problem to the facil-ity 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.

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Theory of probability ( probability theory, probability theory ) > Random process
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