University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
4
2011
10
29
Cover Special Issue vol. 8, no. 4, October 2011
0
EN
10.22111/ijfs.2011.2868
http://ijfs.usb.ac.ir/article_2868.html
http://ijfs.usb.ac.ir/article_2868_3f83c7d9389a4164783e5336fe598543.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
4
2011
10
06
SOME PROPERTIES FOR FUZZY CHANCE CONSTRAINED
PROGRAMMING
1
8
EN
Xiaohu
Yang
Department of Statistics, Xi'an University of Finance and Economics,
Xi'an 710061, China
yxh12@163.com
10.22111/ijfs.2011.305
Convexity theory and duality theory are important issues in math-
ematical programming. Within the framework of credibility theory, this paper
rst introduces the concept of convex fuzzy variables and some basic criteria.
Furthermore, a convexity theorem for fuzzy chance constrained programming
is proved by adding some convexity conditions on the objective and constraint
functions. Finally, a duality theorem for fuzzy linear chance constrained pro-
gramming is proved.
Convexity theorem,Duality theorem,Fuzzy variable,Chance con-
strained programming
http://ijfs.usb.ac.ir/article_305.html
http://ijfs.usb.ac.ir/article_305_6fb6b2d1b824c72a0c944ba1a2867828.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
4
2011
10
07
ALGORITHMS FOR BIOBJECTIVE SHORTEST PATH
PROBLEMS IN FUZZY NETWORKS
9
37
EN
Iraj
Mahdavi
Department of Industrial Engineering, Mazandaran University of Sci-
ence & Technology, Babol, Iran
irajarash@rediffmail.com
Nezam
Mahdavi-Amiri
Faculty of Mathematical Sciences, Sharif University of Tech-
nology, Tehran, Iran
nezamm@sharif.edu
Shahrbanoo
Nejati
Department of Industrial Engineering, Mazandaran University
of Science & Technology, Babol, Iran
nejati sh@yahoo.com
10.22111/ijfs.2011.306
We consider biobjective shortest path problems in networks with
fuzzy arc lengths. Considering the available studies for single objective shortest
path problems in fuzzy networks, using a distance function for comparison of
fuzzy numbers, we propose three approaches for solving the biobjective prob-
lems. The rst and second approaches are extensions of the labeling method to
solve the single objective problem and the third approach is based on dynamic
programming. The labeling methods usually producing several nondominated
paths, we propose a fuzzy number ranking method to determine a fuzzy short-
est path. Illustrative examples are worked out to show the eectiveness of our
algorithms.
Biobjective shortest path,Fuzzy network,Labeling method,Dynamic
programming,Fuzzy ranking methods
http://ijfs.usb.ac.ir/article_306.html
http://ijfs.usb.ac.ir/article_306_645249d97ea17b67c4eb5772a11928ac.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
4
2011
10
07
A FUZZY MINIMUM RISK MODEL FOR THE RAILWAY
TRANSPORTATION PLANNING PROBLEM
39
60
EN
Lixing
Yang
State Key Laboratory of Rail Traffic Control and Safety, Beijing
Jiaotong University, Beijing 100044, China
lxyang@bjtu.edu.cn
Xiang
Li
State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong
University, Beijing 100044, China
xiang-li04@tsinghua.edu.cn
Ziyou
Gao
State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong
University, Beijing 100044, China
gaoziyou@jtys.bjtu.edu.cn
Keping
Li
State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong
University, Beijing 100044, China
likeping@jtys.bjtu.edu.cn
10.22111/ijfs.2011.307
The railway transportation planning under the fuzzy environment
is investigated in this paper. As a main result, a new modeling method, called
minimum risk chance-constrained model, is presented based on the credibility
measure. For the convenience ofs olving the mathematical model, the crisp
equivalents ofc hance functions are analyzed under the condition that the
involved fuzzy parameters are trapezoidal fuzzy variables. An approximate
model is also constructed for the problem based on an improved discretization
method for fuzzy variables and the relevant convergence theorems. To
obtain an approximate solution, a tabu search algorithm is designed for the
presented model. Finally, some numerical experiments are performed to show
the applications ofthe model and the algorithm.
Minimum risk model,Railway transportation planning,Credibility
measure,Discretization method
http://ijfs.usb.ac.ir/article_307.html
http://ijfs.usb.ac.ir/article_307_3d5c42e3f0fbf960235d85616888b3fc.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
4
2011
10
07
MEAN-ABSOLUTE DEVIATION PORTFOLIO SELECTION
MODEL WITH FUZZY RETURNS
61
75
EN
Zhongfeng
Qin
School of Economics and Management, Beihang University, Beijing
100191, China
qin@buaa.edu.cn, qzf05@mails.thu.edu.cn
Meilin
Wen
School of Reliability and Systems Engineering, Beihang University,
Beijing 100191, China
wenmeilin@buaa.edu.cn
Changchao
Gu
Sinopec Management Institute, Beijing 100012, China
guchangchao@gamil.com
10.22111/ijfs.2011.308
In this paper, we consider portfolio selection problem in which
security returns are regarded as fuzzy variables rather than random variables.
We first introduce a concept of absolute deviation for fuzzy variables and
prove some useful properties, which imply that absolute deviation may be
used to measure risk well. Then we propose two mean-absolute deviation
models by defining risk as absolute deviation to search for optimal portfolios.
Furthermore, we design a hybrid intelligent algorithm by integrating genetic
algorithm and fuzzy simulation to solve the proposed models. Finally, we
illustrate this approach with two numerical examples.
Uncertainty modelling,Fuzzy variable,Fuzzy portfolio selection,Credibility theory,Hybrid intelligent algorithm
http://ijfs.usb.ac.ir/article_308.html
http://ijfs.usb.ac.ir/article_308_3b4ec0110e6e5007d107918ec346e5a6.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
4
2011
10
07
FUZZY TRAIN ENERGY CONSUMPTION MINIMIZATION
MODEL AND ALGORITHM
77
91
EN
Xiang
Li
State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiao-
tong University, Beijing 100044, China
xiang-li04@mail.tsinghua.edu.cn
Dan
Ralescu
Department of Mathematical Sciences, University of Cincinnati, Cincin-
nati, Ohio 45221, USA
ralescd@uc.edu
Tao
Tang
State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiao-
tong University, Beijing 100044, China
ttang@bjtu.edu.cn
10.22111/ijfs.2011.309
Train energy saving problem investigates how to control train's
velocity such that the quantity of energy consumption is minimized and some
system constraints are satis ed. On the assumption that the train's weights
on different links are estimated by fuzzy variables when making the train
scheduling strategy, we study the fuzzy train energy saving problem. First, we
propose a fuzzy energy consumption minimization model, which minimizes the
average value and entropy of the fuzzy energy consumption under the maximal
allowable velocity constraint and traversing time constraint. Furthermore, we
analyze the properties of the optimal solution, and then design an iterative
algorithm based on the Karush-Kuhn-Tucker conditions. Finally, we illustrate
a numerical example to show the effectiveness of the proposed model and
algorithm.
Energy consumption,Train scheduling,Karush-Kuhn-Tucker condi-
tions,Fuzzy variable
http://ijfs.usb.ac.ir/article_309.html
http://ijfs.usb.ac.ir/article_309_b33ac36fdf8e3fc3c689b9438a056dfa.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
4
2011
10
07
FLUENCE MAP OPTIMIZATION IN INTENSITY MODULATED
RADIATION THERAPY FOR FUZZY TARGET DOSE
93
105
EN
Alireza
Fakharzadeh Jahromi
Shiraz University of Technology, Shiraz, Fars, Iran
a_ fakharzadeh@sutech.ac.ir
Omolbanin
Bozorg
Shiraz University of Technology, Shiraz, Fars, Iran
o.bozorg@gmail.com
Hamidreza
Maleki
Shiraz University of Technology, Shiraz, Fars, Iran
maleki@sutech.ac.ir
Mohamad Amin
Mosleh-Shirazi
Shiraz University of Medical Sciences, Shiraz, Fars,
mosleh_amin@hotmail.com
10.22111/ijfs.2011.310
Although many methods exist for intensity modulated radiotherapy (IMRT) fluence map optimization for crisp data, based on clinical practice, some of the involved parameters are fuzzy. In this paper, the best fluence maps for an IMRT procedure were identifed as a solution of an optimization problem with a quadratic objective function, where the prescribed target dose vector was fuzzy. First, a defuzzyingprocedure was introduced to change the fuzzy model of the problem into an equivalent non-fuzzy one. Since the solution set was nonconvex, the optimal solution was then obtained by performing a projection operation in applying the gradient method. Numerical simulations for two typical clinical cases (for prostate and head-and-neck cancers, each for two patients) are given.
IMRT,Singed distance,Triangular fuzzy number,Gradient method
http://ijfs.usb.ac.ir/article_310.html
http://ijfs.usb.ac.ir/article_310_624d131dd630762401d6a0a4997854fa.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
4
2011
10
07
COALITIONAL GAME WITH FUZZY PAYOFFS AND
CREDIBILISTIC SHAPLEY VALUE
107
117
EN
Jinwu
Gao
Uncertain Systems Lab, School of Information, Renmin University of
China, Beijing 100872, China
jgao@ruc.edu.cn
Q.
Zhang
Uncertain Systems Lab, School of Information, Renmin University of
China, Beijing 100872, China
zqw2002@163.com
P.
Shen
Uncertain Systems Lab, School of Information, Renmin University of China,
Beijing 100872, China
shenpuchen@163.com
10.22111/ijfs.2011.311
Coalitional game deals with situations that involve cooperations among players, and there are different solution concepts such as the core,the Shapley value and the kernel. In many situations, there is no way to predict the payoff functions except for the expert experiencesand subjective intuitions, which leads to the coalitional game with fuzzy payoffs. Within the framework of credibility theory, this paper employstwo credibilistic approaches to define the behaviors of players under fuzzy situations. Correspondingly, two variations of Shapley value areproposed as the solutions of the coalitional game with fuzzy payoffs. Meanwhile, some characterizations of the credibilistic Shapley valueare investigated. Finally, an example is provided for illustrating the usefulness of the theory developed in this paper.
Coalitional game,Shapley value,Fuzzy variable,Credibility measure
http://ijfs.usb.ac.ir/article_311.html
http://ijfs.usb.ac.ir/article_311_ec8eadf2c503f1494486ac8555956b9a.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
4
2011
10
29
Persian-translation vol. 8, no. 4, October 2011
121
127
EN
10.22111/ijfs.2011.2869
http://ijfs.usb.ac.ir/article_2869.html
http://ijfs.usb.ac.ir/article_2869_0ffa9f8030e868147b8d43909fd9e0de.pdf