University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
3
2012
10
01
Cover vol. 9, no. 3, october 2012
0
EN
10.22111/ijfs.2012.2812
http://ijfs.usb.ac.ir/article_2812.html
http://ijfs.usb.ac.ir/article_2812_5daeaa39b78bba330a5cde3cf79a9e4f.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
3
2012
10
02
NEW MODELS AND ALGORITHMS FOR SOLUTIONS OF
SINGLE-SIGNED FULLY FUZZY LR LINEAR SYSTEMS
1
26
EN
R.
Ezzati
Department of Mathematics, Karaj Branch, Islamic Azad University,
31485 - 313, Karaj, Iran
ezati@kiau.ac.ir
S.
Khezerloo
Department of Mathematics, Karaj Branch, Islamic Azad University,
31485 - 313, Karaj, Iran
S khezerloo@yahoo.com
Z.
Valizadeh
Department of Mathematics, Karaj Branch, Islamic Azad University,
31485 - 313, Karaj, Iran
z valizadeh@kiau.ac.ir
N.
Mahdavi-Amiri
Department of Mathematical Sciences, Sharif University of Tech-
nology, 1458 - 889694, Tehran, Iran
nezamm@sina.sharif.edu
10.22111/ijfs.2012.144
We present a model and propose an approach to compute an approximate solution of Fully Fuzzy Linear System $(FFLS)$ of equations in which all the components of the coefficient matrix are either nonnegative or nonpositive. First, in discussing an $FFLS$ with a nonnegative coefficient matrix, we consider an equivalent $FFLS$ by using an appropriate permutation to simplify fuzzy multiplications. To solve the $m times n$ permutated system, we convert it to three $m times n$ real linear systems, one being concerned with the cores and the other two being related to the left and right spreads. To decide whether the core system is consistent or not, we use the modified Huang algorithm of the class of $ABS$ methods.If the core system is inconsistent, an appropriate unconstrained least squares problem is solved for an approximate solution.The sign of each component of the solution is decided by the sign of its core. Also, to know whether the left and right spread systems are consistent or not, we apply the modified Huang algorithm again. Appropriate constrained least squares problems are solved, when the spread systems are inconsistent or do not satisfy fuzziness conditions.Then, we consider the $FFLS$ with a mixed single-signed coefficient matrix, in which each component of the coefficient matrix is either nonnegative or nonpositive. In this case, we break the $m times n$ coefficient matrix up to two $m times n$ matrices, one having only nonnegative and the other having only nonpositive components, such that their sum yields the original coefficient matrix. Using the distributive law, we convert each $m times n$ $FFLS$ into two real linear systems where the first one is related to the cores with size $m times n$ and the other is $2m times 2n$ and is related to the spreads. Here, we also use the modified Huang algorithm to decide whether these systems are consistent or not. If the first system is inconsistent or the second system does not satisfy the fuzziness conditions, we find an approximate solution by solving a respective least squares problem. We summarize the proposed approach by presenting two computational algorithms. Finally, the algorithms are implemented and effectively tested by solving various randomly generated consistent as well as inconsistent numerical test problems.
LR fuzzy numbers,Single-signed fuzzy numbers,Fully fuzzy linear
systems,ABS algorithms,Least squares problems
http://ijfs.usb.ac.ir/article_144.html
http://ijfs.usb.ac.ir/article_144_dc1df75c9b5c022986a4766b037d1797.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
3
2012
10
02
MULTI-OBJECTIVE OPTIMIZATION WITH PREEMPTIVE
PRIORITY SUBJECT TO FUZZY RELATION
EQUATION CONSTRAINTS
27
45
EN
Esmaile
Khorram
Faculty of Mathematics and Computer Science, Amirkabir Uni-
versity of Technology, 424,Hafez Ave.,15914,Tehran, Iran
eskhor@aut.ac.ir
Vahid
Nozari
Faculty of Mathematics and Computer Science, Amirkabir University
of Technology, 424,Hafez Ave.,15914,Tehran, Iran
vahid78mu@gmail.com
10.22111/ijfs.2012.145
This paper studies a new multi-objective fuzzy optimization prob- lem. The objective function of this study has dierent levels. Therefore, a suitable optimized solution for this problem would be an optimized solution with preemptive priority. Since, the feasible domain is non-convex; the tra- ditional methods cannot be applied. We study this problem and determine some special structures related to the feasible domain, and using them some methods are proposed to reduce the size of the problem. Therefore, the prob- lem is being transferred to a similar 0-1 integer programming and it may be solved by a branch and bound algorithm. After this step the problem changes to solve some consecutive optimized problem with linear objective function on discrete region. Finally, we give some examples to clarify the subject.
Fuzzy relation equation,Preemptive priority,Branch & Bound,Multi
objective,Linear objective,Optimal solution,Binding variable
http://ijfs.usb.ac.ir/article_145.html
http://ijfs.usb.ac.ir/article_145_8b38e0f7556e356816be47b4ddb2691a.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
3
2012
10
02
ORDERED IDEAL INTUITIONISTIC FUZZY MODEL
OF FLOOD ALARM
47
60
EN
Sunny Joseph
Kalayathankal
Department of Mathematics, K.E.College, Mannanam,
Kottayam, 686561, Kerala, India
sunnyjose2000@yahoo.com
G.
Suresh Singh
Department of Mathematics, University of Kerala, Trivandrum,
695581, Kerala, India
sureshsinghg@yahoo.co.in
10.22111/ijfs.2012.146
An efficient flood alarm system may significantly improve public safety and mitigate damages caused by inundation. Flood forecasting is undoubtedly a challenging field of operational hydrology and a huge literature has been developed over the years. In this paper, we first define ordered ideal intuitionistic fuzzy sets and establish some results on them. Then, we define similarity measures between ordered ideal intuitionistic fuzzy sets (OIIFS) and apply these similarity measures to five selected sites of Kerala, India to predict potential flood.
rainfall,Ordered intuitionistic fuzzy set,Flood,Simulation
http://ijfs.usb.ac.ir/article_146.html
http://ijfs.usb.ac.ir/article_146_adef22f160e44c2c5fa1d8cb1e5d8d95.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
3
2012
10
02
PRICING STOCKS BY USING FUZZY DIVIDEND
DISCOUNT MODELS
61
78
EN
Huei-Wen
Lin
Department of Finance and Banking, Aletheia University, 32 Chen-Li
Street, 25103, New Taipei City, Taiwan (R.O.C.)
au4345@mail.au.edu.tw
Jing-Shing
Yao
Department of Mathematics, National Taiwan University, No.1, Sec.
4, Roosevelt Rd., Taipei City 106, Taiwan (R.O.C.)
hflu.chibi@msa.hinet.net
10.22111/ijfs.2012.147
Although the classical dividend discount model (DDM) is a wellknown and widely used model in evaluating the intrinsic price of common stock, the practical pattern of dividends, required rate of return or growth rate of dividend do not generally coincide with any of the model’s assumptions. It is just the opportunity to develop a fuzzy logic system that takes these vague parameters into account. This paper extends the classical DDMs to more realistic fuzzy pricing models in which the inherent imprecise information will be fuzzified as triangular fuzzy numbers, and introduces a novel -signed distance method to defuzzify these fuzzy parameters without considering the membership functions. Through the conscientious mathematical derivation, the fuzzy dividend discount models (FDDMs) proposed in this paper can be regarded as one more explicit extension of the classical (crisp) DDMs, so that stockholders can use it to make a specific analysis and insight into the intrinsic value of stock.
Fuzzy set,Pricing stock,Dividend discount model (DDM),$l$-signed
distance method,Uniform convergence
http://ijfs.usb.ac.ir/article_147.html
http://ijfs.usb.ac.ir/article_147_17293b564c0a711cb9fb3ec93bd30be5.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
3
2012
10
02
ROUGH SET OVER DUAL-UNIVERSES IN FUZZY
APPROXIMATION SPACE
79
91
EN
Ruixia
Yan
School of Management, Shanghai University of Engineering Science,
Shanghai 201620, P. R. China and Glorious Sun School of Business Administration,
Donghua Universty, Shanghai 200051, P. R.China
yanruixia@gmail.com
Jianguo
Zheng
Glorious Sun School of Business Administration, Donghua Univer-
sity, Shanghai 200051, P. R.China
zjg@dhu.edu.cn
Jinliang
Liu
Department of Applied Mathematics, Nanjing University of Finance
and Economics, Nanjing, 210046, P.R.China
liujinliang@vip.163.com
Chaoyong
Qin
College of Mathematics and Information Sciences of Guangxi Univer-
sity, Naning 530004, P. R. China and Glorious Sun School of Business Administration,
Donghua Universty, Shanghai 200051, P. R.China
qcy@dhu.edu.cn
10.22111/ijfs.2012.148
To tackle the problem with inexact, uncertainty and vague knowl- edge, constructive method is utilized to formulate lower and upper approx- imation sets. Rough set model over dual-universes in fuzzy approximation space is constructed. In this paper, we introduce the concept of rough set over dual-universes in fuzzy approximation space by means of cut set. Then, we discuss properties of rough set over dual-universes in fuzzy approximation space from two viewpoints: approximation operators and cut set of fuzzy set. Reduction of attributes and rules extraction of rough set over dual-universes in fuzzy approximation space are presented. Finally, an example of disease diagnoses expert system illustrates the possibility and eciency of rough set over dual-universes in fuzzy approximation space.
http://ijfs.usb.ac.ir/article_148.html
http://ijfs.usb.ac.ir/article_148_67ddd09a31fbe33d3c0112464ab1d0a2.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
3
2012
10
02
A BI-OBJECTIVE PROGRAMMING APPROACH TO SOLVE
MATRIX GAMES WITH PAYOFFS OF ATANASSOV’S
TRIANGULAR INTUITIONISTIC FUZZY NUMBERS
93
110
EN
Deng-Feng
Li
School of Management, Fuzhou University, No. 2, Xueyuan Road,
Daxue New District, Fuzhou 350108, Fujian, China
lidengfeng@fzu.edu.cn, dengfengli@sina.com
Jiang-Xia
Nan
School of Mathematics and Computing Sciences, Guilin University
of Electronic Technology, Guilin, Guangxi 541004, China
nanjiangxia@guet.edu.cn
Zhen-Peng
Tang
School of Management, Fuzhou University, No. 2, Xueyuan Road,
Daxue New District, Fuzhou 350108, Fujian, China
zhenpt@126.com
Ke-Jia
Chen
School of Management, Fuzhou University, No. 2, Xueyuan Road,
Daxue New District, Fuzhou 350108, Fujian, China
kjchen@fzu.edu.cn
Xiao-Dong
Xiang
School of Management, Fuzhou University, No. 2, Xueyuan Road,
Daxue New District, Fuzhou 350108, Fujian, China
xiangxiaodong2@yahoo.com.cn
Fang-Xuan
Hong
School of Management, Fuzhou University, No. 2, Xueyuan Road,
Daxue New District, Fuzhou 350108, Fujian, China
hongfangxuan-2@163.com
10.22111/ijfs.2012.149
The intuitionistic fuzzy set has been applied to game theory very rarely since it was introduced by Atanassov in 1983. The aim of this paper is to develop an effective methodology for solving matrix games with payoffs of Atanassov’s triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, the concepts and ranking order relations of Atanassov’s TIFNs are defined. A pair of bi-objective linear programming models for matrix games with payoffs of Atanassov’s TIFNs is derived from two auxiliary Atanassov’s intuitionistic fuzzy programming models based on the ranking order relations of Atanassov’s TIFNs defined in this paper. An effective methodology based on the weighted average method is developed to determine optimal strategies for two players. The proposed method in this paper is illustrated with a numerical example of the market share competition problem.
Uncertainty,Fuzzy set,Atanassov’s intuitionistic fuzzy set,Fuzzy
number,Matrix game,Mathematical programming
http://ijfs.usb.ac.ir/article_149.html
http://ijfs.usb.ac.ir/article_149_f094614acdcf61ef90e40f0a90cf6e53.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
3
2012
10
02
(T) FUZZY INTEGRAL OF MULTI-DIMENSIONAL FUNCTION
WITH RESPECT TO MULTI-VALUED MEASURE
111
126
EN
Wanli
Liu
Department of Spatial Informatics, China University of Mining and
Technology, Xuzhou, Jiangsu 221116, P. R. China
liuliucumt@126.com
Xiaoqiu
Song
Department of Mathematics, China University of Mining and Tech-
nology, Xuzhou, Jiangsu 221116, P. R. China
songxiaoqiu@cumt.edu.cn
Qiuzhao
Zhang
Department of Spatial Informatics, China University of Mining and
Technology, Xuzhou, Jiangsu 221116, P. R. China
qiuzhaocumt@163.com
Shubi
Zhang
Department of Spatial Informatics, China University of Mining and
Technology, Xuzhou, Jiangsu 221116, P. R. China
zhangsbi@vip.sina.com
10.22111/ijfs.2012.150
Introducing more types of integrals will provide more choices todeal with various types of objectives and components in real problems. Firstly,in this paper, a (T) fuzzy integral, in which the integrand, the measure andthe integration result are all multi-valued, is presented with the introductionof T-norm and T-conorm. Then, some classical results of the integral areobtained based on the properties of T-norm and T-conorm mainly. The pre-sented integral can act as an aggregation tool which is especially useful inmany information fusing and data mining problems such as classication andprogramming.
$mathfrak{T}$-norm,$mathfrak{T}$-conorm,Multi-dimensional function,Multi-valued measure,$(T)$ fuzzy integral
http://ijfs.usb.ac.ir/article_150.html
http://ijfs.usb.ac.ir/article_150_0e59f87cbb7402a1c982c3c0f416b1cd.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
3
2012
10
02
PREDICTING URBAN TRIP GENERATION USING A FUZZY
EXPERT SYSTEM
127
146
EN
Amir Abbas
Rassafi
Faculty of Engineering, Imam Khomeini International Univer-
sity, Qazvin, 34149, Iran
rasafi@ikiu.ac.ir
Roohollah
Rezaei
Faculty of Engineering, Imam Khomeini International University,
Qazvin, 34149, Iran
te rezaei@yahoo.com
Mehdi
Hajizamani
MIT-Portugal Program, Instituto Superior Tcnico, Technical
University of Lisbon, Lisbon, Portugal
mhajizamani@yahoo.com
10.22111/ijfs.2012.151
One of the most important stages in the urban transportation planning procedure is predicting the rate of trips generated by each trac zone. Currently, multiple linear regression models are frequently used as a prediction tool. This method predicts the number of trips produced from, or attracted to each trac zone according to the values of independent variables for that zone. One of the main limitations of this method is its huge dependency on the exact prediction of independent variables in future (horizon of the plan). The other limitation is its many assumptions, which raise challenging questions of its application. The current paper attempts to use fuzzy logic and its capabilities to estimate the trip generation of urban zones. A fuzzy expert system is introduced, which is able to make suitable predictions using uncertain and inexact data. Results of the study on the data for Mashhad (Lon: 59.37 E, Lat: 36.19 N) show that this method can be a good competitor for multiple linear regression method, specially, when there is no exact data for independent variables.
Trip generation,Multiple linear regression,Membership Function,Fuzzy rules,Fuzzy expert system
http://ijfs.usb.ac.ir/article_151.html
http://ijfs.usb.ac.ir/article_151_24ef363709839198fa9ec03c1232b4ff.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
3
2012
10
01
Persian-translation vol. 9, no. 3, october 2012
149
156
EN
10.22111/ijfs.2012.2813
http://ijfs.usb.ac.ir/article_2813.html
http://ijfs.usb.ac.ir/article_2813_5c1b4b9760f4bb9732eea11b508ec0df.pdf