eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2012-10-01
9
3
0
10.22111/ijfs.2012.2812
2812
Cover vol. 9, no. 3, october 2012
http://ijfs.usb.ac.ir/article_2812_5daeaa39b78bba330a5cde3cf79a9e4f.pdf
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2012-10-02
9
3
1
26
10.22111/ijfs.2012.144
144
مقاله پژوهشی
NEW MODELS AND ALGORITHMS FOR SOLUTIONS OF
SINGLE-SIGNED FULLY FUZZY LR LINEAR SYSTEMS
R. Ezzati
ezati@kiau.ac.ir
1
S. Khezerloo
S khezerloo@yahoo.com
2
Z. Valizadeh
z valizadeh@kiau.ac.ir
3
N. Mahdavi-Amiri
nezamm@sina.sharif.edu
4
Department of Mathematics, Karaj Branch, Islamic Azad University,
31485 - 313, Karaj, Iran
Department of Mathematics, Karaj Branch, Islamic Azad University,
31485 - 313, Karaj, Iran
Department of Mathematics, Karaj Branch, Islamic Azad University,
31485 - 313, Karaj, Iran
Department of Mathematical Sciences, Sharif University of Tech-
nology, 1458 - 889694, Tehran, Iran
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.
http://ijfs.usb.ac.ir/article_144_dc1df75c9b5c022986a4766b037d1797.pdf
LR fuzzy numbers
Single-signed fuzzy numbers
Fully fuzzy linear
systems
ABS algorithms
Least squares problems
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2012-10-02
9
3
27
45
10.22111/ijfs.2012.145
145
مقاله پژوهشی
MULTI-OBJECTIVE OPTIMIZATION WITH PREEMPTIVE
PRIORITY SUBJECT TO FUZZY RELATION
EQUATION CONSTRAINTS
Esmaile Khorram
eskhor@aut.ac.ir
1
Vahid Nozari
vahid78mu@gmail.com
2
Faculty of Mathematics and Computer Science, Amirkabir Uni-
versity of Technology, 424,Hafez Ave.,15914,Tehran, Iran
Faculty of Mathematics and Computer Science, Amirkabir University
of Technology, 424,Hafez Ave.,15914,Tehran, Iran
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.
http://ijfs.usb.ac.ir/article_145_8b38e0f7556e356816be47b4ddb2691a.pdf
Fuzzy relation equation
Preemptive priority
Branch & Bound
Multi
objective
Linear objective
Optimal solution
Binding variable
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2012-10-02
9
3
47
60
10.22111/ijfs.2012.146
146
مقاله پژوهشی
ORDERED IDEAL INTUITIONISTIC FUZZY MODEL
OF FLOOD ALARM
Sunny Joseph Kalayathankal
sunnyjose2000@yahoo.com
1
G. Suresh Singh
sureshsinghg@yahoo.co.in
2
Department of Mathematics, K.E.College, Mannanam,
Kottayam, 686561, Kerala, India
Department of Mathematics, University of Kerala, Trivandrum,
695581, Kerala, India
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.
http://ijfs.usb.ac.ir/article_146_adef22f160e44c2c5fa1d8cb1e5d8d95.pdf
Rainfall
Ordered intuitionistic fuzzy set
Flood
Simulation
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2012-10-02
9
3
61
78
10.22111/ijfs.2012.147
147
مقاله پژوهشی
PRICING STOCKS BY USING FUZZY DIVIDEND
DISCOUNT MODELS
Huei-Wen Lin
au4345@mail.au.edu.tw
1
Jing-Shing Yao
hflu.chibi@msa.hinet.net
2
Department of Finance and Banking, Aletheia University, 32 Chen-Li
Street, 25103, New Taipei City, Taiwan (R.O.C.)
Department of Mathematics, National Taiwan University, No.1, Sec.
4, Roosevelt Rd., Taipei City 106, Taiwan (R.O.C.)
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.
http://ijfs.usb.ac.ir/article_147_17293b564c0a711cb9fb3ec93bd30be5.pdf
Fuzzy set
Pricing stock
Dividend discount model (DDM)
$l$-signed
distance method
Uniform convergence
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2012-10-02
9
3
79
91
10.22111/ijfs.2012.148
148
مقاله پژوهشی
ROUGH SET OVER DUAL-UNIVERSES IN FUZZY
APPROXIMATION SPACE
Ruixia Yan
yanruixia@gmail.com
1
Jianguo Zheng
zjg@dhu.edu.cn
2
Jinliang Liu
liujinliang@vip.163.com
3
Chaoyong Qin
qcy@dhu.edu.cn
4
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
Glorious Sun School of Business Administration, Donghua Univer-
sity, Shanghai 200051, P. R.China
Department of Applied Mathematics, Nanjing University of Finance
and Economics, Nanjing, 210046, P.R.China
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
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_67ddd09a31fbe33d3c0112464ab1d0a2.pdf
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2012-10-02
9
3
93
110
10.22111/ijfs.2012.149
149
مقاله پژوهشی
A BI-OBJECTIVE PROGRAMMING APPROACH TO SOLVE
MATRIX GAMES WITH PAYOFFS OF ATANASSOV’S
TRIANGULAR INTUITIONISTIC FUZZY NUMBERS
Deng-Feng Li
lidengfeng@fzu.edu.cn, dengfengli@sina.com
1
Jiang-Xia Nan
nanjiangxia@guet.edu.cn
2
Zhen-Peng Tang
zhenpt@126.com
3
Ke-Jia Chen
kjchen@fzu.edu.cn
4
Xiao-Dong Xiang
xiangxiaodong2@yahoo.com.cn
5
Fang-Xuan Hong
hongfangxuan-2@163.com
6
School of Management, Fuzhou University, No. 2, Xueyuan Road,
Daxue New District, Fuzhou 350108, Fujian, China
School of Mathematics and Computing Sciences, Guilin University
of Electronic Technology, Guilin, Guangxi 541004, China
School of Management, Fuzhou University, No. 2, Xueyuan Road,
Daxue New District, Fuzhou 350108, Fujian, China
School of Management, Fuzhou University, No. 2, Xueyuan Road,
Daxue New District, Fuzhou 350108, Fujian, China
School of Management, Fuzhou University, No. 2, Xueyuan Road,
Daxue New District, Fuzhou 350108, Fujian, China
School of Management, Fuzhou University, No. 2, Xueyuan Road,
Daxue New District, Fuzhou 350108, Fujian, China
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.
http://ijfs.usb.ac.ir/article_149_f094614acdcf61ef90e40f0a90cf6e53.pdf
Uncertainty
Fuzzy set
Atanassov’s intuitionistic fuzzy set
Fuzzy
number
Matrix game
Mathematical programming
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2012-10-02
9
3
111
126
10.22111/ijfs.2012.150
150
مقاله پژوهشی
(T) FUZZY INTEGRAL OF MULTI-DIMENSIONAL FUNCTION
WITH RESPECT TO MULTI-VALUED MEASURE
Wanli Liu
liuliucumt@126.com
1
Xiaoqiu Song
songxiaoqiu@cumt.edu.cn
2
Qiuzhao Zhang
qiuzhaocumt@163.com
3
Shubi Zhang
zhangsbi@vip.sina.com
4
Department of Spatial Informatics, China University of Mining and
Technology, Xuzhou, Jiangsu 221116, P. R. China
Department of Mathematics, China University of Mining and Tech-
nology, Xuzhou, Jiangsu 221116, P. R. China
Department of Spatial Informatics, China University of Mining and
Technology, Xuzhou, Jiangsu 221116, P. R. China
Department of Spatial Informatics, China University of Mining and
Technology, Xuzhou, Jiangsu 221116, P. R. China
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.
http://ijfs.usb.ac.ir/article_150_0e59f87cbb7402a1c982c3c0f416b1cd.pdf
$mathfrak{T}$-norm
$mathfrak{T}$-conorm
Multi-dimensional function
Multi-valued measure
$(T)$ fuzzy integral
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2012-10-02
9
3
127
146
10.22111/ijfs.2012.151
151
مقاله پژوهشی
PREDICTING URBAN TRIP GENERATION USING A FUZZY
EXPERT SYSTEM
Amir Abbas Rassafi
rasafi@ikiu.ac.ir
1
Roohollah Rezaei
te rezaei@yahoo.com
2
Mehdi Hajizamani
mhajizamani@yahoo.com
3
Faculty of Engineering, Imam Khomeini International Univer-
sity, Qazvin, 34149, Iran
Faculty of Engineering, Imam Khomeini International University,
Qazvin, 34149, Iran
MIT-Portugal Program, Instituto Superior Tcnico, Technical
University of Lisbon, Lisbon, Portugal
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.
http://ijfs.usb.ac.ir/article_151_24ef363709839198fa9ec03c1232b4ff.pdf
Trip generation
Multiple linear regression
Membership function
Fuzzy rules
Fuzzy expert system
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2012-10-01
9
3
149
156
10.22111/ijfs.2012.2813
2813
Persian-translation vol. 9, no. 3, october 2012
http://ijfs.usb.ac.ir/article_2813_5c1b4b9760f4bb9732eea11b508ec0df.pdf