ORIGINAL_ARTICLE
Cover vol. 9, no. 3, october 2012
http://ijfs.usb.ac.ir/article_2812_5daeaa39b78bba330a5cde3cf79a9e4f.pdf
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10.22111/ijfs.2012.2812
ORIGINAL_ARTICLE
NEW MODELS AND ALGORITHMS FOR SOLUTIONS OF
SINGLE-SIGNED FULLY FUZZY LR LINEAR SYSTEMS
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
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10.22111/ijfs.2012.144
LR fuzzy numbers
Single-signed fuzzy numbers
Fully fuzzy linear
systems
ABS algorithms
Least squares problems
R.
Ezzati
ezati@kiau.ac.ir
true
1
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
AUTHOR
S.
Khezerloo
S khezerloo@yahoo.com
true
2
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
AUTHOR
Z.
Valizadeh
z valizadeh@kiau.ac.ir
true
3
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
AUTHOR
N.
Mahdavi-Amiri
nezamm@sina.sharif.edu
true
4
Department of Mathematical Sciences, Sharif University of Tech-
nology, 1458 - 889694, Tehran, Iran
Department of Mathematical Sciences, Sharif University of Tech-
nology, 1458 - 889694, Tehran, Iran
Department of Mathematical Sciences, Sharif University of Tech-
nology, 1458 - 889694, Tehran, Iran
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64
ORIGINAL_ARTICLE
MULTI-OBJECTIVE OPTIMIZATION WITH PREEMPTIVE
PRIORITY SUBJECT TO FUZZY RELATION
EQUATION CONSTRAINTS
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
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45
10.22111/ijfs.2012.145
Fuzzy relation equation
Preemptive priority
Branch & Bound
Multi
objective
Linear objective
Optimal solution
Binding variable
Esmaile
Khorram
eskhor@aut.ac.ir
true
1
Faculty of Mathematics and Computer Science, Amirkabir Uni-
versity of Technology, 424,Hafez Ave.,15914,Tehran, Iran
Faculty of Mathematics and Computer Science, Amirkabir Uni-
versity of Technology, 424,Hafez Ave.,15914,Tehran, Iran
Faculty of Mathematics and Computer Science, Amirkabir Uni-
versity of Technology, 424,Hafez Ave.,15914,Tehran, Iran
LEAD_AUTHOR
Vahid
Nozari
vahid78mu@gmail.com
true
2
Faculty of Mathematics and Computer Science, Amirkabir University
of Technology, 424,Hafez Ave.,15914,Tehran, Iran
Faculty of Mathematics and Computer Science, Amirkabir University
of Technology, 424,Hafez Ave.,15914,Tehran, Iran
Faculty of Mathematics and Computer Science, Amirkabir University
of Technology, 424,Hafez Ave.,15914,Tehran, Iran
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ORIGINAL_ARTICLE
ORDERED IDEAL INTUITIONISTIC FUZZY MODEL
OF FLOOD ALARM
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
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60
10.22111/ijfs.2012.146
Rainfall
Ordered intuitionistic fuzzy set
Flood
Simulation
Sunny Joseph
Kalayathankal
sunnyjose2000@yahoo.com
true
1
Department of Mathematics, K.E.College, Mannanam,
Kottayam, 686561, Kerala, India
Department of Mathematics, K.E.College, Mannanam,
Kottayam, 686561, Kerala, India
Department of Mathematics, K.E.College, Mannanam,
Kottayam, 686561, Kerala, India
LEAD_AUTHOR
G.
Suresh Singh
sureshsinghg@yahoo.co.in
true
2
Department of Mathematics, University of Kerala, Trivandrum,
695581, Kerala, India
Department of Mathematics, University of Kerala, Trivandrum,
695581, Kerala, India
Department of Mathematics, University of Kerala, Trivandrum,
695581, Kerala, India
AUTHOR
[1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
1
[2] J. J. Buckley, K. D.Reilly and L. J. Jowers, Simulating continuous fuzzy systems, Iranian
2
Journal of Fuzzy Systems, 2(1) (2005), 1-18.
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[3] J. M. Cadenas and J. L. Verdegay, A primer on fuzzy optimization models and methods,
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Iranian Journal of Fuzzy Systems, 3(1) (2006), 1-21.
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[4] S. M. Chen, S. M Yeh and P. H. Hasiao, A comparison of similarity measures of fuzzy values,
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[5] Dubois and Prade, Two fold fuzzy sets and rough sets - some issues in knowledge representation,
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Fuzzy Sets and Systems, (1987), 3-18.
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intuitionistic fuzzy soft model of flood alarm, Iranian Journal of Fuzzy Systems, 8(1) (2011),
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[8] S. J. Kalayathankal, G. Suresh Singh and P. B. Vinodkumar, OIIF model of flood alarm,
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Global Journal of Mathematical Sciences: Theory and Practical, 1(1) (2009), 1-8.
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[9] S. J. Kalayathankal and G. Suresh Singh, IFS model of flood alarm, Global Journal of Pure
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and Applied Mathematics, 9 (2009), 15-22.
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[11] S. J. Kalayathankal, G. Suresh Singh and P. B. Vinodkumar, Ordered intuitionistic fuzzy soft
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sets, Journal of Fuzzy Mathematics, 18(4) (2010), 991-998.
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[12] S. Li Chen, The application of comprehensive fuzzy judgement in the interpretation of waterflooded
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reservoirs, The Journal of Fuzzy Mathematics, 9(3) (2001), 739-743.
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[13] I. Mahdavi, N. Mahdavi-Amiri, A. Heidarzade and R. Nourifar, Designing a model of fuzzy
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TOPSIS in multiple criteria decision making, Applied Mathematics and Computation, 206
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(2008), 607617.
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[14] P. C. Nayak, K. P. Sudheer and K. S. Ramasastri, Fuzzy computing based rainfall-runoff
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model for real time flood forecasting, Hydrological Processes, 19 (2005), 955-968.
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[15] W. Pedrycz, Distributed and collaborative fuzzy modeling, Iranian Journal of Fuzzy Systems,
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4(1) (2007), 1-19.
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[16] M. M. Xia and Z. S. Xu, Some new similarity measures for intuitionistic fuzzy values and
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their application in group decision making, Journal of Systems Science and Systems Engineering,
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19 (2010), 430-452.
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[17] Z. S. Xu and R. R. Yager, Dynamic intuitionistic fuzzy multi-attribute decision making,
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International Journal of Approximate Reasoning, 48 (2008), 246-262.
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to pattern recognitions, Journal of Southeast University, 23 (2007), 139-143.
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[19] Z. S. Xu and J. Chen, An overview of distance and similarity measures of intuitionistic
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fuzzy sets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,
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16 (2008), 529-555.
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[20] Z. S. Xu and R. R. Yager, Intuitionistic and interval-valued intutionistic fuzzy preference
40
relations and their measures of similarity for the evaluation of agreement within a group,
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Fuzzy Optimization and Decision Making, 8 (2009), 123-139.
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[21] Z. S. Xu, J. Chen and J. J. Wu, Clustering algorithm for intuitionistic fuzzy sets, Information
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Sciences, 178 (2008), 3775-3790.
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[22] Z. Xu, Some similarity measures of intuitionistic fuzzy sets and their applications to multiple
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attribute decision making, Fuzzy Optim.Decis.Making, 6 (2007), 109-121.
46
[23] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
47
ORIGINAL_ARTICLE
PRICING STOCKS BY USING FUZZY DIVIDEND
DISCOUNT MODELS
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
2012-10-02T11:23:20
2018-05-25T11:23:20
61
78
10.22111/ijfs.2012.147
Fuzzy set
Pricing stock
Dividend discount model (DDM)
$l$-signed
distance method
Uniform convergence
Huei-Wen
Lin
au4345@mail.au.edu.tw
true
1
Department of Finance and Banking, Aletheia University, 32 Chen-Li
Street, 25103, New Taipei City, Taiwan (R.O.C.)
Department of Finance and Banking, Aletheia University, 32 Chen-Li
Street, 25103, New Taipei City, Taiwan (R.O.C.)
Department of Finance and Banking, Aletheia University, 32 Chen-Li
Street, 25103, New Taipei City, Taiwan (R.O.C.)
LEAD_AUTHOR
Jing-Shing
Yao
hflu.chibi@msa.hinet.net
true
2
Department of Mathematics, National Taiwan University, No.1, Sec.
4, Roosevelt Rd., Taipei City 106, Taiwan (R.O.C.)
Department of Mathematics, National Taiwan University, No.1, Sec.
4, Roosevelt Rd., Taipei City 106, Taiwan (R.O.C.)
Department of Mathematics, National Taiwan University, No.1, Sec.
4, Roosevelt Rd., Taipei City 106, Taiwan (R.O.C.)
AUTHOR
[1] L. Brand, Advance calculus: an introduction to classical analysis, New York, 1955.
1
[2] E. F. Brigham, Fundamentals of nancial management, The Dryden Press, New York, 1992.
2
[3] J. J. Buckley, The fuzzy mathematics of nance, Fuzzy Sets and Systems, 21 (1987), 257-273.
3
[4] H. Dourra and P. Siy, Investment using technical analysis and fuzzy logic, Fuzzy Sets and
4
Systems, 127 (2002), 221-240.
5
[5] M. J. Gordon, The investment, nancing, and valuation of the corporation, Homewood,
6
Illinois: Richard D. Irwin, 1962.
7
[6] W. J. Hurley and L. D. Johnson, A realistic dividend valuation model, Financial Analysts
8
Journal, July-August(1994), 50-54.
9
[7] A. Kaufmann and M. M. Gupta, Introduction to fuzzy arithmetic: theory and applications,
10
Van Nostrand Reinhold, New York, 1991.
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[8] D. Kuchta, Fuzzy capital budgeting, Fuzzy Sets and Systems, 111 (2000), 367-385.
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[9] R. J. Kuo, C. H. Chen and Y. C. Hwang, An intelligent stock trading decision support
13
system through integration of genetic algorithm based fuzzy neural network and articial
14
neural network, Fuzzy Sets and Systems, 118 (2001), 21-45.
15
[10] M. L. Leibowitz and S. Kogelman, The growth illusion: the P/E 'cost' of earnings growth,
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[11] M. Li Calzi, Towards a general setting for the fuzzy mathematics of nance, Fuzzy Sets and
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22
(2009), 49-59.
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Moore-smith convergence, Journal of Mathematical Analysis and Applications, 76 (1980),
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1(1) (2004), 43-56.
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Applications, 22 (2002), 33-39.
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[20] Y. F. Wang, Mining stock price using fuzzy rough set system, Expert Systems with Applications,
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24 (2003), 13-23.
37
[21] J. S. Yao and K. M. Wu, Ranking fuzzy numbers based on decomposition principle and signed
38
distance, Fuzzy Sets and Systems, 116 (2000), 275-288.
39
[22] R. Zhao and R. Govind, Defuzzication of fuzzy intervals, Fuzzy Sets and Systems, 43 (1991),
40
ORIGINAL_ARTICLE
ROUGH SET OVER DUAL-UNIVERSES IN FUZZY
APPROXIMATION SPACE
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
2012-10-02T11:23:20
2018-05-25T11:23:20
79
91
10.22111/ijfs.2012.148
Ruixia
Yan
yanruixia@gmail.com
true
1
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
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
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
LEAD_AUTHOR
Jianguo
Zheng
zjg@dhu.edu.cn
true
2
Glorious Sun School of Business Administration, Donghua Univer-
sity, Shanghai 200051, P. R.China
Glorious Sun School of Business Administration, Donghua Univer-
sity, Shanghai 200051, P. R.China
Glorious Sun School of Business Administration, Donghua Univer-
sity, Shanghai 200051, P. R.China
AUTHOR
Jinliang
Liu
liujinliang@vip.163.com
true
3
Department of Applied Mathematics, Nanjing University of Finance
and Economics, Nanjing, 210046, P.R.China
Department of Applied Mathematics, Nanjing University of Finance
and Economics, Nanjing, 210046, P.R.China
Department of Applied Mathematics, Nanjing University of Finance
and Economics, Nanjing, 210046, P.R.China
AUTHOR
Chaoyong
Qin
qcy@dhu.edu.cn
true
4
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
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
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
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[1] D. Dubois and H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of
1
General Systems, 17(2-3) (1990), 191-209.
2
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4
dominance relations, European Journal of Operational Research, 117(1) (1999), 63-83.
5
[4] T. Li, Rough approximation operators on two universes of discourse and their fuzzy exten-
6
sions, Fuzzy Sets and Systems, 159(22) (2008), 3033-3050.
7
[5] T. Li and W. Zhang, Rough fuzzy approximations on two universes of discourse, Information
8
Sciences, 178(3) (2008), 892-906.
9
[6] G. Liu, Rough set theory based on two universal sets and its applications, Knowledge-Based
10
Systems, 2009.
11
[7] G. Liu and W. Zhu, The algebraic structures of generalized rough set theory, Information
12
Sciences, 178(21) (2008), 4105-4113.
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[8] N. Mac Parthalain and Q. Shen, Exploring the boundary region of tolerance rough sets for
14
feature selection, Pattern Recognition, 42(5) (2009), 655-667.
15
[9] J. Mi, Y. Leung, H. Zhao and T. Feng, Generalized fuzzy rough sets determined by a triangular
16
norm, Information Sciences, 178(16) (2008), 3203-3213.
17
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18
(1982), 341-356.
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[11] Z. Pawlak, Rough sets: theoretical aspects of reasoning about data, Springer, 1991.
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21
34(5) (2005), 603-613.
22
[13] D. Pei and Z. Xu, Rough set models on two universes, International Journal of General
23
Systems, 33(5) (2004), 569-581.
24
[14] S. Roman and V. Daniel, A genaralized denition of rough approximations based on similar-
25
ity, IEEE Transactions on Knowledge and Data Engineering, 12 (2000), 331-336.
26
[15] Y. Shen and F. Wang, Variable precision rough set model over two universes and its prop-
27
erties, Soft Computing-A Fusion of Foundations, Methodologies and Applications, 15(3)
28
(2011), 557-567.
29
[16] A. Skowron and J. Stepaniuk, Tolerance approximation spaces, Fundamenta Informaticae,
30
27(2/3) (1996), 245-253.
31
[17] B. Sun and W. Ma, Fuzzy rough set model on two dierent universes and its application,
32
Applied Mathematical Modelling, 2010.
33
[18] S. Wong, L. Wang and Y. Yao, On modeling uncertainty with interval structures, Computa-
34
tional Intelligence, 11(2) (1995), 406-426.
35
[19] W. Wu, Y. Leung and J. Mi, On characterizations of-fuzzy rough approximation operators,
36
Fuzzy Sets and Systems, 154(1) (2005), 76-102.
37
[20] W.Wu, Y. Leung and W. Zhang, On generalized rough fuzzy approximation operators, Trans-
38
actions on Rough Sets V, (2006), 263-284.
39
[21] Q. Wu and Z. Liu, Real formal concept analysis based on grey-rough set theory, Knowledge-
40
Based Systems, 22(1) (2009), 38-45.
41
[22] W. Wu, J. Mi and W. Zhang, Generalized fuzzy rough sets, Information Sciences, 151 (2003),
42
[23] W. Wu and W. Zhang, Constructive and axiomatic approaches of fuzzy approximation oper-
43
ators, Information Sciences, 159(3-4) (2004), 233-254.
44
[24] J. Z. R. Yan and J. Liu, Rough set over dual-universes and its applications in: expert systems,
45
ICIC Express Letters, 4(3) (2010), 833-838.
46
[25] R. Yan, J. Zheng, J. Liu and Y. Zhai, Research on the model of rough set over dual-universes,
47
Knowledge-Based Systems, 23(8) (2010), 817-822.
48
[26] Y. Yao, Probabilistic rough set approximations, International Journal of Approximate Rea-
49
soning, 49(2) (2008), 255-271.
50
[27] Y. Yao, Generalized rough set models, Rough Sets in Knowledge Discovery, 1 (1998), 286-318.
51
[28] Y. Yao and T. Lin, Generalization of rough sets using modal logic, Intelligent Automation
52
and Soft Computing, 2(2) (1996), 103-120.
53
[29] L. Zadeh, Fuzzy sets, Information and control, 8(3) (1965), 338-353.
54
[30] K. Zaras, Rough approximation of a preference relation by a multi-attribute dominance for
55
deterministic, stochastic and fuzzy decision problems, European Journal of Operational Re-
56
search, 159(1) (2004), 196-206.
57
[31] H. Zhang, W. Zhang and W. Wu, On characterization of generalized interval-valued fuzzy
58
rough sets on two universes of discourse, International Journal of Approximate Reasoning,
59
51(1) (2009), 56-70.
60
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61
46(1) (1993), 39-59.
62
ORIGINAL_ARTICLE
A BI-OBJECTIVE PROGRAMMING APPROACH TO SOLVE
MATRIX GAMES WITH PAYOFFS OF ATANASSOV’S
TRIANGULAR INTUITIONISTIC FUZZY NUMBERS
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
2012-10-02T11:23:20
2018-05-25T11:23:20
93
110
10.22111/ijfs.2012.149
Uncertainty
Fuzzy set
Atanassov’s intuitionistic fuzzy set
Fuzzy
number
Matrix game
Mathematical programming
Deng-Feng
Li
lidengfeng@fzu.edu.cn, dengfengli@sina.com
true
1
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
AUTHOR
Jiang-Xia
Nan
nanjiangxia@guet.edu.cn
true
2
School of Mathematics and Computing Sciences, Guilin University
of Electronic Technology, Guilin, Guangxi 541004, China
School of Mathematics and Computing Sciences, Guilin University
of Electronic Technology, Guilin, Guangxi 541004, China
School of Mathematics and Computing Sciences, Guilin University
of Electronic Technology, Guilin, Guangxi 541004, China
LEAD_AUTHOR
Zhen-Peng
Tang
zhenpt@126.com
true
3
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
AUTHOR
Ke-Jia
Chen
kjchen@fzu.edu.cn
true
4
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
AUTHOR
Xiao-Dong
Xiang
xiangxiaodong2@yahoo.com.cn
true
5
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
AUTHOR
Fang-Xuan
Hong
hongfangxuan-2@163.com
true
6
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
AUTHOR
[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
1
[2] K. T. Atanassov, Intuitionistic fuzzy sets, Springer-Verlag, Heidelberg, Germany, 1999.
2
[3] K. T. Atanassov and G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and
3
Systems, 31 (1989), 343-349.
4
[4] K. T. Atanassov, Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade’s
5
paper Terminological difficulties in fuzzy set theory - the case of ”intuitionistic fuzzy sets”,
6
Fuzzy Sets and Systems, 156 (2005), 496-499.
7
[5] C. R. Bector and S. Chandra, Fuzzy mathematical programming and fuzzy matrix games,
8
Springer Verlag, Berlin, Germany, 2005.
9
[6] C. R. Bector, S. Chandra and V. Vijay, Matrix games with fuzzy goals and fuzzy linear
10
programming duality, Fuzzy Optimization and Decision Making, 3 (2004), 255-269.
11
[7] C. R. Bector, S. Chandra and V. Vijay, Duality in linear programming with fuzzy parameters
12
and matrix games with fuzzy pay-offs, Fuzzy Sets and Systems, 46(2) (2004), 253-269.
13
[8] R. A. Borzooei and Y. B. Jun, Intuitionistic fuzzy hyper bck-ideals of hyper bck-al gebras,
14
Iranian Journal of Fuzzy Systems, 1(1) (2004), 65-78.
15
[9] P. Burillo and H. Bustince, Vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems,
16
79 (1996), 403-405.
17
[10] L. Campos, Fuzzy linear programming models to solve fuzzy matrix games, Fuzzy Sets and
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Systems, 32 (1989), 275-289.
19
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Kybernetes, 20 (1991), 17-23.
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[12] L. Campos, A. Gonzalez and M. A. Vila, On the use of the ranking function approach to
22
solve fuzzy matrix games in a direct way, Fuzzy Sets and Systems, 49 (1992), 193-203.
23
[13] S. K. De, R. Biswas and A. R. Roy, An application of intuitionistic fuzzy sets in medical
24
diagnosis, Fuzzy Sets and Systems, 117 (2001), 209-213.
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[14] G. Deschrijver, Arithmetic operators in interval-valued fuzzy set theory, Information Sciences,
26
177(14) (2007), 2906-2924.
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[15] G. Deschrijver and E. E. Kerre, On the relationship between some extensions of fuzzy set
28
theory, Fuzzy Sets and Systems, 133 (2003), 227-235.
29
[16] G. Deschrijver and E. E. Kerre, On the position of intuitionistic fuzzy set theory in the
30
framework of theories modeling imprecision, Information Sciences, 177 (2007), 1860-1866.
31
[17] D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade, Terminological difficulties in
32
fuzzy set theory-the case of ”Intuitionistic Fuzzy Sets”, Fuzzy Sets and Systems, 156 (3)
33
(2005), 485-491.
34
[18] D. Dubois and H. Prade, fuzzy sets and systems: theory and applications, Mathematics in
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Science and Engineering, Academic Press, Berlin, Germany, 144 (1980).
36
[19] J. G. Garc and S. E. Rodabaugh, Order-theoretic, topological, categorical redundancies of
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interval-valued sets, grey sets, vague sets, interval-valued ”intuitionistic” sets, ”intuitionistic”
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fuzzy sets and topologies, Fuzzy Sets and Systems, 156(3) (2005), 445-484.
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[20] W. L. Gau and D. J. Buehrer, Vague sets, IEEE Transaction on Systems, Man, and Cybernetics,
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23 (1993), 610-614.
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[21] J. Goguen, L-fuzzy sets, Journal of Mathematical Analysis and Applications, 18 (1967),
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and Natural Computation, 1(1) (2005), 1-26.
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[23] A. Khan, Y. B. Jun and M. Shabir, Ordered semigroups characterized by their intuitionistic
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fuzzy bi-ideals, Iranian Journal of Fuzzy Systems, 7(2) (2010), 55-69.
46
[24] D. F. Li, Fuzzy constrained matrix games with fuzzy payoffs, The Journal of Fuzzy Mathematics,
47
7(4) (1999), 873-880.
48
[25] D. F. Li, A fuzzy multiobjective programming approach to solve fuzzy matrix games, The
49
Journal of Fuzzy Mathematics, 7(4) (1999), 907-912.
50
[26] D. F. Li, Multiattribute decision making models and methods using intuitionistic fuzzy sets,
51
Journal of Computer and System Sciences, 70 (2005), 73-85.
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[27] D. F. Li, A note on using intuitionistic fuzzy sets for fault-tree analysis on printed circuit
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[28] D. F Li, A ratio ranking method of triangular intuitionistic fuzzy numbers and its application
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ORIGINAL_ARTICLE
(T) FUZZY INTEGRAL OF MULTI-DIMENSIONAL FUNCTION
WITH RESPECT TO MULTI-VALUED MEASURE
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
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10.22111/ijfs.2012.150
$mathfrak{T}$-norm
$mathfrak{T}$-conorm
Multi-dimensional function
Multi-valued measure
$(T)$ fuzzy integral
Wanli
Liu
liuliucumt@126.com
true
1
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
Department of Spatial Informatics, China University of Mining and
Technology, Xuzhou, Jiangsu 221116, P. R. China
LEAD_AUTHOR
Xiaoqiu
Song
songxiaoqiu@cumt.edu.cn
true
2
Department of Mathematics, China University of Mining and Tech-
nology, Xuzhou, Jiangsu 221116, P. R. China
Department of Mathematics, China University of Mining and Tech-
nology, Xuzhou, Jiangsu 221116, P. R. China
Department of Mathematics, China University of Mining and Tech-
nology, Xuzhou, Jiangsu 221116, P. R. China
AUTHOR
Qiuzhao
Zhang
qiuzhaocumt@163.com
true
3
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
Department of Spatial Informatics, China University of Mining and
Technology, Xuzhou, Jiangsu 221116, P. R. China
AUTHOR
Shubi
Zhang
zhangsbi@vip.sina.com
true
4
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
Department of Spatial Informatics, China University of Mining and
Technology, Xuzhou, Jiangsu 221116, P. R. China
AUTHOR
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1
continuous multifunctions, Iranian Journal of Fuzzy Systems, 8(3) (2011), 149-158.
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12
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[8] C. Guo and D. Zhang, On set-valued fuzzy measure, Information Sciences, 160 (2004), 13-25.
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[9] L. Jang, T. Kim and J. Jeon, on set-valued Choquet integrals and convergence theorems II,
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structions and parameterized families, Fuzzy Sets and Systems, 145 (2004), 411-438.
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t-norms, Fuzzy Sets and Systems, 145 (2004), 439-454.
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65
ORIGINAL_ARTICLE
PREDICTING URBAN TRIP GENERATION USING A FUZZY
EXPERT SYSTEM
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
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10.22111/ijfs.2012.151
Trip generation
Multiple linear regression
Membership function
Fuzzy rules
Fuzzy expert system
Amir Abbas
Rassafi
rasafi@ikiu.ac.ir
true
1
Faculty of Engineering, Imam Khomeini International Univer-
sity, Qazvin, 34149, Iran
Faculty of Engineering, Imam Khomeini International Univer-
sity, Qazvin, 34149, Iran
Faculty of Engineering, Imam Khomeini International Univer-
sity, Qazvin, 34149, Iran
LEAD_AUTHOR
Roohollah
Rezaei
te rezaei@yahoo.com
true
2
Faculty of Engineering, Imam Khomeini International University,
Qazvin, 34149, Iran
Faculty of Engineering, Imam Khomeini International University,
Qazvin, 34149, Iran
Faculty of Engineering, Imam Khomeini International University,
Qazvin, 34149, Iran
AUTHOR
Mehdi
Hajizamani
mhajizamani@yahoo.com
true
3
MIT-Portugal Program, Instituto Superior Tcnico, Technical
University of Lisbon, Lisbon, Portugal
MIT-Portugal Program, Instituto Superior Tcnico, Technical
University of Lisbon, Lisbon, Portugal
MIT-Portugal Program, Instituto Superior Tcnico, Technical
University of Lisbon, Lisbon, Portugal
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ORIGINAL_ARTICLE
Persian-translation vol. 9, no. 3, october 2012
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