اخبار و اعلانات

دانشگاه سیستان و بلوچستان

آمار

تعداد نشریات26
تعداد شماره‌ها550
تعداد مقالات5,698
تعداد مشاهده مقاله7,965,781
تعداد دریافت فایل اصل مقاله5,348,932
Ezzati, R., Khezerloo, S., Valizadeh, Z., Mahdavi-Amiri, N.. (1391). NEW MODELS AND ALGORITHMS FOR SOLUTIONS OF SINGLE-SIGNED FULLY FUZZY LR LINEAR SYSTEMS. نشریه علمی دانشگاه سیستان و بلوچستان, 9(3), 1-26. doi: 10.22111/ijfs.2012.144
R. Ezzati; S. Khezerloo; Z. Valizadeh; N. Mahdavi-Amiri. "NEW MODELS AND ALGORITHMS FOR SOLUTIONS OF SINGLE-SIGNED FULLY FUZZY LR LINEAR SYSTEMS". نشریه علمی دانشگاه سیستان و بلوچستان, 9, 3, 1391, 1-26. doi: 10.22111/ijfs.2012.144
Ezzati, R., Khezerloo, S., Valizadeh, Z., Mahdavi-Amiri, N.. (1391). 'NEW MODELS AND ALGORITHMS FOR SOLUTIONS OF SINGLE-SIGNED FULLY FUZZY LR LINEAR SYSTEMS', نشریه علمی دانشگاه سیستان و بلوچستان, 9(3), pp. 1-26. doi: 10.22111/ijfs.2012.144
Ezzati, R., Khezerloo, S., Valizadeh, Z., Mahdavi-Amiri, N.. NEW MODELS AND ALGORITHMS FOR SOLUTIONS OF SINGLE-SIGNED FULLY FUZZY LR LINEAR SYSTEMS. نشریه علمی دانشگاه سیستان و بلوچستان, 1391; 9(3): 1-26. doi: 10.22111/ijfs.2012.144

NEW MODELS AND ALGORITHMS FOR SOLUTIONS OF SINGLE-SIGNED FULLY FUZZY LR LINEAR SYSTEMS

Iranian Journal of Fuzzy Systems
مقاله 2، دوره 9، شماره 3، تابستان 2012، صفحه 1-26  XML اصل مقاله (472.99 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2012.144
نویسندگان
R. Ezzatiorcid 1؛ S. Khezerloo1؛ Z. Valizadeh1؛ N. Mahdavi-Amiri email 2
1Department of Mathematics, Karaj Branch, Islamic Azad University, 31485 - 313, Karaj, Iran
2Department of Mathematical Sciences, Sharif University of Tech- nology, 1458 - 889694, Tehran, Iran
چکیده
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.
کلیدواژه‌ها
LR fuzzy numbers؛ Single-signed fuzzy numbers؛ Fully fuzzy linear systems؛ ABS algorithms؛ Least squares problems
مراجع

[1] J. Aba y, C. G. Broyden and E. Spedicato, A class of direct methods for linear systems,
Numerische Mathematik, 45 (1984), 361-376.
[2] J. Aba y and E. Spedicato, ABS projection alegorithms: mathematical techniques for linear
and nonlinear equations, John Wiley and Sons, 1989.
[3] S. Abbasbandy, A. Jafarian and R. Ezzati, Conjugate gradient method for fuzzy symmetric
positive de nite system of linear equations, Applied Mathematics and Computation, 171
(2005), 1184-1191.
[4] S. Abbasbandy and M. Alavi, A method for solving fuzzy linear systems, Iranian Journal of
Fuzzy Systems, 2(2) (2005), 37-43.
[5] S. Abbasbandy, B. Asady and M. Alavi, Fuzzy general linear systems, Applied Mathematics
and Computation, 169 (2005), 34-40.
[6] T. Allahviranloo, Numerical methods for fuzzy system of linear equations, Applied Mathe-
matics and Computation, 155 (2004), 493-502.

[7] T. Allahviranloo, Revised solution of an overdetermined fuzzy linear system of equations,
International Journal of Computational Cognition, 6(3) (2008), 66-70.
[8] T. Allahviranloo, Successive over relaxation iterative method for fuzzy system of linear equa-
tions, Applied Mathematics and Computation, 162 (2005), 189-196.
[9] T. Allahviranloo, The Adomian decomposition method for fuzzy system of linear equations,
Applied Mathematics and Computation, 163 (2005), 553-563.
[10] T. Allahviranloo, E. Ahmady, N. Ahmady and K. Shams Alketaby, Block Jacobi two-stage
method with Gauss-Sidel inner iterations for fuzzy system of linear equations, Applied Math-
ematics and Computation, 175 (2006), 1217-1228.
[11] M. S. Bazaraa, H. D. Sherali and C. M. Shetty, Nonlinear programming: theory and algo-
rithms, John Wiley and Sons, 2006.
[12] J. J. Buckley and Y. Qu, Solving system of linear fuzzy equations, Fuzzy Sets and Systems,
43 (1991), 33-43.
[13] M. Dehghan and B. Hashemi, Iterative the solution of fuzzy linear systems, Applied Mathe-
matics and Computation, 175 (2006), 645-674.
[14] M. Dehghan and B. Hashemi, Solution of the fully fuzzy linear systems using the decompo-
sition procedure, Applied Mathematics and Computation, 182 (2006), 1568-1580.
[15] M. Dehghan, B. Hashemi and M. Ghatee, Computational methods for solving fully fuzzy
linear systems, Applied Mathematics and Computation, 179 (2006), 328-343.
[16] M. Dehghan, B. Hashemi and M. Ghatee, Solution of the fully fuzzy linear systems using
iterative techniques, Chaos Solutions and Fractals, 34 (2007), 316-336.
[17] D. Dubois and H. Prade, Fuzzy sets and systems: theory and applications, Academic Press,
New York, 1980.
[18] H. Esmaeili, N. Mahdavi-Amiri and E. Spedicato, A class of ABS algorithms for Diophantine
linear systems, Numerische Mathematik, 90 (2001), 101-115.
[19] R. Ezzati, Approximate symmetric least square solutions of general fuzzy linear systems,
Applied and Computational Mathematics, 9(2) (2010), 220-225.
[20] R. Ezzati, Solving fuzzy linear systems, Soft Computing, 15 (2011), 193-197.
[21] M. Friedman, M. Ming and A. Kandel, Fuzzy linear systems, Fuzzy Sets and Systems, 96
(1998), 201-209.
[22] R. Ghanbari, N. Mahdavi-Amiri and R. Yousefpour, Exact and approximate solutions of fuzzy
LR linear systems: new algorithms using a least squares model and ABS approach, Iranian
Journal of Fuzzy Systems, 7(2) (2010), 1-18.
[23] M. S. Hashemi, M. K. Mirnia and S. Shahmorad, Solving fuzzy linear systems by using the
schur complement when cocent matrix is an M-matrix, Iranian Journal of Fuzzy Systems,
15(3) (2008), 15-29.
[24] A. Kau man and M. M. Gupta, Introduction to fuzzy arithmetic: theory and application,
Van Nostrand Reinhold, New York, 1991.
[25] M. Khorramizadeh and N. Mahdavi-Amiri, Integer extended ABS algorithms and possible
control of intermediate results for linear Diophantine systems, 4OR: A Quarterly Journal of
Operations Research, 7(2) (2009), 145-167.
[26] M. Khorramizadeh and N. Mahdavi-Amiri, On solving linear Diophantine systems using
generalized Rosser's algorithm, Bulletin of Iranian Mathematical Society, 34(2) (2008), 1-
25.
[27] J. Nocedal and S. J. Wright, Numerical optimization, Springer, 2006.
[28] E. Spedicato, E. Bodon, A. Del Popolo and N. Mahdavi-Amiri, ABS methods and ABSPACK
for linear systems and optimization: a review, 4OR, 1 (2003), 51-66.
[29] L. A. Zadeh, A fuzzy-set-theoretic interpretation of linguistic hedges, Journal of Cybernetics,
2 (1972), 4-34.
[30] L. A. Zadeh, The concept of the linguistic variable and its application to approximate rea-
soning, Information Sciences, 8 (1975), 199-249.
[31] H. J. Zimmermann, Fuzzy set theory and its applications, Kluwer Academic Press, Dordrecht,
1991.

آمار
تعداد مشاهده مقاله: 2,607
تعداد دریافت فایل اصل مقاله: 1,233


Contact Us | Help & Support | Site Map

Journal Management System. Designed by sinaweb.