A method for solving fully fuzzy linear system with trapezoidal fuzzy numbers

Iranian Journal of Optimization

مقاله 5، دوره 4، شماره 2، مهر 2012، صفحه 312-323   

نوع مقاله: Research Paper

نویسندگان

A. Kumar¹؛ A. Bansal^{* 2}؛ A. Neetu³

¹aSchool of Mathematics and Computer Applications, Thapar University, Patiala- 147004, India

²Computer Science and Engineering Department, Thapar University, Patiala- 147004, India

³School of Mathematics and Computer Applications, Thapar University, Patiala- 147004, India

چکیده

Different methods have been proposed for finding the non-negative solution of fully fuzzy linear system (FFLS) i.e. fuzzy linear system with fuzzy coefficients involving fuzzy variables. To the best of our knowledge, there is no method in the literature for finding the non-negative solution of a FFLS without any restriction on the coefficient matrix. In this paper a new computational method is proposed to solve FFLS without any restriction on the coefficient matrix by representing all the parameters as trapezoidal fuzzy numbers.

کلیدواژه‌ها

fully fuzzy linear systems (FFLS)؛ fuzzy matrix؛ trapezoidal fuzzy numbers

مراجع

[1] Abbasbandy S., Ezzati R., Jafarian A., LU decomposition method for solving fuzzy system of linear equations. Applied Mathematics and Computation 172, 633–643, 2006.

[2] Abbasbandy S., Jafarian A., Steepest descent method for system of fuzzy linear equations. Applied Mathematics and Computation 175, 823–833,2006.

[3] Abbasbandy S., Jafarian A., Ezzati R., Conjugate gradient method for fuzzy symmetric positive-definite system of linear equations. Applied Mathematics and Computation 171, 1184–1191, 2005.

[4] Allahviranloo T., Numerical methods for fuzzy system of linear equations. Applied Mathematics and Computation 155, 493–502, 2004.

[5] Allahviranloo T., Successive over relaxation iterative method for fuzzy system of linear equations. Applied Mathematics and Computation 162,189–196, 2004.

[6] Allahviranloo T., The adomian decomposition method for fuzzy system of linear equations. Applied Mathematics and Computation 163, 553-563,2005.

[7] Buckley J. J., Qu Y., Solving systems of linear fuzzy equations. Fuzzy Sets and Systems 43, 33–43, 1991.

[8] Dehghan M., Hashemi B., Ghatee M., Computational methods for solving fully fuzzy linear systems. Applied Mathematics and Computation, 179, 328-343, 2006.

[9] Dehghan M., Hashemi B., Solution of the fully fuzzy linear system using the     decomposition procedure.Applied Mathematics and Computation,182, 1568-1580, 2006.

[10] Dehghan M., Hashemi B., Ghatee M., Solution of the fully fuzzy linear system using iterative techniques. Chaos, Solitons and Fractals, 34, 316-336, 2007.

[11] Dubois D., Prade H., Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, 1980.

[12] Dubois D., Prade H., Systems of linear fuzzy constraints.Fuzzy Sets and Systems, 3, 37–48, 1980.

[13] Friedman M., Ming M., Kandel A., Fuzzy linear systems. Fuzzy Sets and Systems, 96, 201–209, 1998.

[14] Friedman M., Ming M., Kandel A., Duality in fuzzy linear systems. Fuzzy Sets and Systems, 109, 55-58, 2000.

[15] Kauffmann A., Gupta M. M., Introduction to Fuzzy Arithmetic: Theory and Applications, Van Nostrand Reinhold, New York 1991.

[16] Mosleh M., Abbasbandy S., Otadi M., Full fuzzy linear systems of the form              Ax+B=Cx+D, Proceedings First Joint Congress on Fuzzy and Intelligent systems 2007.

[17] Muzzioli S., Reynaerts H., Fuzzy linear systems of the form . Fuzzy Sets and Systems 157, 939 – 951, 2006.

[18] Nasseri S. H., Sohrabi M., Ardil E., Solving fully fuzzy linear systems by use of a certain decomposition of the coefficient matrix. International Journal of Computational and Mathematical Sciences, 2, 140142, 2008.

[19] Nasseri S. H., Zahmatkesh F., Huang method for solving fully fuzzy linear system of equations. The Journal of Mathematics and Computer Science, 1, 1-5, 2010.

[20] Sun X., Guo S., Solution to general fuzzy linear system and its necessary and sufficient condition. Fuzzy Information and Engineering 3, 317-327, 2009.

[21] Yin J. F., Wang K., Splitting iterative methods for fuzzy system of linear equations. Computational Mathematics and Modeling 20, 326–335, 2009.

[22] Zadeh L. A., Fuzzy sets. Information and Control 8, 338–353, 1965.

[23] Zhao R., Govind R., Solution of algebraic equations involving generalized fuzzy numbers. Information Sciences, 56, 199-243, 1991.