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

Subject Areas : Operation Research

A. Kumar ¹ , A. Bansal ² , A. Neetu ³

1 - aSchool of Mathematics and Computer Applications, Thapar University, Patiala- 147004, India
2 - Computer Science and Engineering Department, Thapar University, Patiala- 147004, India
3 - School of Mathematics and Computer Applications, Thapar University, Patiala- 147004, India

Received: 2010-01-25 Accepted : 2010-02-25 Published : 2012-07-01

Keywords:

References:

[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.