Fuzzy system of linear equations

Pages: 619 - 627, Issue special, November 2013

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Purnima Pandit - Department of Applied Mathematics, Faculty of Technology and Engineering, The M. S. University of Baroda, Vadodara, Gujarat, India (email)

Abstract: Real life applications arising in various fields of Engineering and Sciences like Electrical, Civil, Economics, Dietary etc. can be modeled using system of linear equations. In such models it may happen that the values of the parameters are not known or they cannot be stated precisely only their estimation due to experimental data or experts knowledge is available. In such situation it is convenient to represent such parameters by fuzzy numbers (refer [22]). Klir, [15] gave the results for the existence of solution of linear algebraic equation involving fuzzy numbers. The method to obtain solution of system of linear equations with all the involved parameters being fuzzy is proposed here. The $\alpha$-cut technique is well known in obtaining weak solutions, (refer [7]) for fully fuzzy systems of linear equations (FFSL). In this paper, the conditions for the existence and uniqueness of the fuzzy solution are proved.

Keywords:  Fuzzy numbers, fully fuzzy linear equations, $\alpha$-cut, level cut, weak solutions, parallel computing.
Mathematics Subject Classification:  Primary: 03E72.

Received: September 2012;      Revised: March 2013;      Published: November 2013.