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Solving systems of linear fuzzy equations by parametric functions – an improved algorithm. (English) Zbl 1121.65026
Summary: J. J. Buckley and Y. Qu [ibid. 43, No. 1, 33–43 (1991; Zbl 0741.65023)] proposed a method to solve systems of linear fuzzy equations. Basically, in their method the solutions of all systems of linear crisp equations formed by the α-levels are calculated. We propose a new method for solving systems of linear fuzzy equations based on a practical algorithm using parametric functions in which the variables are given by the fuzzy coefficients of the system. By observing the monotonicity of the parametric functions in each variable, i.e. each fuzzy coefficient in the system, we improve the algorithm by calculating less parametric functions and less evaluations of these parametric functions. We show that our algorithm is much more efficient than the method of Buckley and Qu [loc. cit.].
65F05Direct methods for linear systems and matrix inversion (numerical linear algebra)
15A06Linear equations (linear algebra)
15A33Matrices over special rings
08A72Fuzzy algebraic structures