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 \(\alpha\)-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.].


65F05 Direct numerical methods for linear systems and matrix inversion
15A06 Linear equations (linear algebraic aspects)
15B33 Matrices over special rings (quaternions, finite fields, etc.)
08A72 Fuzzy algebraic structures


Zbl 0741.65023
Full Text: DOI


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