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Unique solvability of max-min fuzzy equations and strong regularity of matrices over fuzzy algebra. (English) Zbl 0852.15011
Summary: A matrix is said to have strongly linearly independent columns (or, in the case of square matrices, to be strongly regular) if for some vector \(b\) the system \(A\otimes x=b\) has a unique solution. We formulate a necessary and sufficient condition for a system of linear equations over a fuzzy algebra to have a unique solution and prove the equivalence of strong regularity and the trapezoidal property. Moreover, an algorithm for testing these properties is discussed.

MSC:
15B33 Matrices over special rings (quaternions, finite fields, etc.)
15A06 Linear equations (linear algebraic aspects)
03E72 Theory of fuzzy sets, etc.
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