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Solutions of fuzzy relation equations based on continuous t-norms. (English) Zbl 1122.03054

Summary: This study is concerned with fuzzy relation equations with continuous t-norms in the form \(ATR = B\), where \(A\) and \(B\) are fuzzy subsets of \(X\) and \(Y\), respectively; \(R \subset X \times Y\) is a fuzzy relation, and \(T\) is a continuous t-norm. The problem is how to determine \(A\) from \(R\) and \(B\). First, an “if and only if” condition of being solvable is presented. Novel algorithms are then presented for determining minimal solutions when \(X\) and \(Y\) are finite. The proposed algorithms generate all minimal solutions for the equations, making them efficient solving procedures.

MSC:

03E72 Theory of fuzzy sets, etc.
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