## 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:

 3e+72 Theory of fuzzy sets, etc.
Full Text:

### References:

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