Solutions of fuzzy relation equations based on continuous t-norms

This study is concerned with fuzzy relation equations with continuous t-norms in the form ATR=B, where A and B are the fuzzy subsets of X and Y, respectively; [email protected]?XxY 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.

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