Solutions of fuzzy relation equations based on continuous t-norms

  title={Solutions of fuzzy relation equations based on continuous t-norms},
  author={Bih-Sheue Shieh},
  journal={Inf. Sci.},
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; R X · 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… CONTINUE READING
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