Solutions of fuzzy relation equations based on continuous t-norms

  • Authors:

  • Bih-Sheue Shieh

  • Affiliations:

  • Department of Mathematics Education, National University of Tainan 33, Section 2, Shu-Lin Street, Tainan 700, Taiwan

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2007

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Abstract

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@?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.