Approximate solutions of systems of fuzzy relation equations

摘要

We generalize our previous results regarding approximate solutions of fuzzy relation equations (Yuan and Klir, 1993) to systems of fuzzy relation equations. By employing the equality index proposed by Gottwald (1985), we introduce a goodness measure of the performance of approximate solutions and derive a lower bound and an upper bound of solvability of systems of fuzzy relation equations. We also show that our results generalize those presented for one-dimensional fuzzy relation equations (Nola et al., 1989).