Novel neural algorithms based on fuzzy δ rules for solving fuzzy relation equations: Part III

In our previous work (Li and Ruan, 1997) we proposed a max-min operator network and a series of training algorithms, called fuzzy δ rules, which could be used to solve fuzzy relation equations. The most basic and important result is the convergence theorem of fuzzy perceptron based on max-min operators. This convergence theorem has been extended to the max-times operator network in (Li and Ruan 1997). In this paper, we will further extend the fuzzy δ rule and its convergence theorem to the case of max-* operator network in which * is a t-norm. An equivalence theorem points out that the neural algorithm in solving this kind of fuzzy relation equations is equivalent to the fuzzy solving method (non-neural) in Di Nola et al. (1984) and Gottwald (1984). The proof and simulation will be given.