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

Abstract 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.

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