New algorithms of neural fuzzy relation systems with min-implication composition

Abstract

Min-implication fuzzy relation equations based on Booleantype implications can also be viewed as a way of implementing fuzzy associative memories with perfect recall. In this paper, fuzzy associative memories with perfect recall are constructed, and new on-line learning algorithms adapting the weights of its interconnections are incorporated into this neural network when the solution set of the fuzzy relation equation is non-empty. These weight matrices are actually the least solution matrix and all maximal solution matrices of the fuzzy relation equation, respectively. The complete solution set of min-implication fuzzy relation equation can be determined by the maximal solution set of this equation. © Springer-Verlag Berlin Heidelberg 2005.