Permutation-based finite implicative fuzzy associative memories

Implicative fuzzy associative memories (IFAMs) are single layer feedforward fuzzy neural networks whose synaptic weights and threshold values are given by implicative fuzzy learning. Despite an excellent tolerance with respect to either pasitive or negative noise, IFAMs are not suited for patterns corrupted by mixed noise. This paper presents a solution to this problem. Precisely, we first introduce the class of finite IFAMs by replacing the unit interval by a finite chain image. Then, we generalize both finite IFAMs and their dual versions by means of a permutation on image. The resulting models are referred to as permutation-based finite IFAMs (π-IFAMs). We show that a π-IFAM can be viewed as a finite IFAM, but defined on an alternative lattice structure image. Thus, π-IFAMs also exhibit optimal absolute storage capacity and one step convergence in the autoassociative case. Furthermore, computational experiments revealed that a certain π-IFAM, called Lukasiewicz πμ-IFAM, outperformed several other associative memory models for the reconstruction of gray-scale patterns corrupted by salt and pepper noise.