A New Class of Implicative Fuzzy Associative Memories for the Reconstruction of Gray-Scale Images Corrupted by Salt and Pepper Noise

Implicative fuzzy associative memories (IFAMs) and their dual versions (dual IFAMs) are associative memories that exhibit an excellent tolerance with respect to either eroded or dilated patterns, but they are not suited for the reconstruction of patterns corrupted by mixed noise such as salt and pepper noise. This paper presents a solution to this problem by introducing the class of permutation-based finite IFAMs, or simply π-IFAMs. In few words, π-IFAMs are IFAMs defined on a finite chain equipped with an unusual ordering scheme. Such as the original IFAMs, the novel models exhibit optimal absolute storage capacity and one step convergence in the auto associative case. Computational experiments revealed that a certain π-IFAM, called Lukasiewicz π
_μ
-IFAM, outperformed several other associative memories models for the reconstruction of gray-scale patterns corrupted by salt and pepper noise.