Quantale-based autoassociative memories with an application to the storage of color images

•Novel quantale-based memories that generalize several lattice computing approaches.•Fundamental theorems on the convergence, storage, and recall properties.•Sparsely connected version with applications to color images.•Potential applications to other multivalued patterns such as hyperspectral images.

In recent years, lattice computing has emerged as a new paradigm for processing lattice ordered data such as intervals, Type-1 and Type-2 fuzzy sets, vectors, images, symbols, graphs, etc. Here, the word “lattice” refers to a mathematical structure that is defined as a special type of a partially ordered set (poset). In particular, a complete lattice is a poset that contains the infimum as well as the supremum of each of its subsets. In this paper, we introduce the quantale-based associative memory (QAM), where the notion of a quantale is defined as a complete lattice together with a binary operation that commutes with the supremum operator. We show that QAMs can be effectively used for the storage and the recall of color images.