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.