This is the first chapter associated with an application of lattice algebra. The specific application is in the field of associative memories, a field that goes back to the early days of artificial intelligence. It is for this observation that the first section of this chapter provides a historical background of associative memories. Section 5.2 is fully devoted to lattice-based associative memories, including auto-associative memories and bidirectional associative memories. These memories are tested for their performance in the presence of noise or missing data. A method of enhancing performance in the presence of noise or missing data, called the kernel method, is thoroughly discussed. This method relies on the notion of morphological independence and morphological strong independence. An algorithm for computing kernels for bidirectional memories by induced morphological independence is given in subsection 5.2.6. The chapter concludes with an addendum that discusses the strengths and weaknesses of the lattice matrix approach to associative memories.