Lattice fuzzy transforms from the perspective of mathematical morphology

The compositions of direct and inverse fuzzy transforms constitute powerful tools in knowledge extraction and representation that have been applied to a large variety of problems in computational intelligence as well as in image processing and computer vision. Fuzzy transforms (FTs) have linear as well as lattice-based versions. In this paper, we extend the latter FTs, known as lattice FTs, and relate these operators and their underlying mathematical structures to the ones of mathematical morphology (MM), in particular to the ones of MM on complete lattices and LL-fuzzy MM.