L-Fuzzy mathematical morphology: An extension of interval-valued and intuitionistic fuzzy mathematical morphology

The concept of an L-fuzzy set generalizes not only the concept of a fuzzy set but also the concepts of interval-valued fuzzy sets and intuitionistic fuzzy sets (as will become clear in this paper). In addition, the class of L-fuzzy sets forms a complete lattice whenever the underlying set L constitutes a complete lattice. Based on these observations, we develop a general approach towards L-fuzzy mathematical morphology in this paper. Our focus is in particular on the construction and on the properties of interval-valued and intutionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of L-fuzzy mathematical morphology.