Constructing a fuzzy mathematical morphology: alternative ways

The authors propose two definitions for fuzzy mathematical morphology. They extend the set of possible operations on fuzzy sets by adding morphological operations, taking into account a fuzzy neighborhood. They are compatible with classical mathematical morphology on binary sets or gray-level functions with binary structuring elements. Their properties are presented and comparisons are made between the two approaches. Fuzzy mathematical morphology provides new operations on fuzzy sets and can be applied in particular for introducing spatial uncertain information in a decision process for data fusion