Algebraic Properties of Fuzzy Morphological Operators based on Uninorms

In this paper, an approach to fuzzy mathematical morphology based on conjunctive uninorms is studied. It is proved that the most suitable conjunctive uninorms to be used in this framework are two special kinds of both, representable and idempotent uninorms. For these operators, it is proved that the most usual algebraic and morphological properties are preserved, such as, duality, monotonicity, interaction with union and intersection, invariance under translating and scaling, local knowledge property, extensivity, idempotence, and many others.