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In this paper, a new approach to fuzzy mathematical morphology based on discrete t-norms is studied. 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, extensitivity, idempotence, and many others. In fact, all properties satisfied...
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...
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