Aggregation of Operators of Fuzzy Relational Mathematical Morphology: Erosion and Dilation

Abstract

Revising the definitions of fuzzy relational erosion and dilation introduced by N. Madrid et al. (L-fuzzy relational mathematical morphology based on adjoint triples. Inf. Sci. 474, 75-89, 2019), we define the structured versions of these operators and study their basic properties. Our principal interest is aggregation of fuzzy relational, specifically structured, erosions and dilations. We base such aggregation on a dual pair of binary operators ( , ) (e.g. a t-norm and the t-conorm); is applied for aggregation of erosions and for aggregation of dilations.