Structure of (weakly associative) micanorms

Yang introduced binary MICA (Monotonic Identity Commutative Aggregation) operations called micanorms and micanorms with three weak forms of associativity. This paper investigates general and specific structure of those micanorms. For this, we first recall (weakly associative) micanorms introduced by Yang. Next, we introduce a construction to characterize those micanorms in general. Finally, we consider similar constructions to specify them together with some examples to illustrate those constructions. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.