On Self-Aggregations of Min-Subgroups

Preservation of structures under aggregation functions is an active area research with applications in many fields. Among such structures, min-subgroups play important role, for instance, mathematical morphology, where they can be used to model translation invariance. Aggregation has only been studied binary functions. However, results concerning preservation the min-subgroup structure aggregations do not generalize arbitrary input size since are associative. In this article, we prove that self-aggregation preserve structure. Moreover, show whenever function strictly increasing on its diagonal, a and have same level sets.