Abstract: We considered the interrelations among the basic algebraic properties of grouping functions, such as idempotency, strict monotonicity, Archimedean property. We gave the results that the ordinal sum of a series of grouping functions was still a grouping function by means of a way similar to the ordinal sum of semigroups. Furthermore, we rectified several errors in describing the above properties about overlap functions in the existing literature.

Key words: grouping function, idempotent element, limit condition, Archimedean, ordinal sum