Ordinal sum construction for uninorms and generalized uninorms

•The most general semigroups that yield uninorms via the ordinal sum construction are identified.•Ordinal sum of uninorms is introduced.•Relations between several types of generalized uninorms are shown.•Continuous additive generators that yield generalized uninorms are characterized.

The ordinal sum construction yielding uninorms is studied. A special case when all summands in the ordinal sum are isomorphic to uninorms is discussed and the most general semigroups that yield a uninorm via the ordinal sum construction, called generalized uninorms, are studied.