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.