Non-commutative ordinal sum construction

The construction methods for associative functions are discussed. The focus is on summand-based construction methods as an extension of the ordinal sum and the z -ordinal sum. While the ordinal sum and the z -ordinal sum can be assumed to be commutative summand-based construction methods, since they construct commutative functions from commutative summands, the non-commutative ordinal sum, which constructs non-commutative functions from commutative summands is introduced. The decomposition of a semi-t-operator via a non-commutative ordinal sum is also shown.