Dominance of Ordinal Sums of TL and TP

Dominance is a relation on operations which are defined on a common poset. We treat the dominance relation on the set of ordinal sum t-norms which involve either exclusively the Lukasiewicz t-norm or exclusively the product t-norm as summand operations. We show that in both cases, the question of dominance can be reduced to a simple property of the idempotent elements of the dominating t-norm. We finally discuss the obtained results and possibilities of their generalization.

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