Convex combinations of strict t-norms

Alsina, Frank, and Schweizer posed a question whether a non-trivial convex combination of triangular norms can ever be a triangular norm. In this paper we deal with the class of strict t-norms with well-defined first partial derivatives along their zero borders. We show that the answer to the question is negative for certain couples of such t-norms and we state out possible further research.

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