In this contribution we will investigate triangular norms T1, T2, T3 such that T1 < T2 < T3 and T3(x, y) - T2(x, y) = T2(x, 1 - y) - T1(x, 1- y). This is an open problem that was published in the monograph by Alsina, Frank and Schweizer. A partial solution to this problem in the case when T2 is the product t-norm, was published already in the mentioned monograph. Further progress in solving the problem for Frank t-norms was done by Havlena at a students' conference. In this contribution, we aim to present another solution to this problem that, in a sense, generalizes the well-known ordinal sum construction for t-norms.(c) 2022 Elsevier B.V. All rights reserved.
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