Convex linear T–S functions: A generalization of Frank's equation

The main purpose of this paper is to solve the functional equation , for 0≤λ≤∞ and a pair (T,S) of a t-norm T and a t-conorm S. This equation arises when we consider a convex linear combination of a t-norm and a t-conorm, and set out the problem of finding the intersection of the segments determined by the pairs (Min,Max) and (T,S).