Convex linear T-S functions: A generalization of Frank's equation
The main purpose of this paper is to solve the functional equation T + lambda S = Min + lambda Max, for 0 <= lambda <= infinity 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). (C) 2013 Elsevier B.V. All rights reserved.
frank's equation convex linear combination aggregation function associativity copula dual copula triangular norm triangular conorm