R-implications and the Exchange Principle:A Complete Characterization
Balasubramaniam Jayaram, Michał Baczyński, Radko Mesiar · 2011
It is well-known that the residual I T of a leftcontinuous t-norm T satisfies the exchange principle (EP), viz., I T (x, I T (y, z)) = I T (y, I T (x, z)) for all x, y, z ∈ [0, 1].However, the left-continuity of T is only sufficient and not necessary, as many examples in the literature illustrate.In this work we study the necessary conditions on a t-norm T for its residual to satisfy (EP).The work presents a complete characterization of the class of t-norms whose residuals satisfy (EP).