Distributivity of implication operations over t-representable t-norms in interval-valued fuzzy set theory: The case of nilpotent t-norms

In this article we discuss the distributive equation of implications I(x,T1(y,z))=T2(I(x,y),I(x,z))I(x,T1(y,z))=T2(I(x,y),I(x,z)) over t-representable t-norms generated from nilpotent t-norms in interval-valued fuzzy sets theory. As a byproduct result we show all solutions of some functional equation related to this case.