Distributivity of Implication Operations over t-Representable T-Norms Generated from Nilpotent T-Norms

Recently, in [3], we have discussed the distributive equation of implications I(x, T1(y, z)) = T2(I(x, y), I(x, z)) over t-representable t-norms generated from strict t-norms in interval-valued fuzzy sets theory. In this work we continue these investigations, but for t-representable t-norms generated from nilpotent t-norms. As a byproduct result we show all solutions of some functional equation related to this case.

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