Distributivity of implication operations over t-representable T-norms generated from nilpotent T-norms

Authors:
Michał Baczyński
Affiliations:
Institute of Mathematics, University of Silesia, Katowice, ul. Bankowa, Poland
Venue:
WILF'11 Proceedings of the 9th international conference on Fuzzy logic and applications
Year:
2011

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Abstract

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.