Kybernetika 55 no. 1, 24-43, 2019

On the distributivity equation for uni-nullnorms

Ya-Ming Wang and Hua-Wen LiuDOI: 10.14736/kyb-2019-1-0024


A uni-nullnorm is a special case of 2-uninorms obtained by letting a uninorm and a nullnorm share the same underlying t-conorm. This paper is mainly devoted to solving the distributivity equation between uni-nullnorms with continuous Archimedean underlying t-norms and t-conorms and some binary operators, such as, continuous t-norms, continuous t-conorms, uninorms, and nullnorms. The new results differ from the previous ones about the distributivity in the class of 2-uninorms, which have not yet been fully characterized.


uninorms, fuzzy connectives, T-norms, T-conorms, uni-nullnorms, nullnorms, distributivity equation


46F10, 62E86


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