On the distributivity for the ordinal sums of implications over t-norms and t-conorms.

Recently, ordinal sums of fuzzy implications yielding fuzzy implications have been extensively studied. In particular, Drygaś and Król proposed a new method to construct fuzzy implications inspired by the constructions of residual implications of ordinal sums of triangular norms and ordinal sums of overlap functions. Compared with the other ones, one of the greatest advantages of the ordinal sums of implications constructed by Drygaś and Król is that they are fuzzy implications satisfying left ordering property. In this article, we focus on the distributivity for the ordinal sums of implications constructed by Drygaś and Król. More specifically, we present the necessary and sufficient conditions for the solutions of the distributivity equations involving fuzzy implications in the sense of Drygaś and Król. [ABSTRACT FROM AUTHOR]