Residual implications and left-continuous t-norms which are ordinal sums of semigroups

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Abstract

It is known that left-continuous t-norms which are the ordinal sums of semigroups can be represented as ordinal sums of left-continuous t-subnorms. The structure of the related residual implications is shown to be an ordinal sum of residual implications linked to the corresponding left-continuous t-subnorms. Residual implications related to t-subnorms generated by continuous additive generators are also investigated, and several examples are given.

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