Kybernetika 62 no. 2, 163-189, 2026

Migrativity of continuous t-conorms with respect to ordinal sum implications

Xinxin Yan and Hongjun ZhouDOI: 10.14736/kyb-2026-2-0163

Abstract:

The topic of migrativity among aggregation functions is of significant interest from both theoretical and practical perspectives within the field of fuzzy set theory. Nonetheless, there is a scarcity of characterizations in the existing literature concerning the migrativity of ordinal sum implications, especially when the ordinal summands are positioned along the major diagonal line of $[0,1]^{2}$, and this area has not been thoroughly investigated. The present paper aims to fill this gap by conducting a detailed study on the migrativity of t-conorms with respect to ordinal sum implications. We provide the structural solutions to the migrative functional equation for t-conorms with respect to ordinal sum implications, which depend on the position of parameter $\alpha$ within the range of natural negation $N$. The characterizations under which t-conorms are $\alpha$-migrative with respect to ordinal sum implications are obtained by presenting ordinal sum representations of the underlying functions.

Keywords:

T-conorm, Migrativity, Ordinal sum implication

Classification:

03B52, 03E72

paper.pdf

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