Self-dual pseudo-uninorms

Document Type : Research Paper

Author

Dept. Mathematics, Slovak University of Technology, Radlisnkeho 11, 810 05 Bratislava, Slovakia

10.22111/ijfs.2026.53842.9539

Abstract

Uninorms are a common generalization of t-norms and t-conorms, which are mutually dual aggregation functions. However, no uninorm is self-dual. In this paper, we show that dropping the axiom of commutativity allows a construction for self-dual pseudo-uninorms. We characterize three important classes of self-dual pseudo-uninorms, namely the representable pseudo-uninorms, pseudo-uninorms with all elements idempotent and those pseudo-uninorms that have both underlying functions continuous. Finally, it is proven that each self-dual pseudo-uninorm has continuous underlying functions. Note such a slight change has only a little effect on the continuity and commutativity of the pseudo-uninorm.

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References

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Iranian Journal of Fuzzy Systems
Volume 23, Issue 2
March and April 2026
Pages 53-64

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