Commutative, associative and non-decreasing functions continuous around diagonal

Document Type : Research Paper

Author

Mathematical Institute, Slovak Academy of Sciences, 81473 Bratislava, Slovakia

Abstract

We characterize all functions that can be obtained as a $z$-ordinal sum of semigroups related to continuous t-norms, t-conorms, representable uninorms and idempotent semigroups. We show that this class of functions is bigger than the class of $n$-uninorms with continuous underlying functions. Vice versa, we show that the characterization of $n$-uninorms with continuous underlying functions via $z$-ordinal sum can be extended
to any  commutative, associative and non-decreasing binary function on the unit interval, which has continuous Archimedean components and is continuous on the diagonal.

Keywords

Iranian Journal of Fuzzy Systems
Volume 19, Issue 2
March and April 2022
Pages 31-48

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