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The structure of pseudo-n-uninorms with continuous underlying functions

  • Juraj Kalafut EMAIL logo and Andrea Mesiarová-Zemánková
Published/Copyright: December 12, 2025
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Abstract

The characterization of pseudo-n-uninorms with continuous underlying functions, i.e., the non-commutative version of n-uninorms, where all underlying (pseudo-)t-norms and (pseudo-)t-conorms are continuous, is discussed. The structure of an n-uninorm, which can be decomposed by the z-ordinal sum and the structure of a pseudo-n-uninorm, which cannot be decomposed by this approach, in general, are compared. It is shown that any pseudo-n-uninorm with continuous underlying functions can be decomposed via non-commutative ordinal sum into trivial and representable summands.

MSC 2010: P26B99; 20M10

Funding statement: This work was supported by Grants VEGA 1/0036/23, VEGA 2/0128/24 and APVV-20-0069.

  1. (Communicated by Anatolij Dvurečenskij)

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Received: 2025-06-17
Accepted: 2025-08-22
Published Online: 2025-12-12
Published in Print: 2025-12-17

© 2025 Mathematical Institute Slovak Academy of Sciences

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