Kybernetika 61 no. 5, 712-740, 2025

Constructions of uninorms with ordinal sum underlying t-norms (t-conorms) on bounded lattices

Hua-Wen LiuDOI: 10.14736/kyb-2025-5-0712

Abstract:

Uninorms are a special type of aggregation operators proposed by Yager and Rybalov in 1996, and since then, there have been numerous research achievements on uninorms on the unit real interval. In 2015, the concept of uninorms was extended to a more general algebraic structure - bounded lattices. This article aims to study the construction of uninorms on bounded lattices. We first provide the construction methods of uninorms on bounded lattices by using ordinal sum t-norms or ordinal sum t-conorms. Then, we clarify that the new methods are the extensions of some construction methods in literature. Finally, some illustrative examples for the new constructions of uninorms on bounded lattices are provided. This study is the first attempt to construct using the ordinal sum underlying operators and it will open up new ideas for in-depth analysis of the structure of uninorms on bounded lattices.

Keywords:

aggregation operators, uninorms, bounded lattices, t-norms, ordinal sums

Classification:

03E72, 03B52, 03G10, 94D05

paper.pdf

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