Idempotent uninorms on a complete chain

Ouyang, Yao; Zhang, Huapeng; Wang, Zhudeng; Baets, Bernard De

doi:10.1016/j.fss.2022.03.003

Cited by 12 publications

(1 citation statement)

References 16 publications

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“…Nowadays, ‫-ݐ‬norm and ‫-ݐ‬conorms have been extended from [0, 1] to more general lattice-ordered structure (e.g., bounded lattice) [1,3,6,11]. Since 2015, the research on uninorms has also been extended to the bounded lattice [2,7,[13][14][15]. Among them, the Quite recently, Ouyang-Zhang [9] proposed an effective approach to construct uninorms via closure (interior) operators on a bounded lattice.…”

Section: Introductionmentioning

confidence: 99%

On Constructing Uninorms via Closure (Interior) Operators on a Bounded Lattice

Xie,

2023

JMI

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Quite recently, Ouyang-Zhang proposed an interesting approach to construct uninorms via closure (interior) operators on a bounded lattice. In which, they defined an important closure (interior) operator by the notion of universally comparable element when the bounded lattice is complete. However, their operators are not well defined in general when the bounded lattice is not complete. In this paper, we define a closure (interior) operator on bounded lattice, and prove that these operators reduce into Ouyang-Zhang’s operators when the bounded lattice is complete. Hence our closure (interior) operator can be regarded as the extension of Ouyang-Zhang’s closure (interior) operator to noncomplete bounded lattice. At last, the uninorms corresponding to the closure (resp., interior) operator are constructed and discussed

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