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Uninorms on bounded trellises
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DOI：10.1016/j.fss.2024.108898.png)
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Abstract
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In this paper, we construct uninorms on a bounded trellis based on t-(co)norms on a perpendicular to(proves)semi-trellis and closure (interior) operators. The key is how to ensure the monotonicity of the constructed binary operation, which is closely related to the neutral element. We propose the uninorms on bounded trellises and study some basic properties. Specially, the neutral element must be middle-transitive if there is a uninorm on a bounded trellis. Based on this, we introduce the construction method according to the left- and middle-transitive neutral element via t -norms, t-superconorms and closure operators on bounded trellises satisfying (CC1). Similarly, we provide the construction method when the neutral element is right- and middle-transitive via t-conorms, t-subnorms and interior operators on bounded trellises satisfying (CC2). Finally, we give two methods of constructing uninorms if the neutral element is middle-transitive and is not in any cycle.
Keywords:
Uninorm
Closure operator
Interior operator
T-subnorm
Bounded trellis
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