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Triangular norms on bounded trellises
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DOI：10.1016/j.fss.2023.01.003.png)
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摘要
En 中文
In this paper, we introduce the notion of a t-norm on bounded pseudo-ordered sets and in particular on bounded trellises (also known as weakly associative lattices), and provide some basic examples. The impact of abandoning transitivity is considerable: on a proper bounded trellis, the meet operation is not a t-norm, and there might actually exist no or even multiple maximal t-norms. We provide a first generic construction method that allows to extend a t-norm on an interior range of a given perpendicular to-semi-trellis to the entire perpendicular to-semi-trellis. Also, we discuss at length an instantiation of this method based on a particular interior range, namely a finite sub-trellis of the set of right-transitive elements of a given trellis. We pay specific attention to bounded pseudo-chains and modular trellises. (c) 2023 Elsevier B.V. All rights reserved.
Keyword:
Binary operation
Pseudo -ordered set
Trellis
t -norm
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2.7
论文数:
7.6K
被引数:
1.5W
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