Ordinal sum of two binary operations being a t-norm on bounded lattice

Xinxing Wu; Qin Zhang; Xu Zhang; Gül Deniz Çaylı; Lidong Wang

doi:10.1109/tfuzz.2021.3066120

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arXiv · 2003.03013

Ordinal sum of two binary operations being a t-norm on bounded lattice

Xinxing Wu·Qin Zhang·Xu Zhang·Gül Deniz Çaylı·Lidong Wang

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Abstract

The ordinal sum of t-norms on a bounded lattice has been used to construct other t-norms. However, an ordinal sum of binary operations (not necessarily t-norms) defined on the fixed subintervals of a bounded lattice may not be a t-norm. Some necessary and sufficient conditions are presented in this paper for ensuring that an ordinal sum on a bounded lattice of two binary operations is, in fact, a t-norm. In particular, the results presented here provide an answer to an open problem put forward by Ertu\u{g}rul and Ye\c{s}ilyurt [Ordinal sums of triangular norms on bounded lattices, Inf. Sci., 517 (2020) 198-216].

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Xinxing Wu, Qin Zhang, Xu Zhang, Gül Deniz Çaylı, Lidong Wang. 2020-03-06. Ordinal sum of two binary operations being a t-norm on bounded lattice. https://doi.org/10.1109/tfuzz.2021.3066120

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