Two examples of subalgebras of the set of functions between bounded lattices
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This paper deals with the convolution operations on the set of functions between bounded lattices. Firstly, we show a subset of the set of functions that is both a bisemilattice and a Birkhoff system under the convolution operations and then show another subset of the set of functions that is a bounded distributive lattice under the convolution operations, while the domain lattice of the functions does not need to be distributive.
KeywordsConvolution operations Bisemilattice Birkhoff system Distributive lattice
The authors thank the referees for their valuable comments and suggestions.
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Conflict of interest
All the authors in the paper have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
- Harding J, Walker C (2018) A topos view of the type-2 fuzzy truth value algebra. arXiv:1810.07565