Abstract
A 2-dimension linguistic lattice implication algebra (2DL-LIA) can build a bridge between logical algebra and 2-dimension fuzzy linguistic information. In this paper, the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed. Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated. Moreover, it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.
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Supported by the National Natural Science Foundation of China(11501523, 61673320).
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Zhu, H., Zhao, Jb. On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras. Appl. Math. J. Chin. Univ. 38, 274–292 (2023). https://doi.org/10.1007/s11766-023-4308-5
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DOI: https://doi.org/10.1007/s11766-023-4308-5
Keywords
- derivation
- Boolean element
- Lattice implication algebra (LIA)
- 2-dimension linguistic lattice implication algebra (2DL-LIA)
- 2-dimension fuzzy linguistic information