On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras
Hua Zhu, Jian-bin Zhao · Applied mathematics/Applied Mathematics. A Journal of Chinese Universities/Gao-xiao yingyong shuxue xuebao · 2023
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.