The \(\Theta \) – \(\Xi \) function is a unified framework for 0-overlap functions and 1-grouping functions on the unit interval. Building upon this, the present article extends the concept to complete lattices and provides constructions of \(\Theta \) – \(\Xi \) functions on complete lattices. Additionally, our paper explores the algebraic relationship between 0-overlap functions and 1-grouping functions on a totally ordered complete lattice, demonstrating that the set of all 0-overlap functions and the set of all 1-grouping functions on a totally ordered complete lattice are isomorphic as lattices.
