Several constructions of quasi-Θ - Ξ functions on bounded lattices

In recent years, overlap and grouping functions, two pivotal types of aggregation functions, have gained growing significance and played an increasingly critical role in diverse academic disciplines. As a result, theoretical research related to their derivative notions has drawn significant scholarly interest in the academic community. Serving as a unified framework for 0-overlap and 1-grouping functions derived from overlap and grouping functions respectively,Θ - Ξ function has been widely studied by numerous scholars since its proposal by Qiao and has gradually emerged as a research focus. The primary focus of this paper lies in constructing quasi-Θ - Ξ functions on bounded lattices. First, the formal definition of quasi-Θ - Ξ functions over bounded lattices is elaborated. Next, basic property of such functions are examined, and the constructions of quasi-Θ - Ξ functions on bounded lattices is further completedthrough two types of special unary functions. On this basis, multiple methods for constructing quasi-Θ - Ξ functions on bounded lattices are proposed as well.