Binary relations induced from quasi-overlap functions and quasi-grouping functions on a bounded lattice

Binary relations induced from aggregation operations on a bounded lattice have received more and more attention. In this paper, we investigate binary relations induced from a quasi-overlap function and a quasi-grouping function on a bounded lattice L, respectively. At first, we provide a new approach to generate binary relations by a lattice-valued quasi-overlap function and a lattice-valued quasi-grouping function. In this new approach, we get rid of the restriction of the Intermediate Value Theorem, which is the main tool in the case L= [0 , 1]. Then we discuss the connections between the induced binary relations and the natural order on L. Finally, we demonstrate the conditions under which the binary relations can become a reflexive, anti-symmetric, transitive relation as well as a partial order. In particular, we explore the binary relations induced from two classes of special quasi-overlap (resp. grouping) functions, which are generated by a quasi-pseudo-automorphism and a 0 _L, 1 _L-aggregation function, respectively.