On Extensions of Quasi-Overlap and Quasi-Grouping Functions Defined on Bounded Lattices

TL;DR

This paper introduces a method to extend quasi-overlap and grouping functions from a sublattice to a larger bounded lattice using a generalized sublattice concept, enhancing their applicability.

Contribution

It presents a novel extension technique for quasi-overlap and grouping functions based on a broader sublattice definition, expanding their theoretical framework.

Findings

Extension method for quasi-overlap functions

Extension method for quasi-grouping functions

Applicability to more general lattice structures

Abstract

In this paper, we propose a method of extending quasi-overlap and grouping functions defined on a sublattice $ M $ of a bounded lattice $ L $ to this lattice considering a more general version of sublattice definition, introduced by Palmeira and Bedregral.