Lattice-valued overlap and quasi-overlap functions

As an important class of aggregation operators, the notion of overlap functions was first presented in 2009 in order to be considered for applications in image processing context. Later, many other researches arised bringing some variations of those functions for different purposes. Here, our main goal is defining overlap functions on lattices and discuss how a weakned version of it, named quasi-overlaps, works when continuity is eliminated from the definition. Some properties of quasi-overlaps on lattices, namely convex sum, migrativity, homogeneity, idempotency and cancellation law are investigated. Also, Finally, properties related to continuity as Archimedean and limiting are studied. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

Overlap functions, an important class of aggregation operators, were first introduced in 2009 for applications in image processing. Quasi-overlaps, a weakened version, on lattices were discussed without continuity, exploring properties like convex sum, migrativity, homogeneity, idempotency, and cancellation law. Properties related to continuity, such as Archimedean and limiting, were also studied.