Quasi-overlap and quasi-grouping functions on bounded pseudo-ordered sets

Abstract

In this article, we first introduce quasi-overlap and quasi-grouping functions on bounded pseudo-ordered sets, respectively, and give their respective preliminary constructions and the induced quasi-overlap functions on quotient posets.. We then explore the invariant properties under weighting and automorphisms. We also introduce the migrativity, the homogeneity, the idempotency, the cancellation law, the Archimedean and limiting properties of quasi-overlap functions and discuss their relations. We finally present two constructing methods of quasi-overlap functions, which are based on boundary-faithful mappings and adjunctions on bounded psosets and the transitive-endpoints of a bounded trellis, respectively. The corresponding statements are valid for quasi-grouping functions as well.