Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Wang, Xue-ping, Liu, Hong-fei
Institution: Sichuan Normal University
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G144394107
OpenAlex ID: W7214044321