Quasi-regular relations: A new class of relations on sets

Abstract

Following Jiang Guanghao and Xu Luoshan?s concept of conjugative, dually conjugative, normal and dually normal relations on sets, the concept of quasi-regular relations is introduced. Characterizations of quasi-regular relations are obtained and it is shown when an anti-order relation is quasiregular. Some nontrivial examples of quasi-regular relations are given. At the end we introduce dually quasi-regular relations and give a connection between these two types of relations.