Dual minus partial order

TL;DR

This paper introduces the Dual-minus partial order and related variants, providing characterizations and establishing their relationships with existing partial orders in the mathematical framework.

Contribution

It defines the Dual-minus partial order, characterizes it, and shows how it relates to other known partial orders, expanding the theoretical understanding of these structures.

Findings

Dual-minus partial order characterized and defined

Dual-minus star and sharp partial orders introduced

Relationships among various partial orders established

Abstract

In this paper, we introduce the Dual-minus partial order, get some characterizations of the partial order, and prove that both the dual star partial order and the dual sharp partial order are Dual-minus-type partial orders. Based on the Dual-minus partial order, we introduce the Dual-minus sharp partial order and the Dual-minus star partial order, which are also Dual-minus-type partial orders. In addition, we discuss relationships among the Dual-minus sharp partial order, the D-sharp partial order and the G-sharp partial order(the Dual-minus star partial order, the D-star partial order and the P-star partial order).