Hybrid ordered ideals in ordered semirings

Abstract

Fuzzy sets, soft sets, and their generalisations have always been important tools for mathematicians and researchers working with uncertainty. Jun proposed a hybrid structure that combined the concepts of a fuzzy set and a soft set. It should be noted that hybrid structures are a combination of soft set and fuzzy set speculation. Our aim is to explore the concept of hybrid ordered ideals and hybrid interior ideals in ordered semirings, as well as look at some of their related properties, which is one of the important aspects of this paper. In order to investigate the structure theory of hybrid ideals in ordered semirings, we define hybrid composition and hybrid addition. We also establish and characterise the regularity of ordered semirings in terms of hybrid structures.