Hybrid structures applied to hemirings

Abstract

Using the notions of a soft set and a fuzzy set, Jun's introduced a new type of notion called a hybrid structure, which is a generalization of soft set and fuzzy set. In this paper, we apply hybrid structure in hemirings and introduce the concept of hybrid h-ideals of hemirings and the related properties are investigated. Some operational properties of hybrid structures are first investigated. The concepts of a hybrid h-sum and a hybrid h-product are discussed and the related properties are investigated. The notions of hybrid h-ideals, hybrid h-bi-ideals and hybrid h-quasi-ideals are introduced and several properties are provided. The notion of a hybrid level set is introduced and the basic properties of hybrid h-ideals, hybrid h-bi-ideals and hybrid h-quasi-ideals are studied in detail. The characterizations of h-hemiregular hemirings are discussed and several important results of a h-hemiregular hemirings are provided.