Hybrid structures applied to hemirings

Article type: Research Article

Authors: Khan, Asghar^{a; *} | Hadi, Asmat^a | Ibrar, Muhammad^a | Jun, Y.B.^b

Affiliations: [a] Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan | [b] Department of Mathematics Education and RINS, Gyeongsang National University, Chinju, Korea

Correspondence: [*] Corresponding author. Asghar Khan, Department of Mathematics, Abdul Wali Khan University, Mardan, 23200, KPK, Pakistan. E-mail: asghar@awkum.edu.pk.

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.

Keywords: Hybrid structure, hybrid structures operations, hybrid h-sum, hybrid h-product, hybrid h-ideals, hybrid h-bi (h-quasi)-ideals, h-Hemiregular hemirings.

DOI: 10.3233/JIFS-171587

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 4873-4889, 2019