Affiliations:
Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei Province, China
Correspondence:
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Corresponding author. Jianming Zhan. Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei Province 445000, China. Tel.: +86 0718-8437732. E-mail: zhanjianming@hotmail.com.
Abstract: A novel congruence relation U (μ, t) on an n-ary semigroup S is established. We show that U (μ, t) is a congruence relation on an n-ary semigroup S if μ is a fuzzy ideal of S. Based on this idea, we construct the lower and upper approximations in an n-ary semigroup. Furthermore, we introduce the notions of rough ideals and rough prime ideals by means of fuzzy ideals of an n-ary semigroup. In particular, the concepts of rough n-ary semigroups, rough homomorphisms are introduced and some relative properties are also investigated.
