Roughness in n-ary semigroups based on fuzzy ideals
Jianming Zhan, Xiao-Wu Zhou, Dajing Xiang · Journal of Intelligent & Fuzzy Systems · 2016
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.