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: [email protected].
Abstract: In this paper, we consider the t-level relation of μ by U (μ, t) = {(x, y) ∈ S × S| (μ (x) ∧ μ (y)) ∨ IdS (x, y) ≥ t} of an n-ary semigroup S, which is a congruence relation on S if μ is a fuzzy ideal of S. Based on this novel idea, some basic operations of the lower and upper rough approximations of a soft set are discussed. Furthermore, we propose rough soft n-ary semigroups (ideals, prime ideals) based on a congruence relation in n-ary semigroups. Finally, two kinds of decision making methods for rough soft sets on n-ary semigroups are investigated.
