LAUSR

Let I be a normal hyperideal of a Krasner (m,n)-hyperring R, we define the relation ≡I by x ≡I y if and only if f (x,−y, (m−2) 0 )∩ I , ∅, which is an equivalence relation on R. By means of this idea, we propose rough soft hyperrings (hyperideals) with respect to a normal hyperideal in a Krasner (m,n)-hyperring. Some lower and upper rough soft hyperideals with respect to a normal hyperideal are investigated, respectively. Further, we define the t-level set U(μ, t) = {(x, y) ∈ R × R| ∧ z∈ f (x,−y, (m−2) 0 ) μ(z) ≥ t} of a Krasner (m,n)-hyperring R and prove that it is an equivalence relation on R if μ is a fuzzy normal hyperideal of R. By means of this novel idea, we propose rough soft hyperideals by means of fuzzy normal hyperideals in Krasner (m,n)hyperrings. Finally, two novel kinds of decision making methods to rough soft Krasner (m,n)-hyperrings are established.