Applications of rough soft sets to Krasner (m,n)-hyperrings and corresponding decision making methods

Abstract

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?0, 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(?,t) = {(x,y) ? R x R| ? z?f(x,-y, (m-2)0) ?(z)? t} of a Krasner (m,n)-hyperring R and prove that it is an equivalence relation on R if ? 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.