A Novel Rough Soft Hemirings Based on a Congruence Relation and Corresponding Decision-Making Methods
Xueling Ma, Jianming Zhan and Violeta Leoreanu-Fotea
By means of a novel t-level relation U(μ, t) = {(x, y) ∈ S × S| ∨x+a+z=y+b+z μ(a) ∧ μ(b) ≥ t for all a, b, z ∈ S} of a hemiring S, which is a congruence relation on S if μ is a fuzzy strong h-ideal of S, we propose rough soft strong h-ideals with respect to the above congruence relation in hemirings. Some lower and upper rough soft strong h-ideals with respect to U(μ, t) over hemirings are investigated, respectively. Finally, we put forth a novel kind of decision making method to rough soft hemirings with respect to the congruence relation.
Keywords: Hemiring; (fuzzy) strong h-ideal; rough soft hemiring; congruence relation; decision making
2000 Mathematics Subject Classification: 16Y99; 13E05; 03G25