Roughness in Hemirings Based on Fuzzy Strong h-Ideals
Jianming Zhan, Kuanyun Zhu and Violeta Leoreanu-Fotea
A novel congruence relation of hemirings is established. We show that U (μ, t) is a congruence relation on S if μ is a fuzzy strong h-ideal of a hemiring S. Based on this idea, we construct lower and upper approximations in a hemiring with respect to a fuzzy strong h-ideal of a hemiring. Some novel characterizations of rough hemirings based on fuzzy strong h-ideals are discussed. In particular, the characterizations of two kinds of hemirings are investigated by means of fuzzy strong h-ideals.
Keywords: Fuzzy set, rough set, lower(upper) approximation, fuzzy strong h-ideal, idempotent hemiring.