Fuzzy Ideals and Roughness in Seminearrings

Seminearrings are the generalization of well-known algebraic structures such as semirings, nearrings and rings. In this work, we discuss results on fuzzy ideals and rough sets in seminearrings. Initially, we introduce the notion of fuzzy ideal of a seminearring S, which is the generalization of fuzzy ideal of a nearring. Then we prove that the level set σt(t [0,σ(0)]) is a strong ideal of S if and only if the fuzzy set σ is a fuzzy ideal of S. Later, we define upper approximations and lower approximations of a subset of a seminearring with respect to the equivalence relations Q(E) and Q(E,a) on S induced by strong ideals and equiprime strong ideals, respectively. Further, we characterize the relationship among these approximations and are explained with suitable examples.