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 [Formula: see text] which is the generalization of fuzzy ideal of a nearring. Then we prove that the level set [Formula: see text]) is a strong ideal of [Formula: see text] if and only if the fuzzy set [Formula: see text] is a fuzzy ideal of [Formula: see text] Later, we define upper approximations and lower approximations of a subset of a seminearring with respect to the equivalence relations [Formula: see text] and [Formula: see text] on [Formula: see text] induced by strong ideals and equiprime strong ideals, respectively. Further, we characterize the relationship among these approximations and are explained with suitable examples.