Paper Title
Approximations In Algebraic Systems

Abstract
We introduce the notions of lower and upper approximations for the fuzzy ideal of a right near-ring N. We dene a fuzzy congruence relation on N and obtain elementary properties of these approximations. We prove that the lower and upper approximations are the fuzzy ideals of N. We Find that if an fuzzy ideal has the insertion of factors property then corresponding rough ideal has the same property. Finally, we discuss rough fuzzy prime ideals of near-rings and related algebraic systems. We also discuss notions concerned to essential and uniform rough ideals module over a near-ring. Keywords- Algebraic systems, Nearring, lower and upper approximations