Lower and Upper Approximation of Fuzzy Ideals in a Semiring

he fuzzy set introduced by L.A.Zadeh [16] in 1965 and the rough set introduced by Pawlak [12] in 1982 are generalizations of the classical set theory. Both these set theories are new mathematical tool to deal the uncertain, vague, imprecise and inexact data. In Zadeh fuzzy set theory, the degree of membership of elements of a set plays the key role, whereas in Pawlak rough set theory, the equivalence classes of a set are used to define the lower and upper approximation of a set.