LetSbe a completely simple semigroup represented as a Rees matrix semigroupM(I,G,P) with normalized sandwich matrixP. On the congruence latticeC(S) ofSwe consider the relationsTi,KandTrwhich identify congruences with the same left trace, kernel and right trace, respectively. These are equivalences whose classes are intervals. The upper and lower ends of these intervals induce the following operators onC(S)Tl, K, Tr, tl, kandtr.We construct here the semigroup generated by these operators as a homomorphic image of a semigroup given by generators and relations and demonstrate the minimality of the latter.