Before revision:  We define the least upper bound and the greatest lower bound for both sides of the matching market , and we prove that with these binary operations the set of random stable matchings forms two dual lattices.
After revision:  We define a partial order on the random stable set and present two intuitive binary operations to compute the least upper bound and the greatest lower bound for both sides of the matching market , and we prove that with these binary operations the set of random stable matchings forms two dual lattices.