More examples:
Sigma_direction(north_west) (U: A < B, V: B < A) = (direction(north_west A B))

To deal with uncertainties, belief values can be associated with the objects, clusters, or cluster strings.
Sigma_direction(north_west) (U: A < B 0.8, V: B < A 0.7) = (direction(north_west A B) 0.7)