The ranking representation r=(r_1,...,r_m) contains the ranks assigned to the objects,
and means that the ith object is in r_ith position.
The ordering representation o=(o_1,...,o_m) means that object o_i is in the ith position.
Let us consider the following example to illustrate both notations: a judge, which has to rank three holidays destinations according to its preferences, O1 = Countryside, O2 =Mountain and O3 = Sea, ranks first Sea, second Countryside, and last Mountain. The ordering result of the judge is o = (3, 1, 2) whereas the ranking result is r = (2, 3, 1).