**
**#### 3.5.4 Concluding Remarks

All the three ranking methods use a procedure, which has a
common general structure, comprising two steps. In the first step an intermediate
aggregated relational structure is created from the individual preference data.
In the second step, the aggregated relational structure is used to determine
the final rank–order structure.

The input to the second step is a fuzzy relation for both the
fuzzy methods. Naturally, these methods use fuzzy logic in the second step and
the results are also in the fuzzy form. But the final structure they are looking
for is not the same. Fuzzy method–2 assumes a total –linear–order and determines
the final output membership function according to this assumption. If the data
cannot be fitted to such a model, then we shall obtain low membership function
values. In Fuzzy method–1, the precondition is a more general relational structure
in which equivalent non–dominated layers are successively determined. Moreover,
it is possible that in the set of alternatives (or in a part of it) such layers
do not exit. In this case, we may find alternatives not belonging to a core,
but with membership values close to the maximum. This is a sign of instability
of the results ( implied by the input data).

The method Electre constructs a non–fuzzy relationship
in the first step (although in a sub–step one can find fuzzy elements),
and in this respect it differs from both the fuzzy methods. But in the second
step, the same approach is used as in Fuzzy method–1 In this respect, the
only difference is that the concepts of classical logic are used. Therefore,
the results issued by Electre are in a non–fuzzy form. The strength and
stability of the relational structure can be characterized by parameters controlling
the ELECTRE procedure.

The three ranking methods described above can be applied to
the same problems, and their results can reflect the same phenomena from different
aspects, which may provide a deeper understanding of the information represented
in the data than any single method.