Normalization of attribute values in MADM violates the conditions of consistent choice IV, DI and α

In this paper we analyze the influence of various normalization methods (simple, Nijkamp's and vector) on the results of the well-known methods of M(ultiple) A(ttribute) D(ecision) M(aking): SAW, TOPSIS and ELECTRE. It is shown that the final choice recommended by the MADM methods depends on: 1) the type of normalization used; 2) the type of the Likert scale; and 3) the formulation of the attributes. This means that these MADM methods do not satisfy the conditions of consistent choice: independence of the value scale (IV), and descriptive invariability (DI). Also, it is shown that the MADM methods violate the contraction consistency condition α: If an alternative A is the best in a set S of alternatives, then it should be the best in any subset of S to which it belongs. We conclude that the normalization procedures analyzed here could cause inconsistent choices.