Geodesic
Normalization of Attribute Values in MADM Violates the Conditions of Consistent Choice IV, DI and $alpha$
Yugoslav journal of operations research, Tome 10 (2000) no. 1, p. 109 .

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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 $\alpha$: lf 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.
Classification : 90B50
Keywords: Normalization, benefit and cost attributes, Likert-type scale, conditions of consistent choice 
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     author = {Dubravka M. Pavli\v{c}i\'c},
     title = {Normalization of {Attribute} {Values} in {MADM} {Violates} the {Conditions} of {Consistent} {Choice} {IV,} {DI} and $alpha$},
     journal = {Yugoslav journal of operations research},
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Dubravka M. Pavličić. Normalization of Attribute Values in MADM Violates the Conditions of Consistent Choice IV, DI and $alpha$. Yugoslav journal of operations research, Tome 10 (2000) no. 1, p. 109 . http://geodesic.mathdoc.fr/item/YJOR_2000_10_1_a9/