Page 211 - Materials Chemistry, Second Edition

10.3 Generic structure of MADM methods 209
Any negative values in the indicator scores also needs to be transformed, as negative
values will affect the final outcome of MADM method. Shifting of all indicator score values
above zero is commonly used method to handle negative values (Kalbar et al., 2012).

10.3.2 Normalization of attributes
Normalization of the attributes is not required in all of the MADM methods, but many
compensatory MADM methods like maximin, simple additive weighting, TOPSIS,
ELECTRE, etc., require normalization to perform the further mathematical procedures with
comparable scales. Before proceeding towards normalization, it is important to note different
types of attributes as given by Yoon and Hwang (1995).

• Benefit attributes: Offer an increasing monotonic utility; that is, the higher the attribute
value, the more its preference; for example, fuel efficiency.
• Cost attributes: Offer a decreasing monotonic utility; that is, the higher the attribute value,
the less its preference; for example, production cost.
• Nonmonotonic attribute: Offer nonmonotonic utility, such as room temperature in an office,
or blood sugar level in human body, where maximum utility is located somewhere in the
middle of an attribute range.
Shih et al. (2007) organized a few conventional normalization methods in tabular form
based on the works of Milani et al. (2005), Yoon and Hwang (1995), and Hwang and Yoon
(1981). Vector normalization and linear normalization are commonly used normalization
methods in MADM.

10.3.3 Weighting attributes

It is almost common that DMs may have differences in preferences or importance for var-
ious attributes on which alternatives are to be evaluated or ranked. This preference or impor-
tance can be taken into consideration using assignments of weights to the attributes. The DM
may use a cardinal or ordinal scale to express his or her preference among attributes. MADM
methods require cardinal weights, that is w¼(w 1 , …, w j , … W n ), where w j is weight assigned
to the jth attribute. Cardinal weights are normalized to sum to 1, that is P W j ¼1. Hwang and
Yoon (1981) reported four methods to assign weights, viz., eigenvector method, weighted
least square method, entropy method, and linear programming techniques for
multidimensional analysis of preferences (LINMAP).

10.3.4 Ranking of alternatives
Once the data is transformed and normalized, then the next step of MADM methodology
is to rank the alternative using the attributes normalized score. Each of the MADM methods
has its algorithm or procedure to aggregate and process the data on attributes. The outcome
from MADM methods is most of the time ranking on some index, priority, or relative
measure. MADM methods have their intrinsic properties and, hence, may generate different
ranking for the same decision matrix. Therefore, after ranking of alternatives, sensitivity