Page 210 - Materials Chemistry, Second Edition

208 10. Advancing life cycle sustainability assessment using multiple criteria decision making

benefits and importance of choosing a distance-based method like TOPSIS, Yadav et al. (2019)
developed a free and open-source software (FOSS) named PyTOPS, which efficiently sup-
ports the use of TOPSIS.

10.3 Generic structure of MADM methods

Understanding of decision-making processes requires clarity over a few terminologies that
are commonly used, as explained below (Hwang and Yoon, 1981):
• Objectives: Purpose of solving a problem.
• Characteristics: This is either distinct or common to other elements and helps
understanding an element’s character.
• Attribute or indicator: This is a distinct element that helps in measuring a characteristic.
• Criterion: A criterion is a combination of indicators and helps in understanding the level
up to which the set of indicators can achieve an objective.
• Trade-off: An exchange of one or more attributes within a criterion to achieve a benefit or
advantage.

MADM methods rank or score a finite number of alternatives A i ¼ (A 1 ,A 2 , …,A m ), based
on a set of attributes/criteria/indicators, X j ¼ (X 1 ,X 2 , …,X n ). The information available from
the Decision Makers (DMs) can be represented in the form of a matrix called a decision matrix,
which is shown below:

Criteria=Attributes
⋯ ⋯
X 1 X 2 X 3 X j X n
ðÞ
ðÞ x 2 a 1
A 1 x 1 a 1 ðÞ x 3 a 1 ðÞ ⋯ x n a 1
ðÞ ⋯ x j a 1
ðÞ
ðÞ x 2 a 2
ðÞ ⋯ x j a 2
A 2 x 1 a 2 ðÞ x 3 a 2 ðÞ ⋯ x n a 2
Alternatives=Options ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮
ð
ðÞ ⋯ x j a i
ðÞ x 2 a i
A i x 1 a i ðÞ x 3 a i ðÞ ⋯ x n a m Þ
⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮
ð
ð
ð
ð
ð
A m x 1 a m Þ x 2 a m Þ x 3 a m Þ ⋯ x j a m Þ ⋯ x n a m Þ
10.3.1 Transformation of attributes
Information on alternatives in MADM can be captured by two kinds of attributes: quali-
tative and quantitative. For example, in a problem related to selection of a car, cost and mile-
age can be expressed in quantitative terms (in different units), whereas, reliability of
technology would be expressed in qualitative terms.
Transformation of qualitative attributes into ratio scales is arduous; therefore, most of the
MADM methods resort to either the ordinal scale or the interval scale (Rafiaani et al., 2019;
Hwang and Yoon, 1981). The transformation of the qualitative attribute into ordinal scale is
most commonly practiced. To transform the qualitative attribute to an interval scale, a
10-point scale can be chosen and may be calibrated in one of several ways.