Page 217 - Materials Chemistry, Second Edition

10.5 Challenges in the application of MADM for LCSA 215
unique characteristics. Kalbar et al. (2017a) used linear regression across the indicator scores
to assess preferential independence. Similarly, inputs of an indicator are consistent if it sat-
isfies the condition of asymmetry, transitivity, and comparability.
A detailed discussion about the above requirements and their significance with examples
is provided in French (1986). Sepp€ al€ a et al. (2001) suggest that if inputs for an indicator have
different units then to be consistent during analysis, all the indicators must be transformed
into a common dimensionless unit using an appropriate normalization approach. Different
methods use different aggregation methods with varied types of inputs and have different
procedures for transformation of indicators. Therefore, it is recommended that an aggrega-
tion model must be selected before collecting inputs from stakeholders (Sepp€ al€ a et al.,
2001). In specific cases, a set of indicators may have negative values compared to another
set of indicators with nonnegative values. During this type of scenario, the indicator scores
should be normalized within a value range of 0 to 1 or 1 to 1 (excluding strict negative
and positive values) using suitable normalization technique, thus helping in attaining consis-
tency during analysis (Rowley, 2012).

10.5.5 Weighting of the indicators
Weighting is an essential step in MADM, which facilitates the incorporation of stake-
holders’ preferences. Different weighting sets are subjective, and representing various
stakeholder groups, can be formed to observe the change in the results (Kalbar et al.,
2017a). Zardari et al. (2015) report that pairwise comparison, point allocation, rating methods,
trade-off analysis, and ranking methods are commonly used methods for weighting of
indicators. Each of these weighting methods has its extent of disadvantages (inaccuracy,
confusions regarding foundation of involved theory, and complexity). For example,
Wang et al. (2009) suggest the “equal weights method” is the easiest and most popular
method of assigning weights and requires minimal knowledge or input from decision-maker;
however, equal weights method does not take into account difference in criteria and their
significance in a decision problem. Also, equal weights method does not weight the attribute
equally in its absolute sense, in the case where more than one attribute characterizes a
criterion.
Ahlroth et al. (2011) provided a taxonomy of all available weighting methods divided into
monetary and nonmonetary methods. Kalbar et al. (2017a) report that the most commonly
used monetary methods of weighting are converting impacts or damages into monetary
valuation using willingness-to-pay, and converting damages into cost incurred and midpoint
impacts; and the most commonly used nonmonetary weighting methods are distance-to-
target and panel methods. Panel methods can also be known as subjective weighting (SW).
There are a number of other methods for eliciting weights. Wang et al. (2009) suggests that
other methods of weighting are objective weighting (OW) and combined weighting (CW).
In OW, weight is obtained from mathematical models. CW is a combination of both SW
and OW. Pair-wise comparison, entropy, and additive synthesis are some of the popular
SW, OW, and CW methods, respectively. Zardari et al. (2015) and Eckenrode (1965) suggest
that methods that directly take weights may not be accurate; therefore, a method should be
selected that derives weights from given information. Additionally, one must also look at