5.4.2.2
Weighting-Scaling Checklists
Weighting-scaling checklists summarise impacts of an alternative in terms of an overall index or score. Canter (1996) generalised the form of index as below:
Where Indexj = Composite index for jth alternative
n = number of decision factors
IWi = importance weight of ith decision factor
Rij = scaled rating of jth alternative for ith decision factor.
Weighting - scaling checklists involve the following three important steps.
1. Importance weighting of decision factors.
2. Scaling rating or ranking of alternatives.
3. Development of decision matrix.
Weighting-Scaling checklists represent adaptation of multi-attribute decision making techniques (Lahlou 1991, Lahlou and Canter 1993) used in other fields. Usually a measure of relative importance is derived for each of the environmental parameters listed in the checklist. The impacts of various alternatives are then compared on the basis of these derived values (Smith 1993). Examples of importance-weighting techniques used in EIA studies include the following :
All of the above are well developed techniques within the realm of 'decision science'. A discussion on these techniques is therefore kept outside the ambit of this study.
The step of importance-weighting of the environmental parameters is followed by the next major step, the scaling, rating or ranking of each alternative relative to each decision factor (Lahlou 1991). Established EIA methodologies often utilise unranked paired-comparison technique for this purpose. Usually each alternative is considered relative to every other alternative. This method shows good scope of application in devising an EIA methodology.
Largely following Canter (1996) an illustration is put forward to ellucidate the basic steps involved in the unranked paired comparison technique.
While deciding which alternative is the best it must be borne in mind that the decision factors (the environmental attributes) are not necessarily of the same importance. As an example, let it be supposed that there are four decision factors F1 through F4. The rule of the comparison is that all the factors and a dummy factor F5 will be considered pair wise. In this case following pairs are to be considered; F1-F2, F1-F3, F1-F4, F1-F5, F2-F3, F2-F4, F2-F5, F3-F4, F3-F5, and F4-F5. Total 10 pairs. Thus for N number of factors (including dummy factor) there would be N(N-1)/2 pairs to be compared. The rule of comparison is that while F1 and F2 are being compared, if F1 is more important than F2 then F1 is assigned a weight of 1 while F2 is assigned a weight of 0. It should be noted that the assignment of 0 to a member of a pair does not denote no importance, it simply means that in the pair considered, it is of less importance. The use of this unranked paired-comparison technique for four factors is shown in Table 5.1.
Table 5.1 Example of Paired-Comparison Technique for Importance Weight Assignments
FIC = Factor Importance Coefficient
The dummy factor precludes the net assignment of a value of 0 to any of the basic factors (F1 through F4). The individual weight assignments are summed up and the factor importance coefficient, FIC, is arrived at by dividing the sum value of factor with the sum value of all the factors. Thus FIC for the factor Fi (i=1, 2, 3, 4) may be expressed as
Where i = 1,2,3...... N-1
and N = number of decision factors including dummy factor
Sum of all the FICs should be equal to 1.00
From the FIC column of Table 5.1 one understands that among the four factors F1 is the most important, followed by F4, F2 and F3. This technique is basically a rank ordering technique.
As may be observed from the FIC column of Table 5.1 the type of scales used here is an 'ordinal' one that ranks decision factors in order. It does not convey how much better F1 is than F4, but simply indicates the relative order (Westman 1985). Quantitative degree of difference between 'decision factors', or for that matter between 'alternatives', can be indicated by using internal scales. An internal scale represents equal difference by equal numerical intervals throughout the scale.
After computing the factor importance coefficients, FICs, the same technique of unranked pair comparison may be used for the scaling of alternatives. To illustrate the following example is again borrowed from Canter (1996).
Let there be three alternatives; A1, A2 and A3, to be evaluated relative to the four decision factors F1, F2, F3 and F4 for which the FICs have already been computed. The unranked pair comparison technique would involve preparation of four tables showing ranking of alternatives relative to each of the four factors. Thus for N number of decision factors N such tables would be generated.
For every decision factor, each alternative is considered relative to every other alternative. For each pair of alternatives the more-desirable alternative is assigned a value of 1 and the less-desirable alternative is assigned a value of 0. Relevant information needed for such unranked pair comparison is given in Table 5.2.
Weighting-scaling checklists summarise impacts of an alternative in terms of an overall index or score. Canter (1996) generalised the form of index as below:
Where Indexj = Composite index for jth alternative
n = number of decision factors
IWi = importance weight of ith decision factor
Rij = scaled rating of jth alternative for ith decision factor.
Weighting - scaling checklists involve the following three important steps.
1. Importance weighting of decision factors.
2. Scaling rating or ranking of alternatives.
3. Development of decision matrix.
Weighting-Scaling checklists represent adaptation of multi-attribute decision making techniques (Lahlou 1991, Lahlou and Canter 1993) used in other fields. Usually a measure of relative importance is derived for each of the environmental parameters listed in the checklist. The impacts of various alternatives are then compared on the basis of these derived values (Smith 1993). Examples of importance-weighting techniques used in EIA studies include the following :
| 1. Ranking technique. | 2. Rating technique |
| 3.Unranked pair-wise comparison. | 4. Delphy technique. |
| 5.Nominal group process. | 6. Multiattribute utility measurement. |
| 7.Ranked pair-wise comparison | . |
All of the above are well developed techniques within the realm of 'decision science'. A discussion on these techniques is therefore kept outside the ambit of this study.
The step of importance-weighting of the environmental parameters is followed by the next major step, the scaling, rating or ranking of each alternative relative to each decision factor (Lahlou 1991). Established EIA methodologies often utilise unranked paired-comparison technique for this purpose. Usually each alternative is considered relative to every other alternative. This method shows good scope of application in devising an EIA methodology.
Largely following Canter (1996) an illustration is put forward to ellucidate the basic steps involved in the unranked paired comparison technique.
While deciding which alternative is the best it must be borne in mind that the decision factors (the environmental attributes) are not necessarily of the same importance. As an example, let it be supposed that there are four decision factors F1 through F4. The rule of the comparison is that all the factors and a dummy factor F5 will be considered pair wise. In this case following pairs are to be considered; F1-F2, F1-F3, F1-F4, F1-F5, F2-F3, F2-F4, F2-F5, F3-F4, F3-F5, and F4-F5. Total 10 pairs. Thus for N number of factors (including dummy factor) there would be N(N-1)/2 pairs to be compared. The rule of comparison is that while F1 and F2 are being compared, if F1 is more important than F2 then F1 is assigned a weight of 1 while F2 is assigned a weight of 0. It should be noted that the assignment of 0 to a member of a pair does not denote no importance, it simply means that in the pair considered, it is of less importance. The use of this unranked paired-comparison technique for four factors is shown in Table 5.1.
Table 5.1 Example of Paired-Comparison Technique for Importance Weight Assignments
|
Factor
|
Assignment of weight
|
Sum
|
FIC
|
|||||||||
|
F1
|
1
|
1
|
1
|
1
|
.
|
.
|
.
|
.
|
.
|
.
|
4
|
0.40
|
|
F2
|
0
|
.
|
.
|
.
|
1
|
0
|
1
|
.
|
.
|
.
|
2
|
0.20
|
|
F3
|
.
|
0
|
.
|
.
|
0
|
.
|
.
|
0
|
1
|
.
|
1
|
0.10
|
|
F4
|
.
|
.
|
0
|
.
|
.
|
1
|
.
|
1
|
.
|
1
|
3
|
0.30
|
|
F5 (dummy)
|
.
|
.
|
.
|
0
|
.
|
.
|
0
|
.
|
0
|
0
|
0
|
0.00
|
|
Total
|
.
|
10.00
|
1.00
|
|||||||||
The dummy factor precludes the net assignment of a value of 0 to any of the basic factors (F1 through F4). The individual weight assignments are summed up and the factor importance coefficient, FIC, is arrived at by dividing the sum value of factor with the sum value of all the factors. Thus FIC for the factor Fi (i=1, 2, 3, 4) may be expressed as
Where i = 1,2,3...... N-1
and N = number of decision factors including dummy factor
Sum of all the FICs should be equal to 1.00
From the FIC column of Table 5.1 one understands that among the four factors F1 is the most important, followed by F4, F2 and F3. This technique is basically a rank ordering technique.
As may be observed from the FIC column of Table 5.1 the type of scales used here is an 'ordinal' one that ranks decision factors in order. It does not convey how much better F1 is than F4, but simply indicates the relative order (Westman 1985). Quantitative degree of difference between 'decision factors', or for that matter between 'alternatives', can be indicated by using internal scales. An internal scale represents equal difference by equal numerical intervals throughout the scale.
After computing the factor importance coefficients, FICs, the same technique of unranked pair comparison may be used for the scaling of alternatives. To illustrate the following example is again borrowed from Canter (1996).
Let there be three alternatives; A1, A2 and A3, to be evaluated relative to the four decision factors F1, F2, F3 and F4 for which the FICs have already been computed. The unranked pair comparison technique would involve preparation of four tables showing ranking of alternatives relative to each of the four factors. Thus for N number of decision factors N such tables would be generated.
For every decision factor, each alternative is considered relative to every other alternative. For each pair of alternatives the more-desirable alternative is assigned a value of 1 and the less-desirable alternative is assigned a value of 0. Relevant information needed for such unranked pair comparison is given in Table 5.2.