ESTIMATING WEIGHT

Course: Special Topics in Remote Sensing & GIS

Mirza Muhammad WaqarContact:

mirza.waqar@ist.edu.pk+92-21-34650765-79 EXT:2257

RG712

Estimating Weights

A weight can be defined as a value assigned to an evaluation criterion that indicates its importance relative to other criteria under consideration.

The larger the weight, the more important is the criterion in the overall utility.

Assigning weights of importance to evaluation criteria accounts for:

1. Changes in the range of variation for each evaluation criterion

2. The different degrees of importance being attached to these ranges of variation.

Ranking Method

The simplest method for assessing the importance of weights is to arrange them in rank order in the order of the decision maker’s preference. Straight ranking 1 most important ,2,3…n least

important Inverse ranking 1: least important, 2,3…n most

important Once the ranking established for a set of criteria,

generate numerical weights from rank order ‐information

Ranking Method

P = 0 results in equal weights to all the criteria

P = 1 results in rank sum weight

Site Selection using Ranking Method

Rating Method

The rating methods require the decision maker to estimate weights on the basis of a predetermined scale. i.e. 0 to 100 0 indicted that the criterion can be ignored 100 means only one criterion need to be

considered.

1. Point Allocation Method

50 points to the cost of establishing the plant. (W: 0.5)

30 points to accessibility to the transportation. (W: 0.3)

20 points to the availability of water. (W: 0.2) Sum= 0 (ignore) location Sum=100 Select with

confidence

2. Ratio Estimation Procedure

It starts by assigning an arbitrary weight to the most important criterion, as identified by one of the ranking methods.

A score of 100 is assigned to the most important criterion. Proportionately smaller wrights are then given to criteria lower

in the order. The procedure is continued until a score is assigned to the least

important criterion which shall then be taken as an anchor point for calculating the ratios.

Score of each criterion is divided by the score of the least important criterion Wj/W* where Wj is the score for the jth

criterion and W* is lowest score.

Site Selection using Rating Method

Pair wise Comparison Methods‐

Developed by Saatay (1980) in the context of AHP (Analytic Hierarchy Process)

This method involves pair wise comparisons to ‐create a ratio matrix.

It takes pair wise comparisons as input and ‐produces the relative weights as output.1. Development of the pair wise comparison matrix‐2. Computation of the criterion weights3. Estimation of the consistency ratio

Scale for Pair wise Comparison‐

Example: Site Suitability Analysis

Parameters:1. Price2. Slope3. View

Price is moderately to strongly preferred over slope

Price is very strongly preferred over view Slope is strongly preferred over view

Step1: Development of Pairwise Comparison Matrix

Step2: Computation of the Criterion Weights

This step involves following operations:1. Sum the values in each column of the pair-wise

comparison matrix.2. Divide each element in the matrix by its column

total3. Compute the average of elements in each row of

the normalized matrix.

Step2: Computation of the Criterion Weights

Step3: Estimation of the Consistency Ratio

This step involves following operations: Determine the weighted sum vector by multiplying

the criterion weights with the values of the original pairwise comparison matrix and finally sum these values over rows.

Determine the consistency vector by dividing the weighted sum vector by the criterion weights.

Step3: Estimation of the Consistency Ratio

Step3: Estimation of the Consistency ratio

Computation of Lambda :λ

= λ (3.250+3.119+3.014) / 3 = 3.128

should always be greater than or equal to the λnumber of criterion to be considered.

= n (if the pair wise comparison matrix is a λconsistent matrix)

Step3: Estimation of the Consistency ratio

Computation of CI (Consistency Index) : CI= (λ‐n) / (n-1) = (3.128 3) / (3-1) = 0.064‐

Computation of CR (Consistency Ratio) : CR= CI / RI = 0.064 / 0.58 = 0.110 Where RI is the random index provided by Saaty

and it depends on the number of criterion (n).

Random Inconsistency Index RI

If CR<0.10 the ratio indicates a reasonable level of consistency.

If CR>0.10 the ratio indicates an inconsistent judgment and the relative criterion pair wise comparison matrix needs reconsideration and the whole process must be repeated.

Questions & Discussion