CHAPTER 2: ESTABLISHING REGION MAPS OF LAND VALUE
2.2. Introduction of Analytic Hierarchy Process (AHP)
The Analytic Hierarchy Process (AHP) is a multi-criteria decision-making approach that can be used for solving complex and opinions of the stakeholders on only one assessment but also considering the different criteries at the same time, which can not be done by normal decision- unstructured problems. It helps to capture both qualitative and quantitative aspects of a decision problem and provides a powerful yet simple way of weighting the decision criteria, thus reducing bias in decision-making (Saaty, 1970s; Georgiou et al., 2012; Al-Abadi et al., 2016).
Figure 2.1: AHP diagram (Saaty, 1980)
This model is particularly useful when making decisions in a group is necessary. AHP can help identify and evaluate criteria, analyze the data collected by basing on these criteria, and make the process of making decision faster and more accurate. AHP Processing based on pairs of comparison among indicators, then these pairs are combined.
2.2.2. The basic steps of AHP
- Determining the criteria
Identify the different indicators affecting the object that is being evaluated. For example, there are indicators affecting land plots while conducting valuation as natural indicators, economic indicators - social, environmental indicators, etc.
- Estimating the criteria
Estimating the criteria is identifying the scale of values that norms can get. There are a number of approaches in estimating the norms as follows:
+ Approaching classifying or continuous factors:
This method is used in case the targets have different levels of influence on issues needed assessing. If the values of the indicators represent the continuous variation and there is a clear correlation with each other, a continuous scale is established. To create this scale, the proportion of data need to be reset. The method used is redefining the proportion linearly.
+ Boolean approach
This approach is based on the division into two groups: the appropriate zone (value 1) and the inappropriate zone (value of 0). In this approach, the targets are transferred to Boolean type. Finally they are decoded into the map and overlay to give the regions corresponding to all of the limitations (called constraint criteria). This approach is useful when we know the suitability extent in some specific purposes and often simple. In the case of complex spending and different levels of importance, the method is not appropriate as its drawback is considering factors at the same level of importance.
When the value of the indicator is continuous but has no clear correlation with the appropriate level or when the value is not represented as a number, it can be rated on a classification scale.
- Weighting
Weighting the criteria is a very important job. There are many indicators affecting object need to be evaluated, however the extent of their influence largely vary. Therefore, determining the extent of their relative importance is required.
Indicators' weightings can be calculated through statistical algorithms, measurements, or based on subjective experiences, knowledge of experts. AHP (Analytical Hierarchy Process) developed by Thomas L. Saaty (1970s) is a technical decision in which there is a finite number of options, but each option has different characteristics, so it leads to difficulties in making decisions.
This model is particularly useful when making decisions in a group is necessary.
AHP can help identify and evaluate criteria, analyze the data collected by basing on these criteria, and make the process of making decision faster and more accurate. AHP Processing based on pairs of comparison among indicators, then these pairs are combined. AHP processing can be summarized into the following steps:
1. Identify the possible alternatives, and determine the most important criteria in the evaluation.
2. For each criterion of each pair of alternatives, the decider will express their opinion on the importance of them against each other.
3. The decider will determine the levels of importance among these criteria.
4. Each matrix of importance will be assessed using the numerical values in order to ensure consistency of the answers.
5. Then, each option will be calculated and given the scores. Based on the scores, the decision will be made.
To define weight of target layers, the study used results of research works, expert’s opinions and field investigation combined with Analytical Hiearchy Process (AHP) method (Saaty T.L., 1980).
AHP method solves the problem with 4 basic steps:
Step 1: Construction of Pairwise Comparison Matrices based on Experts opinion consultation. Employing the scale of relative importances, one is able to construct judgment matrices for each selection criterion. This step evaluates the performance of each possible alternative against the other alternatives in terms of the various selection criteria. This task is accomplished by employing the Scale of Relative Importance (Saaty, 1980). This scale and others developed since Saaty’s initial work, permits pairwise comparisons within the AHP. Saaty’s scale of relative importance is shown in table 2.1:
Table 1.1: The Scale of Relative Importance based on AHP method (Saaty, 1980).
1/9 1/7 1/5 1/3 1 3 5 7 9
Extreme strong
Very
strong Strong Moderate Equal Moderate Strong Very strong
Extreme strong Table 2.2: Experts opinion matrix (in case applying for 7 factors,
A1, A2,... A7 is selection criterions) (Saaty, 1980).
A1 A2 A3 A4 A5 A6 A7
A1 1 A12 A13 A14 A15 A16 A17
A2 1/A12 1 A23 A24 A25 A26 A27
A3 1/A13 1/A23 1 A34 A35 A36 A37
A4 1/A14 1/A24 1/A34 1 A45 A46 A47
A5 1/A15 1/A25 1/A35 1/A45 1 A56 A57
A6 1/A16 1/A26 1/A36 1/A46 1/A56 1 A67
A7 1/A17 1/A27 1/A37 1/A47 1/A57 1/A67 1
Step 2: Extraction of Priority Vectors aims to give a Consistency Ratio matrix:
Upon creating alternative judgment matrices for each selection criterion as well as the criteria judgment matrix, the analyst then proceeds to the next step in the analytic hierarchy process, which is to extract the relative importances implied by each matrix.
The crudest method of principal eigenvector attainment is to simply sum the elements in each row and collum () of the matrix and then normalize them by dividing each sum by the total of all row sums. This will result in a vector whose sum is unity and whose first entry is the priority of the first activity, the second of the second activity, and so on.
Step 3: Consistency Evaluation. Execution of this step in the algorithm ensures that each matrix is within an acceptable consistency tolerance, and therefore does not inadvertently violate the comparison values intended by the analyst.
+ The maximum or principal eigenvalue (λmax) is estimated as the average of the entries in consistency vector y and given by the formula (with n is the total number of selection criterions):
+ This maximum eigenvalue is then used to compute the matrix’s consistency index (CI) using:
+ The final step in the consistency evaluation is to examine the ratio of the calculated consistency index and the random index (RI) derived from the number of matrix activities. Random indices for varying matrix sizes are shown in table 2.3:
Table 2.3: Random Indices (Saaty, 1980)
n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
RI 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45 1.49 1.51 1.48 1.56 1.57 1.59
The ratio of CI to RI is called the consistency ratio (CR):
Generally, a consistency ratio of 0.10 or less is acceptable. In the event that the consistency ratio is greater than 0.10, the weight assignments must be re-evaluated within the matrix violating the consistency limits.
Step 4: Determining weight by calculating the ratio of the components in rows and columns:
- Integrating spending
After estimating and weighting spending, integrating them to calculate the appropriate index or the final result of the expenditure.
Appropriate index is calculated as following:
2.2.3. Advantages and Disadvantages of MCA a. Advantages
- Consider different criteria at the same time, which can not be done by normal decision-making processes basing on a single criterion.
- Can be used to sum up the opinions of the stakeholders on only one assessment.
- Is a clear and transparent evaluation method (records scores and importance), easy-tested.
- MCA can assist in communicating with policy makers and sometimes even with the wider community. MCA alleviates subjective or abstract arguments.
b. Disadvantages:
- Difficult to help achieve consensus for controversial issues.
Figure 2.2: AHP mathematical diagram
- By presenting quantitative information (a set of scores), MCA may create the incorrect impression of accuracy due to the fact that MCA relies heavily on experts' opinion.
Thus, multi-criteria analysis is one of some effective tools to value lands. It helps to consider the various diffirent factors which affect the land price at a given time and assess importance of these factors by aggregating scores in order to summarize and give the final result.