Normal Pairwise Comparison Matrices

3.4.2 Generating Criterion Map

Having established a set of criteria for evaluating alternative decision, each criterion should be represented as a map layer in the GIS database. The criterion map represents the spatial distribution of an attribute that measure the degree to which its associated objectives are achieved. The main purpose of generating criterion map is to create hazard criterion map appropriate to vulnerability input map. This procedure for generating criterion maps is based on GIS functions, which include geographical data input; data storage and management; data manipulation and analysis Malczewski, 1999.

3.5 Multi-criteria Evaluation

This research uses AHP Normal Pairwise Comparison Matrix to standardize the criteria and Fuzzy AHP to describe multi-criteria evaluation.

3.5.1 Normal Pairwise Comparison Matrices

The input of fuzzy AHP is crisp Pairwise Comparison Matrix PCM. This matrix shows the rate of relative preference for two criteria with the value from 1 to 9 Table 3.3. 36 Table 3.3 Scale of Relative Importance Source: Saaty, 1980 Intensity of relative importance Definition Explanation 1 Equal importance Two activities contribute equally to the objective 3 Moderate importance of one over another Experience and judgment slightly favor one activity over another 5 Essential or strong importance Experience and judgment strongly favor one activity over another 7 Demonstrated importance An activity is strongly favored and its dominance is demonstrated in practice 9 Extreme importance The evidence favoring one activity over another is of the highest possible order of affirmation 2, 4, 6, 8 Intermediate values between the two adjacent judgments When compromise is needed Reciprocals of above non-zero numbers If an activity has one of the above numbers e.g. 3 compared with a second activity, then the second activity has the reciprocal value i.e., 13 when compared to the first Multi-criteria decision analysis requires the values of the various criteria where the measurement of the values depends on the subjectivity of the personal judgement of decision makers or experts. The evaluation criteria need to be standardized into common scale because they are represented by different measurement scales. The value from PCM can be used for the purpose of rating or standardizing Malczewski, 2003. Criteria standardization is normally done on 0 to 1 scale, or 0-10 or 0-100, etc. The criteria at the lowest level that have different suitability classes are standardized using the maximum Eigenvectors approach on 0 to 1 scale. In mud volcano vulnerability, a map represents each evaluation with values such as Z1, Z2, Z3 and Z4 indicating the degree of vulnerability with 37 respect to a criterion which is based on the requirements. These classes will be rated based on the importance of vulnerability class with respect to a particular criterion.

3.5.2 Fuzzy AHP