Fuzzy AHP Approach in Vulnerability Analysis

Figure 2 Flow of the research process

3.4 Fuzzy AHP Approach in Vulnerability Analysis

The steps of Fuzzy AHP for vulnerability analysis are shown in Figure 3. The crisp PCM is fuzzified using the triangular fuzzy number f = l, m, u. The l lower bound and u upper bound represents the vague range that might exist in the preferences expressed by the decision maker or experts. Conversion from crisp to Fuzzy PCM is shown in Table 1. Table 1 Conversion of crisp PCM to fuzzy PCM Source: Kuswandari, 2004; Prakash, 2003 Crisp PCM value Fuzzy PCM value Crisp PCM value Fuzzy PCM value 1 1, 1, 1 if diagonal 1, 1,3 otherwise 11 11, 11, 11 if diagonal 13, 11, 11 otherwise 2 1, 2, 4 12 14, 12, 11 3 1, 3, 5 13 15, 13, 11 5 3, 5, 7 15 17, 15, 13 7 5, 7, 9 17 19, 17, 15 9 7, 9, 11 19 111, 19, 17 Fuzzy extent analysis then applied to calculate performance ratings and criteria weights for the Fuzzy PCM. Performance ratings are then multiplied by criteria weights according to hierarchy. The result is range of values over which any value can be considered as performance value. Decision maker is then asked to say about hisher confidence regarding their judgment. The confidence level will be taken as α-cut value, which will have value range 0 – 1. Next, decision maker attitude plays a role in deciding the performance value. Since until this point, it still exist certain range of possible values for performance. Decision makers attitude of pessimistic, optimistic or middle will determine which value that will be choose, either may be the lowest value, highest value or middle value respectively. Decision maker attitude of pessimistic is expressed as Optimism Index λ which value is between 0 - 1. Using the optimism index, the fuzzy range is once again converted into a crisp range. 4 Figure 3 Fuzzy AHP steps for vulnerability Analysis 3.5 Generating Vulnerability Map Once weighted performance of each criterion have been converted into crisp performance value, Spatial Analysis over criteria layers can be performed for Fuzzy AHP. Firstly, criteria layers are classified accordingly to the vulnerability class Z1 – Z4. The next step is applying crisp performance value that is acquired from fuzzy AHP process to each criterion map to obtain weighted criteria layers. After that, combines the weighted value of criterion map by summing the crisp performance value of map layers. This will give the final result of vulnerability ratings at the final level. The final vulnerability ratings then classified into final vulnerability map. The classification will be based on the value for Z1 – Z4 that acquired from performancesweights calculation.

3.6 Sensitivity Analysis