# Application of GIS-Interval Rough AHP Methodology for Flood Hazard Mapping in Urban Areas

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}and lies on the alluvial banks of the Danube River, of which 11.9 km

^{2}is covered by water surfaces (Figure 1). A total of 32% of the municipality is highly urbanized. On the non-urban part of it, mostly on the left river bank, the land is flat, swampy and marshy. The area of Palilula is characterized by the highest groundwater level in Belgrade. According to the last census of 2011, the population of the Palilula urban community is 110,637 persons, and it is constantly increasing due to the present process of urbanization [60].

## 3. Methodology

#### 3.1. Methodological Background

#### 3.2. Interval Rough Numbers

#### 3.3. IR’AHP Mathematical Model

_{k}), the same value ($i,j$) is entered,${x}_{ij}^{k}={x}_{ij}^{k\prime}$. For example, an expert during the criterion comparison at the position (1,2) cannot decide between two linguistic values (e.g., 5 and 6), then at the position (1,2) in the matrix Z

_{k}${x}_{12}^{e}=5$ and ${x}_{12}^{e\prime}=6$ are entered.

_{1},Z

_{2},...,Z

_{e}matrix is obtained with e experts giving their comparison in criteria pairs.

_{k}is determined by the consistency of experts’ evaluation. Saaty [86] suggested the consistency ratio (CR) for the consistency check. The calculation of the degree of consistency is done in two steps. In the first step, the consistency index (CI) is calculated $CI=({\lambda}_{\mathrm{max}}-n)/(n-1)$, where $n$ is matrix rank and ${\lambda}_{\mathrm{max}}$ the maximum Eigen value of the comparison matrix.

_{k}at (i,j) enters two values, two CRs are obtained for each expert, CRe and CRe’. Prior to determining the final value ($C{R}_{k}$), the values of CRe and CRe’ must meet the following requirements CRe ≥ 0.1 and CRe’ ≥ 0.1. The final CR is calculated as medium value $C{R}_{k}=(C{R}^{k}+C{R}^{k\prime})/2$.

_{r}for expert e and ${W}_{ke}$ the weight coefficient for expert e. Normalization of the experts’ weight coefficient is carried out using the additive normalization.

^{L}and X*

^{′U}.

^{1L}, X

^{2L},…, X

^{mL}are obtained (where m is the number of experts) for the first rough sequence $RN\left({x}_{ij}^{kL}\right)$ and X

^{1′U}, X

^{2'U},…, X

^{m′U}for the second rough sequence $RN\left({x}_{ij}^{k\prime U}\right)$. For the first group of rough matrices X

^{1L}, X

^{2L},…, X

^{mL}at (ij) rough sequence is obtained as follows:

^{1′U}, X

^{2′U},…, X

^{m′U}at (ij) rough sequence is obtained $RN\left({x}_{ij}^{\prime U}\right)=\left\{\left[\underset{\_}{Lim}({x}_{ij}^{1\prime U}),\text{}\overline{Lim}({x}_{ij}^{1\prime U})\right],\text{}\left[\underset{\_}{Lim}({x}_{ij}^{2\prime U}),\text{}\overline{Lim}({x}_{ij}^{2\prime U})\right],...,\left[\underset{\_}{Lim}({x}_{ij}^{m\prime U}),\text{}\overline{Lim}({x}_{ij}^{m\prime U})\right]\right\}$.

## 4. Estimation of Flood-Prone Areas in Palilula Municipality

#### 4.1. Criteria Selection

#### 4.2. GIS-MCDA

_{15}= 4; z′

_{15}= 5). This means that the expert could not choose one of the values four or five. If there is no uncertainty, then the expert e will undoubtedly select one value. An example of this is for the position of C2–C5 in the matrix DM1. The first expert introduced two same value in the comparison matrix DM1 (z

_{25}= 9; z′

_{25}= 9).

_{k}, (${z}_{ij}^{e};{z}_{ij}^{e\prime}$), two consistency ratios are obtained for each expert CR

^{e}and CR

^{e′}. After calculating the consistency ratio for the comparison matrix (Table 4), it can be concluded that the research is valid, because all values CR

_{e}< 0.1. Thus, e.g., for the first expert (Table 4), it is CR

_{1}= (0.022 + 0.088)/2 = 0.055.

_{k}are transformed into interval rough number $IRN({z}_{ij}^{e})$. Thus, ten interval rough matrices are calculated X

_{k}. Using Equations (22), (23) and experts’ weight coefficients (Table 4), the average interval rough comparison matrix is calculated in evaluation criteria pairs; see Table 5.

#### 4.3. Aggregation of Weighted Linear Combination

_{i}is the normalized value of the factor weight and x

_{i}is the criterion score of factor i.

^{2}, which is about 18.5% of the territory of the community. Under Scenario 2, which uses the fuzzy technique in the AHP method (F’AHP), the FHI 5 area is 8.8 km

^{2}, while in Scenario 3, with the traditional (crisp) AHP method applied, the FHI 5 area is calculated to be 7.8 km

^{2}for the occurrence of floods. Spatially, all three maps shows that these are the parts on the left bank of the Danube, which gravitate towards the sewage network. At the same time, these are the most ecologically-sensitive parts in which uncontrolled floods can lead to catastrophic environmental and social consequences.

## 5. Results-Discussions

^{2}of urban area. The general conclusion is that the risk of flood covers much of the demographic and infrastructural resources of Palilula municipality.

## 6. Conclusions

^{2}or 18.5% of the Palilula municipality has a very high-hazard, the high-hazard area being 23.2% and 21.6% for moderate hazard with respect to the occurrence of flood events. On the other hand, 8.5 km

^{2}or 12.2% of the area has very low and 24.6% has low hazard in the occurrence of floods. From these results, it is evident that Palilula municipality is mostly located in areas of high hazard with the probability of the occurrence of high water and flooding. These parts are mostly on the left bank of the Danube and parts that gravitate toward the sewage canal network of the community.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

- (1)
- Adding of IRN“+”$$IRN(A)+IRN(B)=\left(\left[{a}_{1},{a}_{2}\right],\left[{a}_{3},{a}_{4}\right]\right)+\left(\left[{b}_{1},{b}_{2}\right],\left[{b}_{3},{b}_{4}\right]\right)=\left(\left[{a}_{1}+{b}_{1},{a}_{2}+{b}_{2}\right],\left[{a}_{3}+{b}_{3},{a}_{4}+{b}_{4}\right]\right)$$
- (2)
- Subtraction of IRN“−”$$IRN(A)-IRN(B)=\left(\left[{a}_{1},{a}_{2}\right],\left[{a}_{3},{a}_{4}\right]\right)-\left(\left[{b}_{1},{b}_{2}\right],\left[{b}_{3},{b}_{4}\right]\right)=\left(\left[{a}_{1}-{b}_{4},{a}_{2}-{b}_{3}\right],\left[{a}_{3}-{b}_{2},{a}_{4}-{b}_{1}\right]\right)$$
- (3)
- Multiplication of IRN“×”$$IRN(A)\times IRN(B)=\left(\left[{a}_{1},{a}_{2}\right],\left[{a}_{3},{a}_{4}\right]\right)\times \left(\left[{b}_{1},{b}_{2}\right],\left[{b}_{3},{b}_{4}\right]\right)=\left(\left[{a}_{1}\times {b}_{1},{a}_{2}\times {b}_{2}\right],\left[{a}_{3}\times {b}_{3},{a}_{4}\times {b}_{4}\right]\right)$$
- (4)
- Dividing of IRN“/”$$IRN(A)/IRN(B)=\left(\left[{a}_{1},{a}_{2}\right],\left[{a}_{3},{a}_{4}\right]\right)/\left(\left[{b}_{1},{b}_{2}\right],\left[{b}_{3},{b}_{4}\right]\right)=\left(\left[{a}_{1}/{b}_{4},{a}_{2}/{b}_{3}\right],\left[{a}_{3}/{b}_{2},{a}_{4}/{b}_{1}\right]\right)$$
- (5)
- Scalar multiplication of IRN where $k>0$$$k\times IRN(A)=k\times \left(\left[{a}_{1},{a}_{2}\right],\left[{a}_{3},{a}_{4}\right]\right)=\left(\left[k\times {a}_{1},k\times {a}_{2}\right],\left[k\times {a}_{3},k\times {a}_{4}\right]\right)$$

- (1)
- If the intervals of IRN are not strictly bounded by other intervals, then:
- (a)
- If the condition is satisfied that {${\alpha}^{\prime U}>{\beta}^{\prime U}$ and ${\alpha}^{L}\ge {\beta}^{L}$ } or {${\alpha}^{\prime U}\ge {\beta}^{\prime U}$ and ${\alpha}^{L}<{\beta}^{L}$ }, then $IRN(\alpha )>IRN(\beta )$; Figure A1a.
- (b)
- If the condition is satisfied that {${\alpha}^{\prime U}={\beta}^{\prime U}$ and ${\alpha}^{L}={\beta}^{L}$ }, then $IRN(\alpha )=IRN(\beta )$; Figure A1b.

- (2)
- If the intervals of IRN $IRN(\alpha )$ and $IRN(\beta )$ are strictly bounded by other intervals, then it is necessary to find intersection points $I(\alpha )$ and $I(\beta )$ of IRN $IRN(\alpha )$ and $IRN(\beta )$. Then, if this is satisfied, ${\beta}^{\prime U}<{\alpha}^{\prime U}$ and ${\beta}^{L}>{\alpha}^{L}$.

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$\mathit{n}$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

RI | 0.00 | 0.00 | 0.52 | 0.89 | 1.11 | 1.25 | 1.35 | 1.40 | 1.45 | 1.49 |

Criteria | Fuzzy Membership Function | Control Points/Value Points | Final Utility |
---|---|---|---|

Elevation (C1) | Linear monotonically decreasing | c = 50 m; d = 300 m | 0–50 m equal to 1, 50–300 m between 1 and 0, more than 300 m equal to 0 |

Slope (C2) | Linear monotonically decreasing | c = 1°; d = 35° | 0°–1° equal to 1, 1°–30° between 1 and 0, more than 35° equal to 0 |

Distance from drainage network (C3) | Linear monotonically decreasing | c = 100 m; d = 2000 m | 0–100 m equal to 1, 100–2000 m between 1 and 0, more than 2000 m equal to 0 |

Distance from water surfaces (C4) | Linear monotonically decreasing | c = 100 m; d = 2000 m | 0–100 m equal to 1, 100–2000 m between 1 and 0, more than 2000 m equal to 0 |

Water table(C5) | Linear monotonically decreasing | c = 100 cm; d = 5000 cm | 0–100 cm equal to 1, 100–4000 cm between 1 and 0, more than 5000 cm equal to 0 |

Land cover use (C6) | Discrete categorical data | Water areas equal 1; wetlands equal 0.9; urbanized areas equal 0.8; industrial areas equal 0.7; agriculture equals 0.5; land covered with sparse vegetation equals 0.4; grass and parks equal 0.2; forests equal 0.1 |

Expert 1 | ||||||

C1 | C2 | C3 | C4 | C5 | C6 | |

C1 | (1.00;1.00) | (0.13;0.14) | (5;7) | (0.2;0.25) | (4;5) | (0.13;0.14) |

C2 | (8;7) | (1.00;1.00) | (9;9) | (2;3) | (9;9) | (1.00;1.00) |

C3 | (0.2;0.14) | (0.11;0.11) | (1.00;1.00) | (0.11;0.13) | (0.25;0.33) | (0.11;0.11) |

C4 | (5;4) | (0.5;0.33) | (9;8) | (1.00;1.00) | (7;8) | (0.25;0.33) |

C5 | (0.25;0.2) | (0.11;0.11) | (4;3) | (0.14;0.13) | (1.00;1.00) | (0.11;0.13) |

C6 | (8;7) | (1.00;1.00) | (9;9) | (4;3) | (9;8) | (1.00;1.00) |

… | ||||||

Expert 10 | ||||||

C1 | C2 | C3 | C4 | C5 | C6 | |

C1 | (1.00;1.00) | (0.14;0.11) | (1.00;1.00) | (0.2;0.25) | (6;7) | (0.14;0.11) |

C2 | (7;9) | (1.00;1.00) | (7;8) | (3;4) | (9;9) | (1;2) |

C3 | (1.00;1.00) | (0.14;0.13) | (1.00;1.00) | (0.2;0.25) | (7;8) | (0.14;0.13) |

C4 | (5;4) | (0.33;0.25) | (5;4) | (1.00;1.00) | (9;8) | (0.33;0.25) |

C5 | (0.14;0.17) | (0.11;0.11) | (0.14;0.13) | (0.11;0.13) | (1.00;1.00) | (0.11;0.13) |

C6 | (7;9) | (1;0.5) | (7;8) | (3;4) | (9;8) | (1.00;1.00) |

Expert | CR^{e} | CR^{e'} | CR^{e} | w_{ke} |
---|---|---|---|---|

E 1 | 0.022 | 0.088 | 0.055 | 0.102 |

E 2 | 0.071 | 0.087 | 0.079 | 0.071 |

E 3 | 0.035 | 0.064 | 0.049 | 0.114 |

E 4 | 0.081 | 0.067 | 0.074 | 0.076 |

E 5 | 0.022 | 0.051 | 0.036 | 0.155 |

E 6 | 0.083 | 0.067 | 0.075 | 0.075 |

E 7 | 0.037 | 0.071 | 0.054 | 0.105 |

E 8 | 0.031 | 0.065 | 0.048 | 0.118 |

E 9 | 0.044 | 0.057 | 0.050 | 0.112 |

E 10 | 0.092 | 0.067 | 0.079 | 0.071 |

C1 | C2 | C3 | ... | C6 | |
---|---|---|---|---|---|

C1 | ([1.00,1.00],[1.00,1.00]) | ([0.59,4.41],[0.50,3.69]) | ([0.26,1.08],[0.26,1.34]) | ... | ([0.29,1.84],[0.29,2.43]) |

C2 | ([0.27,1.89],[0.28,2.27]) | ([1.00,1.00],[1.00,1.00]) | ([4.79,6.87],[4.74,6.72]) | ([0.28,2.48],[0.36,2.77]) | |

C3 | ([0.12,0.16],[0.13,0.19]) | ([0.31,2.06],[0.27,2.29]) | ([1.00,1.00],[1.00,1.00]) | ([1.23,6.30],[1.37,6.47]) | |

C4 | ([4.79,6.87],[4.74,6.72]) | ([3.16,7.00],[3.82,7.13]) | ([6.36,8.31],[5.51,7.62]) | ([0.16,0.43],[0.15,0.32]) | |

C5 | ([0.16,0.43],[0.15,0.32]) | ([0.72,5.73],[0.71,6.00]) | ([1.57,4.45],[1.42,4.86]) | ([0.41,4.01],[0.37,4.01]) | |

C6 | ([0.25,1.63],[0.22,1.85]) | ([0.68,6.23],[0.65,5.88]) | ([1.04,5.02],[0.86,5.31]) | ([0.68,6.23],[0.65,5.88]) | |

C7 | ([0.61,1.76],[0.45,1.41]) | ([1.67,6.96],[1.31,6.45]) | ([4.94,8.18],[4.36,7.69]) | ([1.00,1.00],[1.00,1.00]) |

C1 | C2 | C3 | … | C6 | |
---|---|---|---|---|---|

C1 | ([0.05,0.24],[0.04,0.26]) | ([0.02,0.09],[0.02,0.09]) | ([0.02,0.53],[0.02,0.45]) | … | ([0.01,0.51],[0.02,0.51]) |

C2 | ([0.06,0.3],[0.05,0.36]) | ([0.04,0.74],[0.04,0.94]) | ([0.02,0.69],[0.02,0.74]) | ([0.03,0.58],[0.04,0.73]) | |

C3 | ([0.03,0.05],[0.03,0.06]) | ([0.02,0.06],[0.02,0.08]) | ([0.01,0.25],[0.01,0.28]) | ([0.01,0.11],[0.01,0.18]) | |

C4 | ([0.16,0.4],[0.14,0.43]) | ([0.14,0.39],[0.14,0.42]) | ([0.09,0.85],[0.12,0.88]) | ([0.05,1.22],[0.06,1.27]) | |

C5 | ([0.04,0.22],[0.04,0.27]) | ([0.02,0.17],[0.02,0.13]) | ([0.03,0.12],[0.03,0.12]) | ([0.02,0.78],[0.02,0.79]) | |

C6 | ([0.06,0.31],[0.05,0.37]) | ([0.03,0.64],[0.03,0.77]) | ([0.02,0.75],[0.02,0.72]) | ([0.04,0.19],[0.04,0.2]) | |

C7 | ([0.13,0.4],[0.11,0.43]) | ([0.08,0.69],[0.06,0.59]) | ([0.05,0.84],[0.04,0.79]) | ([0.05,1.08],[0.04,1.07]) |

Criteria | Interval Rough Approach | Fuzzy Approach | Crisp Approach | |||
---|---|---|---|---|---|---|

IRN(w_{j}) | Rank | Fuzzy (w_{j}) | Rank | Crisp (w_{j}) | Rank | |

C1 | ([0.02,0.27],[0.02,0.3]) | 5 | (0.08,0.12,0.16) | 5 | 0.122 | 5 |

C2 | ([0.03,0.43],[0.04,0.5]) | 2 | (0.11,0.19,0.21) | 2 | 0.203 | 2 |

C4 | ([0.09,0.68],[0.09,0.7]) | 6 | (0.04,0.08,0.07) | 6 | 0.259 | 6 |

C5 | ([0.01,0.1],[0.01,0.12]) | 1 | (0.25,0.32,0.55) | 1 | 0.120 | 1 |

C6 | ([0.02,0.34],[0.02,0.35]) | 4 | (0.07,0.14,0.15) | 4 | 0.137 | 4 |

C7 | ([0.03,0.42],[0.03,0.43]) | 3 | (0.12,0.15,0.19) | 3 | 0.159 | 3 |

Definition | Crisp Scale | Fuzzy Scale |
---|---|---|

Equal importance | 1 | (1,1,1) |

Somewhat more important | 3 | (2,3,4) |

Much more important | 5 | (4,5,6) |

Very much more important | 7 | (6,7,8) |

Absolutely more important | 9 | (8,9,9) |

Intermediate values | 2, 4, 6, 8 | (x − 1, x, x+1) |

**Table 9.**The areas of classes from the final flood hazard map for the scenarios. IR, interval rough number; F, fuzzy.

Flood Hazard Index | Scenario 1 IR’AHP | Scenario 2 F’AHP | Scenario 3 Crisp AHP | ||||
---|---|---|---|---|---|---|---|

(km^{2}) | % | (km^{2}) | % | (km^{2}) | % | ||

FHI 5 | Very high | 12.9 | 18.5 | 8.8 | 12.6 | 7.8 | 11.2 |

FHI 4 | High | 16.2 | 23.2 | 20.7 | 29.6 | 24.9 | 35.6 |

FHI 3 | Moderate | 15.1 | 21.6 | 17.2 | 24.6 | 15.3 | 21.9 |

FHI 2 | Low | 8.5 | 12.2 | 14.7 | 21.0 | 12.2 | 17.5 |

FHI 1 | Very low | 17.2 | 24.6 | 8.5 | 12.2 | 9.7 | 13.9 |

**Table 10.**Spatial relations of the historical floods locations and flood hazard zones according to the scenarios.

Scenarios | Historically-Flooded Points | Flood Hazard Index (FHI) | ||||
---|---|---|---|---|---|---|

5 | 4 | 3 | 2 | 1 | ||

1 IR’AHP | 31 | 27 (87.1%) | 4 (12.9%) | 0 | 0 | 0 |

2 F’AHP | 31 | 21 (67.7%) | 9 (29.0%) | 1(3.2%) | 0 | 0 |

3 AHP (crisp) | 31 | 17 (54.8%) | 10 (32.3%) | 4 (12.9%) | 0 | 0 |

Land Cover/Infrastructure | Unit | Flood Hazard Index | ||||
---|---|---|---|---|---|---|

5 | 4 | 3 | 2 | 1 | ||

Urban areas | km^{2} | 7.85 | 6.42 | 3.90 | 12.84 | 0.57 |

Grassland | km^{2} | 0.12 | 0.32 | 0.53 | 0.60 | 0.96 |

Forests | km^{2} | 0.24 | 0.63 | 1.69 | 0.81 | 2.38 |

Scrub | km^{2} | 0.17 | 0.29 | 0.31 | 0.18 | 0.12 |

Arable land | km^{2} | 2.06 | 7.85 | 6.42 | 3.90 | 12.84 |

Industrial areas | km^{2} | 0.34 | 0.99 | 0.45 | 0 | 0 |

Parks | km^{2} | 0.009 | 0.45 | 0.086 | 0.107 | 0.003 |

Marshes | km^{2} | 0.92 | 0.22 | 0.02 | 0 | 0 |

Schools and universities | No. | 11 | 17 | 9 | 6 | 0 |

Kindergartens | No. | 9 | 8 | 5 | 2 | 0 |

Residential buildings | No. | 540 | 407 | 449 | 114 | 25 |

Industrial buildings | No. | 11 | 13 | 6 | 0 | 0 |

Medical facilities | No. | 4 | 1 | 1 | 0 | 0 |

Roads | km | 36.77 | 38.54 | 32.30 | 16.94 | 20.80 |

Railroads | km | 0.64 | 2.26 | 3.44 | 0.74 | 0.83 |

Population | thousands | 41,565 | 31,108 | 18,568 | 11,540 | 7856 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gigović, L.; Pamučar, D.; Bajić, Z.; Drobnjak, S.
Application of GIS-Interval Rough AHP Methodology for Flood Hazard Mapping in Urban Areas. *Water* **2017**, *9*, 360.
https://doi.org/10.3390/w9060360

**AMA Style**

Gigović L, Pamučar D, Bajić Z, Drobnjak S.
Application of GIS-Interval Rough AHP Methodology for Flood Hazard Mapping in Urban Areas. *Water*. 2017; 9(6):360.
https://doi.org/10.3390/w9060360

**Chicago/Turabian Style**

Gigović, Ljubomir, Dragan Pamučar, Zoran Bajić, and Siniša Drobnjak.
2017. "Application of GIS-Interval Rough AHP Methodology for Flood Hazard Mapping in Urban Areas" *Water* 9, no. 6: 360.
https://doi.org/10.3390/w9060360