# Non-compensatory decision model for incorporating the sustainable development criteria in flood risk management plans

- 100 Downloads

**Part of the following topical collections:**

## Abstract

It is necessary to incorporate Sustainable Development Goals into the selection of Flood Risk Management Plans (FRMPs). This paper is assessing the FRMPs by grouped Sustainable Development Criteria (SDC) criteria. The utilized Multi-Criteria Decision Making (MCDM) models to evaluate FRMPs were chosen from three groups of compensatory, Semi-non compensatory, and non-compensatory models. Sensitivity and uncertainty analysis of input data such as SDC’s weights and Criteria’ Weight Assessment (IWA) methods were used to compare the results in different groups of MCDMs, IWAs, and their constructions. The results showed that Step-wise Weight Assessment Ratio Analysis (SWARA) had reasonable results as IWA method, while Shannon’s Entropy had not satisfied outcomes. The compensatory model was affected by changes in input data, while Semi-noncompensatory and noncompensatory models had more stable results. Based on the SWARA-PROMETHEE model the combination of designing the warning system and employing a flood insurance program was in the first rank, flood peak alleviation by Golestan-I reservoir is in the second rank, designing a warning system was in the third rank, building a diversion canal and levees in the study area were fourth and fifth rank, respectively. Employing a flood insurance program was in the last priority by SWARA-PROMETHEE model. The combination of SWARA-PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations) model is recommended for the ranking of FRMPs because of the better incorporating SDC in flood management plan in comparison to other models, and demonstrating better results in IWA sensitivity analysis as well as Criteria’ Weight (IW) uncertainty assessment.

## Keywords

Decision support Flood mitigation Flood management Risk management Sustainable development Sustainability## 1 Introduction

Floods can destroy infrastructures and can cause damages rivers and floodplains’ environments [14, 17, 23, 42]. Vulnerability to flood disasters tends to increase globally with climate change [25]. While floods can jeopardize sustainable development, flood protection management should be part of sustainable development. Considering the influence of floods regarding sustainability planning is important for long-term hazard reduction [39]. Although sustainable development is commonly used, there is a limited understanding towards application of this term. At a broader perspective, sustainable development (SD) includes three major objectives: being economically feasible, socially acceptable, and environmentally sound [29].

Evaluation of Flood Risk Management Plans (FRMPs) in a sustainability context can lower costs and reduce fewer impacts on social and environmental through better adaptation to the environment. The use of sustainable development criteria (SDC) to evaluate flood management is thus an ideal option. Since SDC have different values, qualitative or quantitative, comparison between each other is problematic [6, 20]. The consequence of floods on a society be contingent on the affected state’s economic power prior to the flood [21]. To address this issue, Criteria’ Weight Assessment (IWA) methods with different computational processes are used to evaluate SDC preferences. Analytic Hierarchy Process (AHP) method as one of the most wide spreads method in weight assessment, which is used to evaluate tangible and intangible criteria based on pairwise comparisons [13, 45]. Step-wise, Weight Assessment Ratio Analysis (SWARA) is another method for weighing decision attributes using expert opinion, while Shannon’s Entropy method enable decision makers to obtain weights without privileged data or direct judgment of experts [31]. Use of common evaluation measures have difficulties and it becomes necessary to use multiple criteria decision making (MCDM) models for applying SDC in selection of best FRMPs.

Vlsekriterijumska Optimizacija I KOmpromisno Resenje (VIKOR) model is a compensatory MCDM model developed by Opricovic and Tzeng [41], which is intended to solve MCDM problems with conflicting objectives. The reason of choosing VIKOR model is its popularity in MCDM analysis and application of VIKOR method has upward trends in recent studies regarding MCDMs [35]. It is used extensively in water resources management to optimize decisions involving multiple objectives [50]. The integration of suitable scientific data is then essential to contribute in knowledgeable management [33, 50]. VIKOR model is applied to water resources management in the Mlava River [40]. This model is employed to define compromise solution to a decision issue with non-commensurable indices that represent Sustainable Development Goals (SDG). Chang and Hsu [10] used VIKOR model to determine the best feasible solution of land use limitations for Tsen-Wen watershed in southern Taiwan. These examples show the use of compensatory model, VIKOR, in water resources management.

The ranking of flood management projects could also be done through semi-non-compensatory MCDM modeling. ELimination and Et Choice Translating REality (ELECTRE I) model is an outranking (semi-noncompensatory) MCDM model that was developed by Roy [44]. It used extensively for solving selection problems due to the time saving analysis and being easy to use and understand. In this model, ranking of FRMPs is achieved by means of pair-wise comparison. Dominance and non-dominance FRMPs are determined by a concordance and discordance matrix. In semi-noncompensatory model like ELECTRE I, positive high score of one criterion can compensate for negative low score of the other criterion, but not negative high score.

Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE) has a non-compensatory rationality [7]. It is one of the most common ranking MCDM method and is suitable for sustainability assessments [24, 26]. This method is flexible model regarding quantitative input data and has appropriate performance in quantitative analysis in comparison other MCDM models [37]. The criteria’ weights (IW) is linked to the grade of their comparative significance and it is in two phases: enriching the ranking procedure and their link to assist the decision process [49]. The indifference and preference threshold are two parameters which should be considered in this method and as a consequence small difference in a criterion cannot induce large differences in evaluations of FRMPs.

Application of various MCDMs have been reported studies in several water resources management plans [36, 51]. Moreover, several applications of MCDMs in water resources management shows that the models are proper means for making a decision in the area [1, 3, 5, 11, 19, 20]. Yang et al. [51] prioritized water management options for urbanization and climate change scenarios using the ELECTRE model. Purjavad and Shirouyehzad [43] compared three MCDM models, comprising ELECTRE, VIKOR and TOPSIS and conclude that these techniques had different outcomes.

Based on the literature review there were no comparison among compensatory semi-noncompensatory and noncompensatory models in water resources management study. Banihabib et al. [4] conclude that non-compensatory model has less sensitivity to criteria weights and therefore is more reliable in decision making for water shortage mitigation [4]. In water supply–demand strategies decision making, Cambrainha et al. [9] proved the robustness of non-compensatory models in the first three ranks of alternative options [9]. The non-compensatory MCDM models could also reflected the relative importance of the objectives established in integrated rehabilitation management scheme by Tscheikner-Gratl et al. [47, 48]. In this study, in addition to the compensatory and non-compensatory model, the semi-compensatory model is compared based on sensitivity analysis to the input models such as criteria weights value. Moreover, the comparison between MCDM models performed by both mathematical based and expert judgment based processes. Thus, the innovation of this research contains the comparison among these three groups with consideration of SDC attitudes. Sensitivity analysis in input data is important in MCDM evaluation [12]. Sensitivity analysis in IWA is another important issue which were neglected in most of the previous research. In so doing, the current research evaluate different IWA methods with different mathematical based.

In this paper, three models in different categories for applicability in sustainable flood management were evaluated. The VIKOR, ELECTRE I and PROMETHEE models were assessed in the ranking of FRMPs in the Gorganrood River in Iran. These models were compared using IWA sensitivity analysis and IW uncertainty evaluation to demonstrate relative strength and weaknesses. General objective of the research is to evaluate FRMPs with SDC using MCDM models in order to reduce flood damage in the study region. Main goals of the investigation are (I) A sets of SDC parameters were developed for various FRMPs; (II) Compensatory, semi-noncompensatory and noncompensatory MCDMs based on sensitivity analysis have been optimized, and (III) Commonalities and difference in optimal FRMPs have been evaluated.

## 2 Materials and methods

### 2.1 Study area

Gorganrood Basin has 20,380 km^{2} area and is bounded by 37°00′–37°30′ north latitude and 54°00′–54°30′ east longitude. Golestan Province is bordered by the Semnan, North Khorasan, and Mazandaran Provinces, and the Caspian Sea, and the Republic of Turkmenistan. Its land is covered by forests, range lands and farmlands. The case study area has high to moderate precipitation (250 to 450 mm) with absolute minimum and maximum daily temperature between − 1.4 and 46.5° C [22, 46].

### 2.2 FRMPs

FRMP #1: No project case (for contrasting with other FRMPs),

FRMP #2: Flood peak alleviation by Golestan-I Reservoir,

FRMP #3: Building levees in the study reach,

FRMP #4: Building a diversion canal to protect the study area,

FRMP #5: Designing a warning system,

FRMP #6: Employing a flood insurance program,

FRMP #7: Combining FRMPs #5 and #6.

In the FRMP #1 neither structural nor non-structural measures are implemented. Thus, this FRMP reflects environmental and socioeconomic impacts of flood in the current state of the region. FRMP #2 uses flood alleviation capacity of Golestan-I Reservoir, while water level of the reservoir is considered at normal level and used as an initial condition of flood routing of the reservoir. Therefore, construction, operation, maintenance costs and socioeconomic and environmental outcomes of Golestan-I Reservoir are deliberated in FRMP #2. The third FRMP applies levees to safeguard the study reach of the study area at a 50-year flood. Higher return period floods than this can increase the damages in the floodplain more than in natural state. This fact is reflected in the evaluation of criteria by the MCDM models. Based on the flood routing in the river, the levees’ height are determined. The length, side-slopes and the crest width the of the levees equal to 41,150 m, 1/2 and 5 m, respectively. The FRMP #4 considers the construction of a flood diversion canal parallel to a width of 100 m and a depth of 3 m. If flow of this river exceeds 355 m^{3}/s, this flood division canal can carry a surplus flow of as much as 204 m^{3}/s. Thus, the reach is secured for floods up to a peak discharge of 559 m^{3}/s. The FRMP #5 applies warning systems. Comparable to FRMP #1, no physical alterations would be considered under FRMP #5. The FRMP #6 applies flood insurance, which compensates flood damages and any casualties. Similarly, no physical alterations would be considered in the floodplain. Lastly, the FRMP #7 applies both FRMP #5 and FRMP #6. Each FRMP is prioritized based on SDC described below and applied in MCDMs to determine the best FRMP.

### 2.3 Proposed SDCs

Criterion #1:

*Expected Annual Damage (EAD)*is employed based on the amplitude of flood [8, 15, 16, 28, 30, 32, 36].Criterion #2:

*Recovery Rate (RR)*from the flood damages state to normal or better than normal state [8, 15, 32].Criterion #9:

*Gradual change*in system response (damage) to flood flow increase [15].Criterion #4: It is

*Expected Average Number of Casualties (EANC)*per year [8, 15, 28, 32, 36].Criterion #5:

*Feeling safe by people*due to applying a FRMP which assists the social satisfaction of the study area [28, 30].Criterion #6:

*Employment rate*which is a social satisfaction factor [16, 30].Criterion #7: The level of people

*participation*in applying an FRMP, a good criterion of social sustainability [18].Criterion #8: The

*protection of natural environment*which is a criterion of environmental sustainability [16, 30].Criterion #9: The

*wild life habitat conservation*as a criterion to assess the role of FRMPs in environmentally sustainable development [8, 16, 28, 32, 36].Criterion #10: The

*water quality conservation*to improve water resources and environment protection [8, 16, 32].Criterion #11: The

*technical feasibility and construction speed*which makes each FRMP different from other FRMPs in terms of economic feasibility and social satisfaction [16, 30, 32].

Criteria #1, #2, #9 and #11 have more observations than other criteria in published papers. Moreover, SDCs can be classified as qualitative and quantitative. The qualitative criteria are graded by expert, while quantitative criteriaare determined using the formula below.

### 2.4 Evaluation of quantitative criteria

Quantitative criteria values were calculated using Eqs. (1–5). EANC, EAD, and graduality are quantitative criteria. De Bruijn [15] assessed them by following equations.

*P*is flood frequency,

*D*(

*P*) is the expected damage as a function of flood frequency (€ million) and

*C*(

*P*) is the number of dead as function of flood frequency [15].

*Q*is discharge (m

^{3}/s), \(Q_{\mathrm{max} } = Q(P = \frac{1}{10000})\), \(Q_{\mathrm{min} }\) is the highest

*Q*for which \(D = 0\), \(D^{\prime }\) is comparative damage (%), D is damage (€ million) as a function of

*Q*, \(D_{\mathrm{max} } = D(Q_{\mathrm{max} } )\), \(D_{\mathrm{min} } = 0\) and

*n*is the rank number of the discharge level.

### 2.5 IWA method

In this section, the most common weighting methods as AHP (subjective method) and Entropy (objective method) are compared with a new approach in IWA methods. In AHP method, the results of the pair-wise comparison should be tested by consistency ratio and the satisfying results are obtained only if the judgments of experts are in concordance [53]. In Shannon’s Entropy method, computational processes have the superiority to expert judgment [27, 34]. The results obtained by both of subjective and objective methods have number of benefits and shortcomings. Subjective methods reflect the expert judgment directly, while objective methods just use precise analytical methods. To address this issue, SWARA method is suggested by Keršuliene et al. [31] which is able to combine subjective and objective methods. Not only can SWARA use the expert priorities and precise analytical approaches together, but it also offers a chance to estimate the differences of criteria significances.

### 2.6 SWARA method

### 2.7 Compensatory MCDM model

- (1)Computing the standardized decision matrix as Eq. (9).where \(f_{ij}\) is an element of standardized decision matrix and \(x_{ij}\) is the$$f_{ij} = \frac{{x_{ij} }}{{\sqrt {\mathop \sum \nolimits_{i = 1}^{m} x_{ij}^{2} } }}$$(9)
*A*th FRMP performance for*j*th criterion. - (2)Calculating
*S*(utility) and*R*(regret) by Eqs. (10) and (11) as follows:$$S_{i} = \mathop \sum \limits_{j = 1}^{n} w_{j} \cdot \frac{{f_{j}^{*} - f_{ij} }}{{f_{j}^{*} - f_{j}^{ - } }}$$(10)where \(f_{j}^{*} = maxf_{ij}\) and \(f_{j}^{ - } = minf_{ij}\) for positive criteria, \(f_{j}^{*} = minf_{ij}\) and \(f_{j}^{ - } = maxf_{ij}\) for negative criteria and \(W_{j}\) is the weight of the criterion$$R_{i} = \mathrm{max} \left\{ {w_{j} \cdot \frac{{f_{j}^{*} - f_{ij} }}{{f_{j}^{*} - f_{j}^{ - } }}} \right\}$$(11)*j*. \(f_{j}^{*}\) is the ideal solution and \(f_{j}^{ - }\) is the negative-ideal solution. - (3)Calculating
*Q*by Eq. (12).where \(S^{ - } = min S_{i}\), \(S^{*} = max S_{i}\), \(R^{ - } = min R_{i}\), \(R^{*} = max R_{i}\) and ν is defined as a weight of the strategy of “the majority of criteria” or “the maximum group utility”. This parameter could be valued as 0–1 and when the ν > 0.5, the criterion of$$Q_{i} = v\left[ {\frac{{S_{i} - S^{ - } }}{{S^{*} - S^{ - } }}} \right] + \left( {1 - v} \right)\left[ {\frac{{R_{i} - R^{ - } }}{{R^{*} - R^{ - } }}} \right]$$(12)*Q*will incline to majority rule. - (4)
Ranks of the FRMPs were sorted by considering the value of

*S*,*R*and*Q*. The best FRMP has the least value of these three parameters. - (5)The highest ranked FRMP in
*Q*parameter would be the best FRMP if the two following conditions were satisfied:where \(A_{1}\) and \(A_{2}\) are the FRMPs with first and second rank and$$C1:Q\left( {A_{2} } \right) - Q\left( {A_{1} } \right) \ge \frac{1}{n - 1}$$(13)*n*is the total number of the criteria.

*C2*: FRMP that has the first rank in *Q*, should also have the first rank in *S* and *R*, or both of them.

*C2*is not fulfilled, set of FRMPs ranking would be \(A_{1} ,A_{2} , \ldots ,A_{m}\). Where

*A*

_{m}is defined by the Eq. (14).

If circumstance *C1* is not fulfilled, \(A_{1}\) and \(A_{2}\) would be nominated as the best FRMP [41].

### 2.8 Semi-noncompensatory model

*s*, for modeling the preference. For instance, \(AsB\) express that

*A*outranks

*B*or

*A*is at minimum as worthy as

*B*in most of the criteria. First decision matrix normalized and remain process are as follows:

- (1)Determining the concordance matrix in Eq. (16):Where \(C_{ke}\) is sum of the weights of those criteria where FRMP$$C_{ke} = \mathop \sum \limits_{{j \in S_{ke} }} Wj$$(16)
*k*outranks FRMP*e*and \(W_{j}\) is weight of criteria*j*. - (2)Computing the discordance matrix as Eq. (17).where \(I_{ke} = J - S_{ke}\), and \(V_{ij}\) is the weighted standardized matrix component.$$d_{ke} = \frac{{\max_{{j \in I_{ke} }} \left| {V_{kj} - V_{ej} } \right|}}{{\max_{j \in j} \left| {V_{kj} - V_{ej} } \right|}}$$(17)
- (3)Computing concordance dominance matrix as Eqs. (18) and (19).$$f_{ke} = \left\{ {\begin{array}{*{20}c} 1 & {C_{ke} \ge \bar{C}} \\ 0 & {C_{ke} < \bar{C}} \\ \end{array} } \right.$$(18)$$\mathop {\bar{C}}\limits^{{}} = \mathop \sum \limits_{{\begin{array}{*{20}c} {k = 1} \\ {k \ne e} \\ \end{array} }}^{m} \mathop \sum \limits_{{\begin{array}{*{20}c} {e = 1} \\ {e \ne k} \\ \end{array} }}^{m} \frac{{C_{ke} }}{{m\left( {m - 1} \right)}}$$(19)
- (4)Computing discordance dominance matrix as Eq. (20).$$g_{ke} = \left\{ {\begin{array}{*{20}c} 0 & {d_{ke} > \bar{d}} \\ 1 & {d_{ke} \le \bar{d}} \\ \end{array} } \right.$$(20)$$\mathop {\bar{d}}\limits^{{}} = \mathop \sum \limits_{{\begin{array}{*{20}c} {k = 1} \\ {k \ne e} \\ \end{array} }}^{m} \mathop \sum \limits_{{\begin{array}{*{20}c} {e = 1} \\ {e \ne k} \\ \end{array} }}^{m} \frac{{d_{ke} }}{{m\left( {m - 1} \right)}}$$(21)
- (5)Calculating final dominance matrix as Eq. (22).$$h_{ke} = f_{ke} .g_{ke}$$(22)
- (6)
Choosing the best FRMP: in final dominance matrix, numbers show dominance of the FRMPs in each row and beaten of the FRMPs in each column. The FRMP with less difference in sum of row and sum of column, is placed in the higher rank.

### 2.9 PROMETHEE method

PROMETHEE method calculate the net flow between two FRMPs \(A_{i}\) and \(A_{j}\) which is defined as in Eq. (23) [7].

*f*is the preferential function as Eq. (24).

### 2.10 Sensitivity analysis of IW

In order to assess the sensitivity of ranking to weights, the weight of each criterion is descended from minimum to maximum levels, and variation in ranking is examined. Summation of the weights is maintained to equal to one. Thus, every change in the weight of each criterion can cause changes in other weights as Eq. (26).

*i*in sensitivity analysis, \(W_{i}\) previous weight of criterion

*i*, \(W_{j}\) previous weight of criterion

*j*and \(W_{J}^{\prime }\) is improved weight of criterion

*j*.

## 3 Results and discussion

### 3.1 IW results

Decision matrix

Criteria | FRMP1 | FRMP2 | FRMP3 | FRMP4 | FRMP5 | FRMP6 | FRMP7 | \(t_{ind}\) | \(t_{pref}\) |
---|---|---|---|---|---|---|---|---|---|

Criterion #1 | 11,792 | 17767 | 12,574 | 2865 | 12,083 | 11,792 | 12,083 | 1000 | 3000 |

Criterion #2 | 5.7 | 6 | 5.7 | 5.7 | 6.3 | 6.7 | 6.7 | 1 | 2 |

Criterion #9 | 0.83 | 0.8 | 0.73 | 0.94 | 0.86 | 0.83 | 0.83 | 0.05 | 0.1 |

Criterion #4 | 4.4 | 1.9 | 3.8 | 2.2 | 2 | 4.4 | 2 | 0.2 | 1 |

Criterion #5 | 1 | 4 | 3 | 3.5 | 4 | 2.5 | 5 | 0.5 | 2 |

Criterion #6 | 1 | 0.6 | 0.9 | 5.8 | 0.4 | 1 | 0.4 | 0.2 | 1 |

Criterion #7 | 2 | 3 | 3 | 3 | 3.5 | 2.5 | 4 | 0.2 | 1 |

Criterion #8 | 3 | 5 | 1 | 2 | 4 | 3 | 4 | 1 | 2 |

Criterion #9 | 4 | 2 | 2 | 2 | 4 | 4 | 4 | 1 | 2 |

Criterion #10 | 1 | 5 | 2.8 | 3 | 2 | 2 | 2 | 0.5 | 1 |

Criterion #11 | 4 | 2 | 3 | 2.5 | 4 | 3.5 | 3 | 0.5 | 1 |

### 3.2 Results of IWA methods

The results of IWA methods

Criteria No | AHP | SWARA | Shannon’s entropy | SD |
---|---|---|---|---|

Criterion #1 | 0.090 | 0.086 | 0.081 | 0.050 |

Criterion #2 | 0.110 | 0.157 | 0.003 | 0.010 |

Criterion #3 | 0.050 | 0.014 | 0.002 | 0.010 |

Criterion #4 | 0.310 | 0.399 | 0.100 | 0.053 |

Criterion #5 | 0.175 | 0.255 | 0.101 | 0.052 |

Criterion #6 | 0.030 | 0.004 | 0.422 | 0.178 |

Criterion #7 | 0.050 | 0.007 | 0.021 | 0.028 |

Criterion #8 | 0.020 | 0.001 | 0.069 | 0.057 |

Criterion #9 | 0.065 | 0.025 | 0.055 | 0.045 |

Criterion #10 | 0.070 | 0.048 | 0.117 | 0.066 |

Criterion #11 | 0.030 | 0.002 | 0.027 | 0.031 |

### 3.3 Results of MCDM models

#### 3.3.1 MCDM results based on different IWA methods

The results of MCDM models with different IWA methods

FRMP | VIKOR (υ = 0.5) | ELECTRE I | PROMETHEE | ||||||
---|---|---|---|---|---|---|---|---|---|

AHP | SWARA | Entropy | AHP | SWARA | Entropy | AHP | SWARA | Entropy | |

#1 | 6 | 6 | 7 | 5 | 6 | 5 | 7 | 7 | 7 |

#2 | 2 | 2 | 2 | 1 | 2 | 3 | 4 | 2 | 2 |

#3 | 4 | 4 | 6 | 4 | 4 | 4 | 6 | 5 | 6 |

#4 | 3 | 3 | 1 | 2 | 3 | 1 | 3 | 4 | 1 |

#5 | 1 | 1 | 4 | 3 | 3 | 7 | 2 | 3 | 5 |

#6 | 5 | 5 | 5 | 4 | 5 | 2 | 5 | 6 | 3 |

#7 | 1 | 1 | 3 | 1 | 1 | 6 | 1 | 1 | 4 |

Changes in VIKOR results by different υ value

FRMP | AHP-VIKOR | Shannon’s Entropy-VIKOR | |||||
---|---|---|---|---|---|---|---|

υ = 0.1–0.7 | υ = 0.8–0.9 | υ = 0.1 | υ = 0.2 | υ = 0.3 | υ = 0.4–0.6 | υ = 0.7–0.9 | |

#1 | 6 | 7 | 3 | 4 | 6 | 7 | 7 |

#2 | 2 | 4 | 5 | 3 | 2 | 2 | 3 |

#3 | 4 | 6 | 4 | 5 | 7 | 6 | 6 |

#4 | 3 | 3 | 1 | 1 | 1 | 1 | 1 |

#5 | 1 | 2 | 7 | 7 | 5 | 4 | 4 |

#6 | 5 | 5 | 2 | 2 | 3 | 5 | 5 |

#7 | 1 | 1 | 6 | 6 | 4 | 3 | 2 |

#### 3.3.2 Different MCDM model results in FRMP and IW uncertainty

In order to measuring the different MCDM models in FRMP, the SWARA results was used as a benchmark in this part of calculation. Based on the results in SWARA-VIKOR model in Table 3, designing a warning system solely and the combination of designing a warning system and employing a flood insurance program were in the first priority, flood peak alleviation by Golestan-I reservoir was in the second rank, building a diversion canal and levees were in the third and fourth rank, and employing a flood insurance program was in the last priority. In SWARA-ELECTRE I the combination of designing a warning system and employing a flood insurance program was in the first rank, flood peak alleviation by Golestan-I reservoir was in the second rank, building a diversion canal and designing a warning system were in the third rank, building a levees in the study area and employing a flood insurance program were in fourth and fifth ranks. Based on the SWARA-PROMETHEE model the combination of designing the warning system and employing a flood insurance program was in the first rank, flood peak alleviation by Golestan-I reservoir was in the second rank, designing a warning system was in the third rank, building a diversion canal and levees in the study area were fourth and fifth rank, respectively. Employing a flood insurance program was in the last priority by SWARA-PROMETHEE model.

Maximum and minimum value of IW

Criteria | Maximum of weights | Minimum of weights |
---|---|---|

Criterion #1 | 0.18 | 0.021 |

Criterion #2 | 0.19 | 0.023 |

Criterion #3 | 0.16 | 0.021 |

Criterion #4 | 0.36 | 0.11 |

Criterion #5 | 0.3 | 0.1 |

Criterion #6 | 0.1 | 0.012 |

Criterion #7 | 0.19 | 0.012 |

Criterion #8 | 0.08 | 0.013 |

Criterion #9 | 0.19 | 0.02 |

Criterion #10 | 0.15 | 0.02 |

Criterion #11 | 0.1 | 0.012 |

MCDM results based on different IW

#1 | #2 | #3 | #4 | #5 | #6 | #7 | |
---|---|---|---|---|---|---|---|

| |||||||

No changes in weights | 6 | 2 | 4 | 3 | 1 | 5 | 1 |

Max Criterion #1 | 6 | 3 | 4 | 2 | 1 | 5 | 1 |

Max Criterion #2 | 6 | 2 | 5 | 3 | 1 | 4 | 1 |

Min Criterion #2 | 6 | 4 | 3 | 2 | 1 | 5 | 1 |

Max Criterion #3 | 5 | 2 | 4 | 1 | 1 | 3 | 1 |

Max Criterion #6 | 5 | 2 | 3 | 1 | 1 | 4 | 1 |

Max Criterion #10 | 4 | 1 | 2 | 1 | 1 | 3 | 1 |

| |||||||

No changes in weights | 6 | 2 | 4 | 3 | 3 | 5 | 1 |

Max Criterion #2 | 6 | 3 | 5 | 2 | 3 | 4 | 1 |

Max Criterion #3 | 6 | 3 | 5 | 2 | 3 | 4 | 1 |

Min Criterion #4 | 6 | 3 | 5 | 2 | 3 | 4 | 1 |

Max Criterion #9 | 7 | 4 | 6 | 3 | 2 | 5 | 1 |

Min Criterion #10 | 5 | 3 | 4 | 2 | 2 | 4 | 1 |

| |||||||

No changes in weights | 7 | 2 | 5 | 4 | 3 | 6 | 1 |

Max Criterion #6 | 7 | 3 | 5 | 2 | 4 | 6 | 1 |

Max Criterion #11 | 7 | 3 | 5 | 4 | 2 | 6 | 1 |

However, in all of MCDM methods FRMP #7 (the combination of using a flood warning system and applying a flood insurance) was in first rank as a non-structural strategy, variation of Techno-economic and environmental criteria in VIKOR method promoted like FRMPs #4 and #2 as structural measures to the first rank. Therefore, the result of VIKOR model was sensitive to the variation in IW and caused a conflict between structural and non-structural FRMPs for the first rank. The ELECTRE I model selected FRMP #7 a non-structural measure in all IW changes. The PROMETHEE model had better results in comparison to other MCDMs. It showed sensitivity only for the Criterion #6 and Criterion #11 which were not valuable criteria among other SDC and theses few changes in FRMPs priority were not relate to the conflict between structural and non-structural FRMPs. Therefore, MCDM results in different IW prove that PROMETHEE as a non-compensatory model was able to release more stable results in various IW for flood management in the case study area.

## 4 Conclusion

To assess the structural and nonstructural flood risk FRMPs in Gorganrood River, Golestan province of Iran, SDCs approach was useful to incorporate sustainability criteria into flood management. In this paper, seven FRMPs were ranked by three different groups of MCDM models as VIKOR, ELECTRE I, and PROMETHEE. In addition, different IWA methods as AHP, SWARA, and Shannon’s Entropy were employed to evaluate criteria. The sensitivity and uncertainty analysis assessed the efficiency of MCDM models as well as IWA methods. The results in IWA and the concordance results between the MCDMs, the dominance of SWARA, as a new weighing method, and the deficiency of Shannon’s Entropy, as one of the most common weighting methods, were proved. This process highlighted the combination of mathematical technique and expert judgment in SWARA as IWA method. The changes in IWA methods emphasized the sensitivity of VIKOR method due to the υ parameter. This compensatory model had also varied results in IW changes for important criteria, while ELECTRE I and PROMETHEE models had more stable results especially in priority of FRMP #7 (the combination of flood warning system and flood insurance) as a nonstructural FRMP. Based on the IW uncertainty along with sensitivity analysis to IWA methods, SWARA-PROMETHEE as noncompensatory method could be a robust technique to improve the flood management with consideration of SDCs approaches in this case study and this outcome may be applied in flood management based on sustainable development concept in other river basins.

For future works developing a spatial probabilistic multi-criteria structure to prioritize the FRMPs with consideration of hydraulic and hydrology uncertainties are recommended. Assessing the effects of flood factors such as depth, velocity, duration, and arrival time and canal and watershed characteristics as decision criteria can assist decision makers to realize the uncertainty in selection of FRMPs. In addition, a comprehensive comparison among other MCDM techniques is essential to verify or corroborate this study outcome.

## Notes

### Acknowledgements

The authors thank Iran’s Ministry of Energy, Water, and Wastewater Standards and Projects Bureau for funding this research through Contract No. 720/1015/87.

### Compliance with ethical standards

### Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

## References

- 1.Abrishamchi A, Ebrahimian A, Tajrishi M, Mariño MA (2005) Case study: application of multicriteria decision making to urban water supply. J Water Resour Plan Manage 131(4):326–335CrossRefGoogle Scholar
- 2.Ardalan A, Naieni KH, Kabir M-J, Zanganeh A-M, Keshtkar A-A, Honarvar M-R, Osooli M (2009) Evaluation of Golestan province’s early warning system for flash floods, Iran, 2006–7. Int J Biometeorol 53(3):247–254CrossRefGoogle Scholar
- 3.Azarnivand A, Hashemi-Madani FS, Banihabib ME (2014) Extended fuzzy analytic hierarchy process approach in water and environmental management (case study: Lake Urmia Basin, Iran). Environ Earth Sci 73(1):13–26CrossRefGoogle Scholar
- 4.Banihabib ME, Hashemi-Madani FS, Forghani A (2017) Comparison of compensatory and non-compensatory multi criteria decision making models in water resources strategic management. Water Resour Manage 31(12):3745–3759. https://doi.org/10.1007/s11269-017-1702-x CrossRefGoogle Scholar
- 5.Banihabib ME, Hashemi F, Shabestari MH (2016) A framework for sustainable strategic planning of water demand and supply in arid regions. Sustain Dev 25:254–266CrossRefGoogle Scholar
- 6.Banihabib ME, Laghabdoost-Arani A (2014) Multicriteria decision-making for flood management based on sustainable development criteria. Paper presented at the 7th international congress on environmental modelling and software, San Diego, California, USAGoogle Scholar
- 7.Brans JP, Vincke P, Mareschal B (1986) How to select and how to rank projects: the PROMETHEE method. Eur J Oper Res 24(2):228–238MathSciNetzbMATHCrossRefGoogle Scholar
- 8.Brouwer R, Van Ek R (2004) Integrated ecological, economic and social impact assessment of alternative flood control policies in the Netherlands. Ecol Econ 50(1):1–21CrossRefGoogle Scholar
- 9.Cambrainha GM, Fontana ME (2018) A multi-criteria decision making approach to balance water supply-demand strategies in water supply systems. Production. https://doi.org/10.1590/0103-6513.20170062 CrossRefGoogle Scholar
- 10.Chang C-L, Hsu C-H (2009) Multi-criteria analysis via the VIKOR method for prioritizing land-use restraint strategies in the Tseng-Wen reservoir watershed. J Environ Manage 90(11):3226–3230CrossRefGoogle Scholar
- 11.Chen Y, Paydar Z (2012) Evaluation of potential irrigation expansion using a spatial fuzzy multi-criteria decision framework. Environ Model Softw 38:147–157. https://doi.org/10.1016/j.envsoft.2012.05.010 CrossRefGoogle Scholar
- 12.Chen Y, Yu J, Khan S (2010) Spatial sensitivity analysis of multi-criteria weights in GIS-based land suitability evaluation. Environ Model Softw 25(12):1582–1591. https://doi.org/10.1016/j.envsoft.2010.06.001 CrossRefGoogle Scholar
- 13.Chitsaz N, Azarnivand A (2017) Water scarcity management in arid regions based on an extended multiple criteria technique. Water Resour Manage 31(1):233–250. https://doi.org/10.1007/s11269-016-1521-5 CrossRefGoogle Scholar
- 14.Chitsaz N, Banihabib ME (2015) Comparison of different multi criteria decision-making models in prioritizing flood management alternatives. Water Resour Manage 29(8):2503–2525. https://doi.org/10.1007/s11269-015-0954-6 CrossRefGoogle Scholar
- 15.De Bruijn KM (2005) Resilience and flood risk management: a systems approach applied to lowland rivers. Delft University of Technology, TU DelftGoogle Scholar
- 16.De Lange WJ (2006) Multi-criteria decision-making for water resource management in the Berg Water Management Area. University of Stellenbosch, StellenboschGoogle Scholar
- 17.Douven W, Buurman J (2013) Planning practice in support of economically and environmentally sustainable roads in floodplains: the case of the Mekong delta floodplains. J Environ Manage 128:161–168CrossRefGoogle Scholar
- 18.Penning-Rowsell EC, Parker D, Harries T (2008) Systematisation, evaluation and context conditions of structural and non-structural measures for flood risk reduction. CRUE Research Report No I-1: ERA-NET CRUEGoogle Scholar
- 19.Giupponi C (2007) Decision support systems for implementing the european water framework directive: the MULINO approach. Environ Model Softw 22(2):248–258. https://doi.org/10.1016/j.envsoft.2005.07.024 CrossRefGoogle Scholar
- 20.Han Z, Chen G, Li Y, Tang C, Xu L, He Y, Wang W (2015) Numerical simulation of debris-flow behavior incorporating a dynamic method for estimating the entrainment. Eng Geol 190:52–64. https://doi.org/10.1016/j.enggeo.2015.02.009 CrossRefGoogle Scholar
- 21.Hansson K, Danielson M, Ekenberg L (2008) A framework for evaluation of flood management strategies. J Environ Manage 86(3):465–480CrossRefGoogle Scholar
- 22.Hashemi MS, Zare F, Bagheri A, Moridi A (2011) Flood assessment in the context of sustainable development using the DPSIR frameworkGoogle Scholar
- 23.Hassan-Esfahani L, Banihabib ME (2016) The impact of slit and detention dams on debris flow control using GSTARS 3.0. Environ Earth Sci 75(4):1–11CrossRefGoogle Scholar
- 24.Herva M, Roca E (2013) Review of combined approaches and multi-criteria analysis for corporate environmental evaluation. J Clean Prod 39:355–371CrossRefGoogle Scholar
- 25.Hirabayashi Y, Mahendran R, Koirala S, Konoshima L, Yamazaki D, Watanabe S, Kim H, Kanae S (2013) Global flood risk under climate change. Nat Clim Change 3(9):816CrossRefGoogle Scholar
- 26.Huang IB, Keisler J, Linkov I (2011) Multi-criteria decision analysis in environmental sciences: ten years of applications and trends. Sci Total Environ 409(19):3578–3594CrossRefGoogle Scholar
- 27.Hwang CL, Yoon K (1981) Methods for multiple attribute decision making. In: Multiple attribute decision making. Springer, Berlin, pp 58–191CrossRefGoogle Scholar
- 28.Johnson C, Penning-Rowsell E, Tapsell S (2007) Aspiration and reality: flood policy, economic damages and the appraisal process. Area 39(2):214–223CrossRefGoogle Scholar
- 29.Katyal AK, Petrisor IG (2011) Flood management strategies for a holistic sustainable development. Environ Forensics 12(3):206–218CrossRefGoogle Scholar
- 30.Kenyon W (2007) Evaluating flood risk management options in Scotland: a participant-led multi-criteria approach. Ecol Econ 64(1):70–81CrossRefGoogle Scholar
- 31.Keršuliene V, Zavadskas EK, Turskis Z (2010) Selection of rational dispute resolution method by applying new step-wise weight assessment ratio analysis (SWARA). J Bus Econ Manage 11(2):243–258CrossRefGoogle Scholar
- 32.Kubal C, Haase D, Meyer V, Scheuer S (2009) Integrated urban flood risk assessment—adapting a multicriteria approach to a city. Nat Hazards Earth Syst Sci 9(6):1881–1895CrossRefGoogle Scholar
- 33.Liu Y, Gupta H, Springer E, Wagener T (2008) Linking science with environmental decision making: experiences from an integrated modeling approach to supporting sustainable water resources management. Environ Model Softw 23(7):846–858. https://doi.org/10.1016/j.envsoft.2007.10.007 CrossRefGoogle Scholar
- 34.Malekian A, Azarnivand A (2016) Application of integrated Shannon’s entropy and VIKOR techniques in prioritization of flood risk in the Shemshak watershed, Iran. Water Resour Manag 30(1):409–425CrossRefGoogle Scholar
- 35.Mardani A, Zavadskas EK, Govindan K, Senin AA, Jusoh A (2016) VIKOR technique: a systematic review of the state of the art literature on methodologies and applications. Sustainability 8(1):37. https://doi.org/10.3390/su8010037 CrossRefGoogle Scholar
- 36.Meyer V, Scheuer S, Haase D (2009) A multicriteria approach for flood risk mapping exemplified at the Mulde river, Germany. Nat Hazards 48(1):17–39CrossRefGoogle Scholar
- 37.Moghaddam NB, Nasiri M, Mousavi SM (2011) An appropriate multiple criteria decision making method for solving electricity planning problems, addressing sustainability issue. Int J Environ Sci Technol 8(3):605–620. https://doi.org/10.1007/Bf03326246 CrossRefGoogle Scholar
- 38.Morris J, Bailey A, Lawson C, Leeds-Harrison P, Alsop D, Vivash R (2008) The economic dimensions of integrating flood management and agri-environment through washland creation: a case from Somerset, England. J Environ Manage 88(2):372–381CrossRefGoogle Scholar
- 39.Ni J, Sun L, Li T, Huang Z, Borthwick AG (2010) Assessment of flooding impacts in terms of sustainability in mainland China. J Environ Manage 91(10):1930–1942CrossRefGoogle Scholar
- 40.Opricovic S (2009) A compromise solution in water resources planning. Water Resour Manage 23(8):1549–1561CrossRefGoogle Scholar
- 41.Opricovic S, Tzeng G-H (2007) Extended VIKOR method in comparison with outranking methods. Eur J Oper Res 178(2):514–529zbMATHCrossRefGoogle Scholar
- 42.Piton G (2016) Sediment transport control by check dams and open check dams in Alpine torrents. Ph.D., Grenoble AlpesGoogle Scholar
- 43.Purjavad E, Shirouyehzad H (2011) A MCDM approach for prioritizing production lines: a case study. Int J Bus Manage 6(10):p221CrossRefGoogle Scholar
- 44.Roy B (1991) The outranking approach and the foundations of ELECTRE methods. Theor Decis 31(1):49–73MathSciNetCrossRefGoogle Scholar
- 45.Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New York, p 324Google Scholar
- 46.Saghafian B, Farazjoo H, Bozorgy B, Yazdandoost F (2008) Flood intensification due to changes in land use. Water Resour Manage 22(8):1051–1067CrossRefGoogle Scholar
- 47.Tscheikner-Gratl F, Egger P, Rauch W, Kleidorfer M (2017) Comparison of multi-criteria decision support methods for integrated rehabilitation prioritization. Water 9(2):68. https://doi.org/10.3390/w9020068 CrossRefGoogle Scholar
- 48.Tscheikner-Gratl F, Sitzenfrei R, Rauch W, Kleidorfer M (2016) Integrated rehabilitation planning of urban infrastructure systems using a street section priority model. Urban Water J 13(1):28–40. https://doi.org/10.1080/1573062x.2015.1057174 CrossRefGoogle Scholar
- 49.Vansnick JC (1986) On the problem of weights in multiple criteria decision making (the noncompensatory approach). Eur J Oper Res 24(2):288–294MathSciNetzbMATHCrossRefGoogle Scholar
- 50.Wehrmann H, Hübl J, Holzinger G (2006) Classification of dams in torrential watersheds. Paper presented at the proceedings on INTERPRAEVENT conferrenceGoogle Scholar
- 51.Yang J-S, Chung E-S, Kim S-U, Kim T-W, Kim Y (2011) Prioritization of water management under climate change and urbanization using multi-criteria decision making methods. Hydrol Earth Syst Sci Dis 8:9889–9925CrossRefGoogle Scholar
- 52.Yazdandoost F, Bozorgy B (2008) Flood risk management strategies using multi-criteria analysis. Proc ICE-Water Manage 161(5):261–266Google Scholar
- 53.Zavadskas EK, Vilutienė T (2006) A multiple criteria evaluation of multi-family apartment block’s maintenance contractors: I—Model for maintenance contractor evaluation and the determination of its selection criteria. Build Environ 41(5):621–632CrossRefGoogle Scholar