## Abstract

There has been an increasing demand for accurately evaluating flood disaster levels in order to improve public safety and management of water resources. This article reviews the characteristics of the existing subjective and objective assessment methods, and introduces decision maker's preferences in the particle swarm optimization (PSO) algorithm for a better assessment of flood disaster level. The indicator weight vector of the fuzzy clustering iterative (FCI) model is used as the position vector of a particle in the approach herein proposed. The individuals that do not satisfy the preferences are screened out during the evolution process, in order to obtain more reasonable assessment results according to the preferences for the given scenario. The optimal weight vector of flood disaster samples is then obtained using FCI model combined with the proposed PSO with decision maker's preferences, referred to as PSODP algorithm. A case study of Xinjiang autonomous region of China demonstrates the results of flood rating using different decision maker's preferences, and provides several suggestions on preference type choice. This type of analysis could be used by the water conservation department to better classify the level of a disaster and channel resources accordingly, in the best way possible to manage the situation.

## INTRODUCTION

Flood disaster is the most common natural hazard in the world (Nouasse *et al.* 2016). With an increasing awareness about the significance of public safety, a comprehensive and reliable assessment of flood disaster level is becoming critical in order to plan and manage relief projects (Du *et al.* 2015). Flood disaster level evaluation is a fundamental and important task in order to establish a hazard assessment model as a decision basis for managing flood. The degree of flood disaster is influenced by various index factors, such as the population affected by flood disaster, the number of buildings damaged, direct economic loss, etc., to name a few. These factors may also exhibit conflicting nature with each other in certain scenarios. For example, in an underdeveloped area, a flood will influence a large number of people, but the economic losses are small. In contrast, in a developed area, the economic losses are greater, but the number of affected people is relatively small. Hence, assigning appropriate weights to different index factors is a challenging problem for many flood disaster level evaluation models.

Based on the existing literature, the determination of index weights for flood disaster level evaluation can be classified into three categories: subjective weighting methods (Yu & Chen 2005; Yang *et al.* 2013), objective weighting methods (Huang *et al.* 2010; He *et al.* 2011), and comprehensive weighting methods (Yuan *et al.* 2013). However, these methods do not consider the intervention of experts. So far, limited attention has been paid to the role of the preference relationship during the process of evaluating flood hazard level. Therefore, subsequent inclusion of the preference of a decision maker could decrease the reliability of the weight index assignment significantly, and could result in inaccurate decisions due to various uncertainties. However, on the other hand, it is difficult to assess the level of disaster using the simple objective weighting method (or a combination of the objective weights) under different preferences to meet the needs of the actual situation of the affected areas.

Fuzzy set system has recently received increasing attention in water conservation projects (Razavi Toosi & Samani 2014; Chen *et al.* 2015). As an advanced unsupervised classification technique, fuzzy clustering iterative (FCI) model was proposed by Chen (1998) to solve real world optimization problems in water resource management, including runoff classification, water quality assessment, etc. The FCI model utilizes index weight vector to minimize the squared sum of the general Euclidean weighted distance (GEWD) through iterative tuning of parameters. Category eigenvalues are adopted to rank the samples in the same category. Simple FCI model is a sample classification method that tunes weights of the fuzzy class center matrix and fuzzy clustering matrix iteratively. The different weighting of each index will have different influence on the result of the classification and evaluation. If the weight of an attribute is more than that of others, it would imply that this weight corresponds to the most important index. Using this concept, variable weighted FCI model was developed for solving the problem of classification and evaluation recently (Chen 2005; Chen & Guo 2006). He *et al.* (2011) used chaotic differential evolution (CDE) to tune the index weight of FCI for evaluating the flood disaster level. Liao *et al.* (2013) modified the FCI model to provide an effective application for flood classification. Subsequently, Liao *et al.* (2015) incorporated projection pursuit model with the FCI model to obtain more reasonable assessment of flood disaster levels. However, the approach did not take into account any preference relationship of the decision maker. In order to improve the operability further and to facilitate its application, the decision maker's preference is considered while determining the index weights in this article.

In this paper, we introduce the preference of decision maker into the FCI based flood disaster level evaluation model. The weight vector corresponding to the four index factors that affect is defined as a position variable vector of the proposed particle swarm optimization (PSO) algorithm considering the decision maker's preference (PSODP). Three kinds of preferences are considered to assess flood hazard level in Xinjiang autonomous region of China for the historical flood events of 1996. During the algorithm run, if a particle dissatisfies the prescribed preference structure, then it is filtered out (discarded), and a random new particle replaces it in order to maintain the population size of the swarm. The ten available flood disaster samples from Xinjiang are divided into four groups, and the comprehensive evaluation value of each flood disaster is calculated to rank the flood disaster levels in the same category by identifying the degree of each row in the classification-matrix. Finally, the evaluation results under types of preferences of a decision maker are ranked based on the identified degree of each row and the comprehensive evaluation value of each flood disaster sample.

The main contributions of this article are as follows:

- (1)
We first propose a PSO algorithm considering decision maker's preference to optimize FCI model for evaluating flood disaster levels. The comprehensive evaluation value method is incorporated into the FCI model for obtaining more reasonable ranking of the results.

- (2)
The decision maker's preference can be quantified according to the index weight of the factor. More reasonable evaluation schemes are obtained to overcome the shortcomings of traditional methods.

- (3)
Based on a practical flood disaster case study from China, the discussion of three preference schemes indicates that proposed PSODP has a potential to provide the decision maker with a more flexible evaluation scheme.

The remainder of the paper is organized as follows: the next section discusses the existing FCI model, then in the subsequent section an introduction of the standard PSO algorithm is given. Thereafter, the PSODP algorithm combining comprehensive evaluation and FCI model is presented. The practical flood disaster case study is demonstrated in the following section, and then finally conclusions are provided.

## FCI MODEL

As one of the most important concepts in the fuzzy mathematics, FCI model was proposed by Chen (1998). In this theory, a fuzzy membership function can be defined as a rule to explore a mapping between a given set of observations and their relevant factors (Goyal & Gupta 2014; Lai *et al.* 2015). The implementation of the model consists of following steps.

*X*is transformed into the matrix of index normalized eigenvalues as: where

*x*

_{i}_{,max}and

*x*

_{i,}_{min}denote the maximum and minimum values, respectively, of attribute

*i*. Thereafter, the preprocessed data are converted into index normalized eigenvalues set by the Equation (3). where

*r*is the normalized value of attribute

_{ij}*i*at sample

*j*, and lies in the bounds [0,1].

Here, *u _{hj}* expresses the relative membership degree of sample

*j*belonging to level

*h*.

*l*+ 1 iteration can be calculated as shown in the following equations (Chen 1998):

## PARTICLE SWARM OPTIMIZATION

PSO algorithm is a metaheuristic optimization approach proposed by Kennedy & Eberhart (1995). In the PSO algorithm, particles adjust their positions according to their own experience (referred to as ‘cognitive learning’), and the experience of neighboring particles (referred to as ‘social learning’).

*m*particles

**= (**

*X**x*

_{1},

*x*

_{2}, … ,

*x*)

_{m}*in a*

^{T}*d*-dimensional target search space. Let

**and**

*x***denote an**

*v**i*-th particle's position and its flight velocity as

*= (*

**x**_{i}*x*

_{i}_{1},

*x*

_{i}_{2}, … ,

*x*)

_{id}*and*

^{T}**= (**

*v*_{i}*v*

_{i}_{1},

*v*

_{i}_{2}, … ,

*v*)

_{id}*. Furthermore, let*

^{T}**= (**

*p*_{i}*p*

_{i}_{1},

*p*

_{i}_{2}, … ,

*p*)

_{id}*denote the personal best position of the*

^{T}*i*-th particle. Similarly, the global best position among all the particles is denoted by

**= (**

*p*_{g}*p*

_{g}_{1},

*p*

_{g}_{2}, … ,

*p*)

_{gd}*. The velocity and position of the*

^{T}*i*-th particle are calculated as follows:

Here, *t* + 1 is the current iteration number; is the maximum iterations (generations) considered during the search. The above formulas are applied iteratively over each dimension of each individual, checking every time if the current value of *x _{ij}* has resulted in a better evaluation than

*p*, in which case it will be updated.

_{ij}*c*

_{1}and

*c*

_{2}are positive numbers known as acceleration constants;

*r*

_{1}and

*r*

_{2}are uniformly distributed random numbers in the range of (0,1); is the inertia weight which affects the exploration behavior of particles. It is common to assume a linearly decreasing inertia factor as proposed by Shi & Eberhart (1998).

In order to apply PSO to the given problem, the objective and constraints need to be defined. To incorporate the decision maker's preference in the flood disaster level evaluation, the conventional PSO is modified to minimize the squared sum of the GEWD of FCI model subject to the constraint given in Equation (7).

## A PSODP ALGORITHM FOR THE FLOOD DISASTER EVALUATION

Although the existing PSO algorithm is able to tune the weights of FCI model, the size of the components of each position variable (i.e., the weights of FCI model) cannot be controlled. Therefore, this article introduces a filtering mechanism during the search in order to guide it towards solutions preferred by the decision maker's preference. The key steps of the algorithm are discussed below.

### Initialization of the population

Here, *rand* is the uniformly sampled random number between 0 and 1. are the upper and lower bounds, respectively, of *j*-th variable.

### Filter individuals that dissatisfy given preferences

*w*is assigned to the position of each particle (i.e., ). Each variable represents an index of evaluating flood disasters. The variables satisfy the equality constraint . If the decision maker considers that

*k-*th index is most important, then the particle that satisfies the preferences must meet the condition . The particles that do not satisfy this condition are filtered out (discarded). Thus,

*M*particles are selected from the swarm as follows. where is the

*p*-th particle meeting the preference in the (

*t*+ 1)-th iteration. If only single preference is considered, the objective values (using Equation (8)) are calculated for the chosen

*M*particles. The filtering rule needs to be modified accordingly when multiple preferences are considered. In this case, the sequence of index weights should be adjusted in order to meet the preferences of multiple decision makers. For example, suppose the first preference is the first index, the second preference is the second index, … , and the

*j*-th preference is the

*j*-th index (i.e. ). To incorporate this preference structure, the Equation (14) will be replaced by the following formula.

On the basis of the filtering formula (15), *M* particles that meet the given set of preferences are selected from *m* individuals .

### Evaluate the objective function

*l*is set to 0. The corresponding original clustering center matrix is calculated by inserting into the Equation (9). Then, the approximate clustering matrix is explored by substituting into the Equation (10), and the approximate clustering center matrix is obtained by substituting into the Equation (9). We compare corresponding values and , and update the iteration counter by

*l*=

*l*+ 1 until the termination criteria (16) is satisfied or the iteration counter reaches a prescribed maximum limit. in which express the prescribed tolerance values for accuracy of the fuzzy clustering matrix and clustering center matrix, respectively.

The and obtained after the above process represent the best estimates for their optimum values. The objective values are then calculated as , where *P* is the penalty factor. Thus, the given problem has been translated into an unconstrained optimization problem and the objective function value of each particle that satisfies preference and the constraint is evaluated according to obtained , . The optimal individual is denoted by .

### Update the position and velocity

According to the obtained fitness value, the position and velocity are updated using Equations (11) and (12), and the process repeats until the computational budget on maximum generations allowed (*T*_{max}) is over. This concludes the classification of flood disaster samples. Thereafter, identify the level of each flood disaster, and rank them by means of comprehensive evaluation values, as discussed in the next subsection.

### Rank the flood disaster level

*C*is the comprehensive evaluation value of

_{j}*j*-th sample,

*p*is the optimal weight vector under the preference of decision makers,

_{g}*R*= (

*r*) is the normalized values matrix (i.e. Equation (3)). According to the above comprehensive evaluation, a sorting is done within each class, and the precise flood disaster level is obtained.

_{ij}The flowchart of the proposed PSODP for evaluating flood disasters is shown in Figure 1. It is worth mentioning that the comprehensive evaluation value using equal weights should be used in ranking the flood disaster level without any preference (i.e. the regular assessment). This is done in order to evaluate the flood disaster level when no preference is implied. From Figure 1, it can be seen that the presented PSODP attempts to manipulate the variables during the evolution so that they converge towards final solutions that meet the preference criteria. Any type of preference can be assumed to obtain the evaluation results applicable to the given scenario.

## CASE STUDY

In this section, flood disasters of 1996 in Xinjiang autonomous region of China are evaluated and analyzed using the presented model (Yu & Chen 2005; He *et al.* 2011).

### Study area

Xinjiang autonomous region is located at the northwest edge of the China. Xinjiang covers an area of more than 1.66 million km^{2}, one sixth of the total size of China and larger than any other province or autonomous region (Figure 2). It is adjacent to central Asia, deeply inland, away from any ocean. It had 16.89 million inhabitants in 1996. In July 1996, a long period of heavy precipitation resulted in dozens of river floods occurring simultaneously, which influenced 10 areas of Xinjiang. The locations of the administrative organizations of the 10 areas are indicated in Figure 2. In view of four diverse assessment indices (Yu & Chen 2005), including the population affected by flood disaster , the direct economic loss , the area of destroyed buildings , and the area affected by flood disaster , flood loss samples are shown in Table 1.

Areas . | Population affected by flood disaster/10^{4}
. | Direct economic loss/10^{7} Rmb
. | Area of destroyed buildings/10^{4} m^{2}
. | Area affected by flood disaster/10^{4} m^{2}
. |
---|---|---|---|---|

1 Urumqi | 6.0000 | 3.4800 | 20.6900 | 0.1543 |

2 Tacheng | 5.9700 | 1.6080 | 6.2350 | 1.3740 |

3 Bortala | 4.3500 | 0.1770 | 2.8430 | 0.2601 |

4 Changji | 9.4000 | 7.9100 | 54.5000 | 2.3520 |

5 Turpan | 2.9600 | 4.9460 | 58.7280 | 1.6673 |

6 Hami | 2.6200 | 1.8260 | 5.1050 | 0.5458 |

7 Bayingolin | 4.5400 | 7.8800 | 21.7130 | 1.0792 |

8 Kizilsu | 5.6000 | 0.3950 | 1.5560 | 0.3410 |

9 Kashgar | 20.0000 | 1.4300 | 1.8900 | 0.2140 |

10 Bingtuan | 24.7270 | 6.3270 | 13.5920 | 4.6026 |

Areas . | Population affected by flood disaster/10^{4}
. | Direct economic loss/10^{7} Rmb
. | Area of destroyed buildings/10^{4} m^{2}
. | Area affected by flood disaster/10^{4} m^{2}
. |
---|---|---|---|---|

1 Urumqi | 6.0000 | 3.4800 | 20.6900 | 0.1543 |

2 Tacheng | 5.9700 | 1.6080 | 6.2350 | 1.3740 |

3 Bortala | 4.3500 | 0.1770 | 2.8430 | 0.2601 |

4 Changji | 9.4000 | 7.9100 | 54.5000 | 2.3520 |

5 Turpan | 2.9600 | 4.9460 | 58.7280 | 1.6673 |

6 Hami | 2.6200 | 1.8260 | 5.1050 | 0.5458 |

7 Bayingolin | 4.5400 | 7.8800 | 21.7130 | 1.0792 |

8 Kizilsu | 5.6000 | 0.3950 | 1.5560 | 0.3410 |

9 Kashgar | 20.0000 | 1.4300 | 1.8900 | 0.2140 |

10 Bingtuan | 24.7270 | 6.3270 | 13.5920 | 4.6026 |

### Parameters selection

According to the Law of the People's Republic of China on response to emergencies, the natural disasters, accidents and outbreaks related to public health are divided into special major, major, large and general levels, based on the extent of socio-economic harm and other consequences. Accordingly, the flood hazard degree can be divided into four levels, which includes catastrophic disasters, major disasters, large disasters and general disasters. In this article, the degree of flood disaster areas is also thus classified into four levels (i.e. *c* = 4). Considering the people-oriented principle, the factor of population affected by flood disaster is selected as one of the main preferences. Furthermore, the factor of direct economic loss is selected as another preference since the Chinese government has made economic development a prominent objective in recent years. Overall, three kinds of preference schemes are assumed to verify PSODP for FCI model, which are: **preference 1:** the weight of population affected by flood disaster is the highest ; **preference 2**: the weight of direct economy loss is the highest ; **preference 3**: the weight of population affected by the flood disaster is the highest, and the weight of direct economy loss is second .

For obtaining stable evaluation results and satisfying the preference of decision maker, the parameter of absolute errors are set to 10^{−4}, and the maximum iteration number *l* is 10 for the . The penalty factor *P* is set to 10^{6} in this case. The acceleration constants c_{1} and c_{2} are set to 2, the maximal velocity of particle is 0.3, and the weight factor linearly decreases from 1.2 to 0.2. In order to validate the stability of the presented method, PSODP is run 20 times independently to minimize the squared sum of the GEWD in Equation (8). The minimum (Min), maximum (Max), average values (Mean) and standard deviation (Std) of 20 times are shown in Table 2. The maximum number of iterations is set to 1,000. We show results with two different population sizes, 20 and 30, to show the dependence of the results on population size. From Table 2, it can be seen that the proposed approach is able to get good results consistently which is reflected in low standard deviation values.

Decision maker's preference . | Population size . | Mean . | Min . | Max . | Std . |
---|---|---|---|---|---|

Preference 1 | 20 | 2.6176e-02 | 1.8223e-02 | 4.2545e-02 | 5.1118e-03 |

30 | 2.5089e-02 | 1.8390e-02 | 3.5229e-02 | 4.9125e-03 | |

Preference 2 | 20 | 3.4305e-02 | 2.9107e-02 | 4.4790e-02 | 4.5497e-03 |

30 | 3.4428e-02 | 2.8449e-02 | 4.4096e-02 | 4.1262e-03 | |

Preference 3 | 20 | 3.4264e-02 | 2.5179e-02 | 4.8284e-02 | 6.9358e-03 |

30 | 3.2588e-02 | 2.1049e-02 | 4.1908e-02 | 6.4863e-03 |

Decision maker's preference . | Population size . | Mean . | Min . | Max . | Std . |
---|---|---|---|---|---|

Preference 1 | 20 | 2.6176e-02 | 1.8223e-02 | 4.2545e-02 | 5.1118e-03 |

30 | 2.5089e-02 | 1.8390e-02 | 3.5229e-02 | 4.9125e-03 | |

Preference 2 | 20 | 3.4305e-02 | 2.9107e-02 | 4.4790e-02 | 4.5497e-03 |

30 | 3.4428e-02 | 2.8449e-02 | 4.4096e-02 | 4.1262e-03 | |

Preference 3 | 20 | 3.4264e-02 | 2.5179e-02 | 4.8284e-02 | 6.9358e-03 |

30 | 3.2588e-02 | 2.1049e-02 | 4.1908e-02 | 6.4863e-03 |

### Results and discussion

In order to demonstrate the performance of presented PSODP for FCI model, the assessment results are compared with those from the simple FCI (Yu & Chen 2005) and CDE for FCI model (He *et al.* 2011) which do not consider the decision maker's preferences. The results of FCI model optimized using PSO without preferences are also included in the comparison. It is worth mentioning that the ranking of comprehensive evaluation values use equal weight in PSO for FCI model without considering preferences. According to the calculation results of the fuzzy clustering matrix Equation (10) (He *et al.* 2011), Tables 3 and 4 list the assessment indices and ranked results of the abovementioned three kinds of FCI models without considering preferences.

Evaluation method without considering preferences . | Assessment indices . | |||
---|---|---|---|---|

. | . | . | . | |

FCI | 0.2500 | 0.3747 | 0.1640 | 0.2114 |

CDE for FCI | 0.0139 | 0.0244 | 0.8759 | 0.0858 |

PSO for FCI | 0.1091 | 0.0760 | 0.6682 | 0.1469 |

Evaluation method without considering preferences . | Assessment indices . | |||
---|---|---|---|---|

. | . | . | . | |

FCI | 0.2500 | 0.3747 | 0.1640 | 0.2114 |

CDE for FCI | 0.0139 | 0.0244 | 0.8759 | 0.0858 |

PSO for FCI | 0.1091 | 0.0760 | 0.6682 | 0.1469 |

The disaster level . | Evaluation method without considering preferences . | ||
---|---|---|---|

FCI . | CDE for FCI . | PSO for FCI . | |

Catastrophic disaster | 10 | 10 | 10 |

Major disaster | 4 | 5 4 | 4 5 |

7 | |||

5 | |||

Large disaster | 1 | 1 | 7 |

9 | 7 | 1 | |

General disaster | 6 | 2 | 9 |

2 | 6 | 2 | |

3 | 8 | 6 | |

8 | 9 | 8 | |

3 | 3 |

The disaster level . | Evaluation method without considering preferences . | ||
---|---|---|---|

FCI . | CDE for FCI . | PSO for FCI . | |

Catastrophic disaster | 10 | 10 | 10 |

Major disaster | 4 | 5 4 | 4 5 |

7 | |||

5 | |||

Large disaster | 1 | 1 | 7 |

9 | 7 | 1 | |

General disaster | 6 | 2 | 9 |

2 | 6 | 2 | |

3 | 8 | 6 | |

8 | 9 | 8 | |

3 | 3 |

From Table 3, we observe that the weight corresponding to the direct economic loss is the highest (0.3747) for the case of simple FCI. In terms of CDE and PSO for FCI model, the index weight of destroyed building is more than 60%. It shows that the index of destroyed buildings is considered the most prominent, which is clearly unreasonable. Thus, it can be seen from Table 3 that some unreasonable results on index weights are obtained by different FCI models without considering preferences. For example, the index weight of the factor of destroyed buildings calculated by CDE and PSO reach 0.8759 and 0.6682, respectively. That is to say, the importance of destroyed buildings is more than the sum of all the other indices. It is possible to make severe decision-making errors if the relief plans are formulated in terms of destroyed buildings.

Table 4 shows the similar classification results and markedly different ranked results among the three kinds of FCI models without considering preferences. However, once again, the methods face challenges in satisfying the necessity of making appropriate relief aid disaster scheme, when the index weight of the population affected by flood disaster is considered the most important factor.

From a decision-making perspective, the preference of expert decision makers tends to assure the most reasonable relief plan for dealing with the flood disaster loss. Tables 5 and 6 elaborate the optimal evaluation results obtained by PSODP for FCI model with different types of preferences. We select the optimal preference scheme for acquiring more meaningful evaluation results according to the fuzzy clustering matrix in formula (10) and the comprehensive evaluation value in formula (17), which is calculated based on the minimization of the squared sum of the GEWD obtained in Table 2.

Decision maker's preference . | Assessment indices . | |||
---|---|---|---|---|

. | . | . | . | |

Preference 1 | 0.7924 | 0.0485 | 0.0516 | 0.1075 |

Preference 2 | 0.0685 | 0.7301 | 0.0965 | 0.1049 |

Preference 3 | 0.8747 | 0.0726 | 0.0126 | 0.0401 |

Decision maker's preference . | Assessment indices . | |||
---|---|---|---|---|

. | . | . | . | |

Preference 1 | 0.7924 | 0.0485 | 0.0516 | 0.1075 |

Preference 2 | 0.0685 | 0.7301 | 0.0965 | 0.1049 |

Preference 3 | 0.8747 | 0.0726 | 0.0126 | 0.0401 |

The disaster grade . | Evaluation results by PSODP for FCI model with different preferences . | ||
---|---|---|---|

Preference 1 . | Preference 2 . | Preference 3 . | |

Catastrophic disaster | 10 | 4 | 10 |

7 | |||

10 | |||

Major disaster | 9 | 5 | 9 |

1 | |||

Large disaster | 4 | 2 | 4 |

9 | |||

6 | |||

General disaster | 2 | 8 3 | 1 |

1 | 7 | ||

7 | 2 | ||

5 | 8 | ||

8 | 5 | ||

3 | 3 | ||

6 | 6 |

The disaster grade . | Evaluation results by PSODP for FCI model with different preferences . | ||
---|---|---|---|

Preference 1 . | Preference 2 . | Preference 3 . | |

Catastrophic disaster | 10 | 4 | 10 |

7 | |||

10 | |||

Major disaster | 9 | 5 | 9 |

1 | |||

Large disaster | 4 | 2 | 4 |

9 | |||

6 | |||

General disaster | 2 | 8 3 | 1 |

1 | 7 | ||

7 | 2 | ||

5 | 8 | ||

8 | 5 | ||

3 | 3 | ||

6 | 6 |

In Table 5, it is evident that the obtained index weights from the three different scenarios satisfy the preferences. Based on the evaluation results of different preferences as shown in Table 6, it is easy to observe that the flood disaster level and sample rankings have remarkable differences among three kinds of preferences. When we select preference 1 or preference 3, samples 10, 9 and 4 are classified as catastrophic disaster, major disaster, and large disaster, respectively. However, samples 4 and 7 become catastrophic disasters when the preference 2 is chosen by the decision maker. The sample 9 is regarded as large disaster because its direct economy loss is only 1.43 10^{7} Rmb.

In modern society, the principle of people-oriented is violated if we evaluate the flood disaster level in terms of the factor of direct economy loss (i.e. preference 2). A comparison between preference 1 and preference 3 demonstrates that the disasters of samples 1 and 7 are more severe than the disaster of sample 2 in preference 3, though they all belong to general disaster. In preference 1, the optimal index weight of the area affected by flood disaster is 0.1075, which is more than the sum of and . It leads to the disaster of sample 1 being less than the disaster of sample 2. Furthermore, Xinjiang is an underdeveloped region with a vast area and sparse population distribution (only 16.89 million people in 1996). Therefore, the indices of population affected by flood disaster and direct economic loss are more important than the indices of destroyed buildings and area affected by flood disaster in Xinjiang. At the same time, considering the affected population first can better reflect the people-oriented principle. On the other hand, the rapid development of economy is also playing an increasingly prominent role in the quality of social life. Therefore, the assessment scenario is conducive to the recovery of the affected area if the priority of the direct economic loss is second only to that of the population affected by flood disaster. Thus, this article suggests the decision makers select the preference 3 in the practical work for helping government make appropriate relief plans.

## CONCLUSIONS

In this study, a novel PSODP algorithm for FCI model is presented for evaluating the flood disaster levels. Based on fuzzy set theory and swarm intelligence, the method developed in this study is capable of considering the preference of decision makers for each flood disaster index and can achieve more rational evaluation results than traditional assessment methods without considering preferences. By means of the simulations and analysis, the main conclusions drawn from the study can be described as follows:

- (a)
In view of the seriousness of flood disasters, reasonable preference schemes should be devised to meet the actual needs of the scenario. In the assessment process, the presented PSODP for FCI model is able to obtain different evaluation results that satisfy various different types of preferences. Hence, the decision-making authorities can design more reasonable evaluation schemes according the situations of the affected areas.

- (b)
In order to better apply the preference information, the comprehensive evaluation is performed and the obtained optimal weight vector is adopted to sort the samples within the class when the PSODP for FCI model is conducted. Then, the evaluated flood disasters samples can be ranked more appropriately.

- (c)
Based on the people-oriented principle and the actual situation of Xinjiang, preference 3 is recommended to the decision-making authorities for designing appropriate relief programs, since it first considers the population affected by the flood disaster followed by direct economy loss. The evaluation degree of flood disaster may differ, depending on the evaluation scheme adopted, as is the case of sample 9. Considering the innovative evaluation scheme proposed, sample 9 is classified as a major disaster because the population suffering from the flood disaster is as high as 200,000, whereas the direct economic loss is only 1.4300 10

^{7}Rmb. However, adopting a traditional evaluation scheme, it is regarded as a general or large disaster. Therefore, flood disaster evaluation schemes with appropriate preferences should be researched and carefully established in the future in order to improve the management of flood disasters response as well as water resource management. - (d)
The proposed assessment method considering the preference of decision maker is also extendable to be implemented in the other engineering optimization fields, such as enterprise credit level evaluation, power system evaluation,

*et al.*

## ACKNOWLEDGEMENTS

This paper is funded by the National Key Research and Development Project (2016YFC0402208), the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin (China Institute of Water Resources and Hydropower Research) (Grant No. IWHR-SKL-201605), the CRSRI Open Research Program (CKWV2014213/KY), the National Natural Science Foundation (No. 71401049) and China Scholarship Council.

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