2. S. Q. Chen is with the School of Electronics Information Science, Fujian Jiangxia University, Fujian 350108, China
The numbers of social, environmental, and medical emergencies have been increasing in recent years, thereby causing losses of life and property, economic disruption, and environmental degradation, which often have significant effects on social development in certain regions. For example, an outbreak of severe acute respiratory syndrome occurred in 2003, followed by H1N1 bird flu in 2009, and H7N9 avian influenza in 2014. When an emergency occurs, a decision maker (DM) is required to generate an alternative to mitigate or minimize any negative effects as soon as possible. Thus, it is important to identify the best method for generating an effective mitigation plan in a short time to facilitate optimum decision making during an emergency.
The methods that have been used to deal with emergency decisionmaking include multiattribute risk analysis [1], the group analytic network process approach [2], the fault tree analysis (FTA)based method [3], casebased reasoning (CBR) [4], distancebased group decisionmaking [5], the game method [6], the analytic network process [7], and revised PROMETHEE Ⅱ [8]. CBR is used most widely among these various methods. CBR is a process for solving new problems by referring to previous similar cases, which helps the DM to make decisions as quickly as possible based on these precedents. CBR usually includes four steps: 1) representing the target case and the historical case; 2) retrieving the most similar historical case(s) from the case database; 3) adapting the solution to the selected historical cases to the current situation; and 4) updating by adding and deleting the historical case(s) to create a precedent database for solving future problems, if appropriate. Retrieval is regarded as the core of these four steps.
There are many examples of the successful use of CBR, such as Fan et al. [4] used CBR to generate project risk response strategies and emergency alternatives in the case of a gas explosion. Liao et al. [9] applied CBR in the context of environmental emergency preparedness, while Huang et al. [10] applied it to emergency management engineering. Liu et al. [11] used CBR to predict the emergency resource demand. Amailef and Lu [12] applied an ontologysupported CBR approach to emergency responses, while Liu and Yu [13] used CBR to retrieve precedent cases for risk management. As demonstrated by the high number of examples available, CBR is considered to be highly suitable for facilitating emergency decision making.
Previous studies have made significant contributions to the use of CBR during emergency decision making. In some actual situations, the emergency may be changing continuously such as fire hazards and disease infections. Moreover, during decision making processes, the DMs are bounded rationality and they have their own preferences. Thus, it is necessary to consider a special emergency decisionmaking problem with several distinct characteristics, including dynamic changes in the emergency, the preferences of DMs, and the impacts of alternative responses to the emergency. However, existing decisionmaking methods based on CBR do not consider the dynamics of the emergency and the preferences of DMs; therefore, it is necessary to further investigate the emergency decisionmaking problem by considering the characteristics of dynamic change, the preferences of DMs, and alternative implementations.
In order to achieve the aims stated above, we propose a new dynamic case retrieval approach. The proposed method makes three main contributions. First, we incorporate probability into the case representation based on the characteristics of dynamic change and we compute the utility similarity. Probability is a good measure of the possibility of random events. Changes in the emergency's attributes can be estimated based on the probability [3], [14], [15]. Every attribute can have several different states, so the state of the attribute in the next moment can be expressed by the probability of every state. The interval probability can adequately express these potential changes given that the characteristic of uncertainty exists in every emergency. The similarity of the changing trend in the emergency can then be obtained by computing the utility of the interval probability for every attribute. The similarity measurement that incorporates these changes is referred to as the dynamic similarity measurement. Second, we integrate the pairwise comparison matrix and the fuzzy preference matrix into the case retrieval process to express the preferences of DMs. During traditional emergency decision making, the DM is viewed as completely rational, whereas the DM has subjective preferences in practice. Fuzzy and multiplicative preferences are two commonly used methods for characterizing the subjective preferences of a DM [16], which can be expressed as a pairwise comparison matrix and a fuzzy preference matrix, respectively. Finally, the generation of a mitigating strategy is often complicated due to the existence of multiple criteria that affect the effectiveness of the emergency alternative. In this study, we consider the similarity between the target case and historical cases, but we also consider other factors such as the initial response time and the effects of alternative implementations according to the historical cases. Therefore, multicriteria decisionmaking methods with integrated subjective preferences and objective information may prove helpful by allowing DMs to generate emergency mitigation strategies.
The remainder of this paper is organized as follows. In Section Ⅱ, we introduce the emergency decisionmaking problem. In Section Ⅲ, we propose the hybrid approach for selecting an optimal historical case from the historical cases library. In Section Ⅳ, we present a case study based on a fire in a highrise building. Finally, we give our conclusions in Section Ⅴ.
Ⅱ. THE PROBLEMIn this section, we briefly describe the problem of generating the optimum solution in an emergency situation. We suppose that
Due to the dynamics of an emergency case, when we apply the CBR method to generate an alternative path, it is not sufficient to only consider case similarity, but instead the similarity of the trends in the changing characteristics of the emergency also needs to be considered. Thus, we use the interval probability with regard to every state of every attribute to represent the trends in an emergency case.
In this section, we propose a dynamic case retrieval method that integrates subjective preferences and objective information for use in emergency decisionmaking. First, we provide the formula for measuring the emergency case similarity. Second, we provide a measure for calculating the utility similarity of the changing trends during different emergencies. Finally, the most desirable alternative is determined by considering the emergency case similarity, the utility similarity in the changing trends, the initial response time, and the effects of implementing different historical alternatives. In addition, the DM provides his/her preference in terms of the solutions to the emergency and the relative weights for its attributes. The first part of this method is described as follows.
A. Retrieval of the Similar Historical CasesIn this study, we consider two forms of attribute values, i.e., interval number and fuzzy linguistic variables.
First, we calculate the distance between the attributes for the target case
$ d_{ij}=\dfrac{\sqrt{(x_{ij}^{L}x_{0j}^{L})^{2}+(x_{ij}^{U}x_{0j}^{U})^{2}}}{d_{i}^{ {\rm max}}} $  (1) 
where
If attribute value
$ \begin{align} e_{h}&=(e_{h}^{a}, e_{h}^{b}, e_{h}^{c})\notag\\ &=({\rm max}(\frac{h1}{f}, 0), \frac{h}{f}, \min(\frac{h+1}{f}, 1)) \end{align} $  (2) 
where
When the fuzzy linguistic variables are represented as a triangular fuzzy number, the formula for
$ d_{ij}=\dfrac{\sqrt{(x_{ij}^{a}x_{0j}^{a})^{2}+(x_{ij}^{b}x_{0j}^{b})^{2}+(x_{ij}^{c}x_{0j}^{c})^{2}}}{d_{i}^{{\rm max}}} $  (3) 
where
After this process, we use the simple additive weight approach to determine the similarity of the emergency cases. In order to estimate the weight vector
The multiplicative preference relationship between the relative weights of the attributes can be represented as
$ \begin{align} A =\begin{array}{l} \left({{\begin{array}{*{20}c} {a_{11}} & {a_{12}} & \cdots & {a_{1n}} \\ {a_{21}} & {a_{22}} & \cdots & {a_{2n}} \\ \vdots & \vdots & \ddots & \vdots \\ {a_{n1}} & {a_{n2}} & \cdots & {a_{nn}} \\ \end{array}}} \right) \\ \end{array} \end{align} $  (4) 
where
According to Satty's eigenvector method (EM) [18], we can estimate the weight vector
$ AW=\lambda_{{\rm max}}W. $  (5) 
If the multiplicative preference relation
$ AW=nW $  (6) 
which indicates that when the DM provides the multiplicative preference relation, the DM should ensure that the multiplicative preference relation is as consistent as possible.
The DMs have a preference in terms of the attribute weights, but they also want the total distance or extent of the emergency case to be minimized. There is no guarantee that the multiplicative preference relations and the minimum of the total distance would lead to the same estimates for the relative attribute weights, so we introduce the following deviation vector [16]:
$ H=AWnW=(AnI)W $  (7) 
where
$ \begin{align}\label{eq 3.8} &\min z=\alpha\cdot\sum\limits_{i=1}^{m}\sum\limits_{j=1}^{n}w_{j}d_{ij}+\beta\cdot\sum\limits_{j=1}^{n}\varepsilon_{j}\nonumber\\ &{\rm s. t.}~ \begin{cases} AWnWH=0\\ e^{T}W=1 \\ W\geq 0\\ \end{cases} \end{align} $  (8) 
where
$ \varepsilon_{j}=\varepsilon_{j}^{+}\varepsilon_{j}^{}, \quad j=1, \ldots, n $  (9) 
where
$ \begin{align}\label{eq 3.10} &\min z=\alpha\cdot\sum\limits_{i=1}^{m}\sum\limits_{j=1}^{n}w_{j}d_{ij}+\beta\cdot\sum\limits_{j=1}^{n} (\varepsilon_{j}^{+}+\varepsilon_{j}^{})\nonumber\\ &{\rm s. t.}~ \begin{cases} AWnWH^{+}+H^{}=0\\ e^{T}W=1 \\ W, H^{+}, H^{}\geq 0\\ \end{cases} \end{align} $  (10) 
where
Let
$ {\rm Sim}(C_{0}, C_{i})=1\sum\limits_{j=1}^{n}w_{j}d_{ij}. $  (11) 
According to the theory of casebased decision making [20][22], historical emergency cases that share high similarity with the target emergency case are selected as alternatives. Thus, we set a similarity threshold
The probabilities
Definition 1 [23] : If
1)
Thus, if the function
According to the COWA operator, we determine the utility measure for every attribute as follows.
First, we determine the function
$ \begin{align}\label{eq3.12} p_{ij}^{k}&=f_{\rho}(p_{ij}^{Lk}, p_{ij}^{Uk}) \notag\\ &=\int_{0}^{1}\dfrac{d\rho(y)}{dy}[p_{ij}^{Uk}y(p_{ij}^{Uk}p_{ij}^{Lk})] \notag\\ &=p_{ij}^{Lk}+(p_{ij}^{Uk}p_{ij}^{Lk})\int_{0}^{1}\rho(y)dy \end{align} $  (12) 
and because
$ \int _{0}^{1}\rho(y)dy=\dfrac{1\sum\limits_{k=1}^{l_{j}}p_{ij}^{Lk}}{\sum\limits_{k=1}^{l_{j}}p_{ij}^{Uk}\sum\limits_{k=1}^{l_{j}}p_{ij}^{Lk}}. $  (13) 
Second, according to Definition 1 and the function
$ \bar{p}_{ij}^{k}=p_{ij}^{Lk}+(p_{ij}^{Uk}p_{ij}^{Lk})\int_{0}^{1}\rho(y)dy $  (14) 
$ \bar{p}_{0j}^{k}=p_{0j}^{Lk}+(p_{0j}^{Uk}p_{0j}^{Lk})\int_{0}^{1}\rho(y)dy. $  (15) 
Next,
$ u_{ij}=\sum\limits_{k=1}^{l_{j}}u_{ij}^{k}\stackrel{k}{p_{ij}}. $  (16) 
Finally, the utility similarity for the changing trend in the emergency case is calculated by
$ {\rm Sim}' (C_{0}, C_{i})=1\sum\limits_{j=1}^{n}w_{j}u_{ij}u_{0j} $  (17) 
which yields the outcome:
To obtain the most desirable alternative to the emergency, we consider the case similarity, the initial response time, and the effects of implementing the historical case solution. The initial response time is one of the most important factors during emergency decision making. In order to make a more powerful decision in an emergency, we should consider the effects of different solutions to historical cases. The method proposed for selecting the most desirable historical emergency case is explained as follows.
Due to incommensurability among attributes, the decision matrix
$ y_{it}=\frac{z_{it}z_{t}^{\min}}{z_{t}^{{\rm max}}z_{t}^{\min}}, \, \, \, \, i=1, \ldots, m;~t\in O_{1} $  (18) 
$ y_{it}=\frac{z_{t}^{{\rm max}}{z_{it}}}{z_{t}^{{\rm max}}z_{t}^{\min}}, \, \, \, \, i=1, \ldots, m;~t\in O_{2} $  (19) 
where
Next, in some situations, DMs usually prefer to provide a fuzzy preference relation based on an alternative decision, which is given according to the DMs experience and professional knowledge, as studied previously [16]. In order to determine the best alternative, we need to consider the DM's preferences. Given that the DM provides a fuzzy preference matrix based on decision alternatives and a pairwise comparison matrix for the relative weights of the attributes, we combine these together into an integrated decision model to generate overall estimates of the relative weights of the attributes.
The multiplicative preference relation based on the relative weights of the attributes is represented by matrix
$ \begin{align} \label{eq3.20} { Q} = \begin{array}{l} \left({{\begin{array}{*{20}ccccccccccc} {q_{11}} & {q_{12}} & \ldots & {q_{1m}} \\ {q_{21}} & {q_{22}} & \ldots & {q_{2m}} \\ \vdots & \vdots & \ddots & \vdots \\ {q_{m1}} & {q_{m2}} & \ldots & {q_{mm}} \\ \end{array}}} \right) \\ \end{array} \end{align} $  (20) 
where
Thus, we obtain
$ \begin{align} \label{eq3.21} { F} = \begin{array}{l} \left({{\begin{array}{*{20}cccccccccc} {\sum _{j=2}^{m}q_{1j}} & {q_{12}} & \ldots & {q_{1m}} \\ {q_{21}} & {\sum _{j=1, j\neq 2}q_{2j}} & \ldots & {q_{2m}} \\ \vdots & \vdots & \ddots & \vdots \\ {q_{m1}} & {q_{m2}} & \ldots & {\sum _{j=1}^{m1}q_{mj}} \\ \end{array}}} \right). \\ \end{array} \end{align} $  (21) 
Based on matrices
$ \begin{align} &\min J=\alpha\cdot e^{T}(\Gamma^{+}+\Gamma^{})+\beta\cdot e^{T}(\varLambda^{+}+\varLambda^{})\nonumber\\ &{\rm s. t.}~ \begin{cases} [FY(n1)Y]V\Gamma^{+}+\Gamma^{}=0\\ (BmI)V\Lambda^{+}+\Lambda^{}=0 \\ e^{T}V=1\\ W, \Lambda^{+}, \Lambda^{}, \Gamma^{+}, \Gamma^{}\geq 0\\ \end{cases} \end{align} $  (22) 
where
Let
$ U_{i}=\sum\limits_{t=1}^{4}v_{t}y_{it}. $  (23) 
Subsequently, the hybrid similarities can be calculated using (23) and
In this section, we present a case study based on an emergency response to a fire, which illustrates the feasibility and validity of the proposed method. First, we introduce the highrise fire scenario. The dynamic retrieval method is then used to obtain the optimal historical case. In addition, a sensitivity analysis is presented, which shows the impact on retrieval of the factors considered.
A. Introduction of the CaseIn recent years, increasingly higher buildings have exacerbated the risk of fire hazards in China. Thus, generating an effective emergency plan to respond to a highrise fire has attracted significant social attention. In our scenario, a fire control center receives an alarm about a fire in a highrise building. The fire situation
With respect to the changing trends in the emergency, the interval probability of every attribute is shown in Table Ⅲ. Data from the initial response time
$ \begin{align*} &A=\begin{pmatrix} 1 & 0.5 & 1 & 1\\ 2 & 1 & 2 & 0.5\\ 1 & 0.5 & 1 & 2 \\ 1 & 2 & 0.5 & 1\\ \end{pmatrix}. \end{align*} $ 
To solve the problem described above, we used the proposed method to determine the most desirable alternative to the emergency. The computation processes and results are given as follows.
Step 1: Compute the similarity between the historical cases and the target case. For attributes in the form of interval numbers, i.e.,
The weight vector
Based on the experience of experts, the case similarity threshold was set at 0.6 [24]. According to Table Ⅵ, it is clear that cases
Step 2: Compute the utility similarity for the changing trends in the emergency case. First, according to the interval probability of every attribute, we obtained the value of
Step 3: Select the optimal emergency alternative. According to the alternative case library and the decision attribute, the DM provided the fuzzy and multiplicative preference relations as follows.
$ \begin{align*} \!\!\!\!\!\!\!\!\!&B=\begin{pmatrix} 1 & 0.5 & 2 & 3\\ 2 & 1 & 3 & 4\\ 0.5 & 0.3333 & 1 & 2 \\ 0.3333 & 0.25 & 0.5 & 1\\ \end{pmatrix} \end{align*} $ 
$ \begin{align*} &Q=\begin{pmatrix}  & 0.44 & 0.64 & 0.54 & 0.6\\ 0.56 &  & 0.69 & 0.6 & 0.63\\ 0.36 & 0.31 &  & 0.4 & 0.68 \\ 0.46 & 0.4 & 0.6 &  & 0.58 \\ 0.4 & 0.37 & 0.32 &0.42 &  \\ \end{pmatrix}. \end{align*} $ 
To find the best alternative for the DM, we first transformed the linguistic variables into triangular fuzzy numbers using (2), i.e.,
$ \begin{align*} &Y=\begin{pmatrix} 0.5672 & 1 & 0.8333 & 1\\ 0.3566 & 0.6035 & 1 & 0.7500\\ 1 & 0.9328 & 0.5 & 0.3750 \\ 0.1142 & 0 & 0.6667 & 0.3750\\ 0 & 0.0442 & 0 & 0\\ \end{pmatrix}. \end{align*} $ 
Based on the given fuzzy preference relation
$ \begin{align*} &F=\begin{pmatrix} 0.22 & 0.44 & 0.64 & 0.54 & 0.6\\ 0.56 & 2.48 & 0.69 & 0.6 & 0.63\\ 0.36 & 0.31 & 1.75 & 0.4 & 0.68 \\ 0.46 & 0.4 & 0.6 & 2.04 & 0.58\\ 0.4 & 0.37 & 0.32 & 0.42 & 1.09\\ \end{pmatrix}. \end{align*} $ 
According to the fuzzy and multiplicative preference relations and the decision matrix information, we determined the weights of the decision attributes by solving model (22). Table Ⅷ shows the optimal relative weights estimated for the four attributes using different combinations of subjective preferences and objective information. Finally, we obtained the overall weighted assessment values of the five alternatives using (23) and the results are shown in Table Ⅸ.
We performed comparative analysis based on the results obtained using our method and other methods.
First, to obtain the most similar historical case, we used the case retrieval method described by Alptekin and Büyüközkan, which integrates CBR and the analytic hierarchy process (AHP) [25]. The attribute weights produced by AHP comprised
Second, we employed the hybrid similarity measure [4] to compute the similarity between target case
In addition, Li et al. [26] proposed a method for generating emergency alternatives based on similarity case analysis by considering the implementation effects of emergency alternatives belonging to similar cases. Thus, we also used this method to generate emergency alternatives for the highrise fire. First, the attribute weights were determined according to the weight optimization model of Zhao and Yu [27], where the results comprised
1) Impact of the Interval Probability on the Emergency Cases: We conducted the following sensitivity analysis according to the probabilities for each attribute of the target case.
As shown in Table Ⅲ, there are two types of state description: a linguistic description such as
The states of attributes
2) Impact of the Weights of the Four Decision Alternatives on the Case Ranking: We obtained different weights using various combinations of the multiplicative preference relations for the four attributes and the fuzzy preference relations for the five alternatives. When we changed the weight of the decision attribute, the overall ranking values for the historical cases also changed in the corresponding manner. The overall ranking values for the four feasible alternatives with different weights are plotted in Fig. 1, which clearly demonstrate that emergency case
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Fig. 1 Impacts of the weights of the decision attributes on the emergency case ranking. 
In this study, we proposed a dynamic case retrieval method by integrating subjective preferences and objective information to facilitate emergency decision making. In the proposed method, we calculate the weights of the emergency attributes using a pairwise comparison matrix based on the relative weights of the attributes. Next, we calculate the utility similarity of the emergency case with respect to changes in the attributes. An overall weighted assessment value is then calculated for the historical cases to integrate subjective preferences and objective information, and the optimal historical case(s) is retrieved according to the overall assessment value obtained. Furthermore, we conducted a case study, which demonstrated the practical utility of the proposed method.
The proposed method has some distinct characteristics compared with existing methods for generating emergency plans. In particular, the proposed method comprehensively considers the subjective preferences of the DMs as well as the historical data in the process used to generate the emergency plans. As discussed earlier, most existing methods for generating emergency plans using CBR do not consider the subjective preferences of DMs or the degree of similarity in the changes that occur in an emergency case compared with historical precedents. Therefore, the proposed method addresses these deficiencies. Our proposed method also considers the similarity in terms of the changing attributes of an emergency, whereas few existing methods consider the dynamic development of the attributes, although this is important for selecting the optimal emergency alternative. Moreover, we conducted a sensitivity analysis and the data obtained also indicated that it is important to consider this factor.
Therefore, we suggest that the proposed method can yield distinct improvements when generating emergency plans. For example, in terms of the emergency case similarity, our method considers changes in the degree of the emergency, so the emergency plans obtained can respond better to the current emergency. Thus, the proposed method using CBR to integrate subjective preferences and objective information may ultimately facilitate improved decision making because it considers the similarity to previous emergency cases in order to generate the optimal emergency alternative, but it also considers the initial response time and the effects of implementing historical emergency cases, thereby obtaining a more practical emergency alternative.
In terms of future research, the proposed method can be embedded into an emergency decision support system to support DMs with effective decision making during an emergency.
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