Evacuation behavior analysis is deemed to be one aspect of evacuation planning. However, existing studies have not discussed group evacuation decisionmaking in the face of disagreement among decision makers. In this paper, rough set theory is applied to analyze group evacuation decisionmaking in passenger transport hub area with various groups including kin, lover, friend, colleague, and classmate. In the approach, improved tabu searchbased attribute reduction is proposed to find the minimal subset of attributes required to fully describe the information of group evacuation decisionmaking, and value reduction algorithm based on knowledge granulation is used to generate rules of group evacuation decisionmaking. Crossvalidation procedure is adopted to estimate the performance of rough set theory. Experimental results indicate that rough set theory has favorable performance. Thus, the proposed approach provides a new way for evacuation behavior analysis.
Urban passenger transport hub works as the joint of intermodal transit and the distribution center of massive passenger flow. In such densely populated area, small scale emergencies can result in severe consequences and should not be overlooked. It is vital to evacuate people from the affected area promptly. Thus, evacuation planning is very crucial. Evacuation behavior analysis is deemed to be one aspect of evacuation planning. Understanding emergency evacuation behavior would help better emergency evacuation planning.
Over the last few decades, considerable research has focused on evacuation behavior analysis related to hurricane evacuation [
By far, several methods have been put forward for helping us understand evacuation decisionmaking, including contingency table analysis [
Rough set theory can remove redundant information through the reduction and extract decision rules from a large number of original data on the premise of the maintenance of the same classification ability. Knowledge reduction, including attribute reduction and value reduction, is one of the core issues in rough set theory. On the one hand, attribute reduction tends to reduce the complexity and cost of decision process and promote higher rule quality. In order to compute useful reduction of information systems, many researchers have developed some efficient algorithms based on computational intelligence tools of genetic algorithm [
The remainder of this paper is organized as follows. The next section describes evacuation behavior survey in Wuchang Railway Station area for the preparation of data set used in this study. In the following section, rough set theory is introduced, including related concepts, the algorithms for attribution reduction and value reduction, and evaluation of the approach. Section four presents the application of rough set theory on group evacuation decisionmaking and compares the proposed method with other methods in performance. Finally, we conclude the paper with a summary and outlook for further research.
A survey was conducted about emergency evacuation behavior in Wuchang Railway Station area, with the hypothetical event of the toxic gas attack. The questionnaire was designed to collect the following information related to human behavior: (1) personal information including age, gender, education, temperament, and the number of luggage; (2) familiar with the route or not familiar with the route; (3) past experience; (4) the number of group members and group relationship; (5) human behavioral response including first action, evacuation route choice, group evacuation decisionmaking, and so on. Among the above information, the question for past experience is “Did you ever experience gas attack or participate in safety training,” and structured answer is “(1) Never experience gas/training experience/knowledge, (2) Have gas experience/training experience/knowledge.” The structured answer for temperament is “(1) Choleric (You are a strongwilled individual who makes decisions quickly and decisively.), (2) Sanguine (You are affectionate, enjoy social activities, and make friends easily.), (3) Phlegmatic (You are dependable, polite, and eventempered.), and (4) Melancholic (Time alone is vital for this reflective, introspective temperament.)”.
A total of 952 interviews were performed and 909 valid replies were collected. There were 523 (57.5%) valid replies coming from groups and 386 (42.5%) from the single passenger. This paper focuses on the analysis of group evacuation decisionmaking in the face of disagreement among decision makers. In order to select the attributes influencing group evacuation decisionmaking, contingency table analysis was performed to test the correlation between group decisionmaking and the characteristics of individual and group by utilizing statistical analysis software SPSS 19.0. As shown in Table
Chisquare test for group decisionmaking with several factors.
Factors  

Age  Gender  Education  Temperament  Experience  Number of luggage  Familiar with route  Group relationship  
Chisquare  24.604  22.489  25.258  26.315  31.02  12.804  10.303  32.467 

0.017  0.004  0.014  0.01  0.002  0.383  0.85  0.001 
The attribute set and attribute value set.
Class  Attribute set  Attribute value set 

Condition attribute  Age ( 

Gender ( 


Education ( 


Temperament ( 


Experience ( 


Group relationship ( 




Decision attribute  Group decisionmaking ( 

This section introduces rough set theory. Some basic notions are introduced in Section
In this section, some preliminary concepts such as indiscernibility, knowledge granulation, attribute reduction, and value reduction are briefly presented.
Let
For an attribute set
Let
Let
Let
Attribute reduction in rough set theory can preserve the information content while reducing the number of attributes involved. Based on relative partition granularity, a relative reduct can be defined by the following definition.
Let
In particular, a relative reduct with minimal cardinality is called minimal reduct. The goal of attribute reduction is to find a minimal reduct.
The process by which the maximum number of condition attribute values is removed without losing essential information is called value reduction. After value reduction, rules can be generated by associating the condition attribute values with the corresponding decision class value.
Let
The confidence of decision rule
For a certain rule,
In this section, improved tabu searchbased attribute reduction (ITSAR) is proposed to find a minimal reduct of group evacuation decisionmaking. First we introduce the main idea of tabu search, then describe the components of ITSAR, and finally give the ITSAR scheme.
Tabu search (TS) is a metaheuristic optimization method originally proposed by Glover [
ITSAR uses a binary representation for solutions (attribute subsets). Therefore, a trial solution
The role of Tabu List (TL) is to avoid being trapped in local optima. The first and second positions in TL are permanently reserved for two special solutions: solution of all ones (i.e., all attributes are considered), and solution of all zeroes (i.e., all attributes are discarded). The remaining positions in TL are used to save the most recently visited solutions. To improve search performance, dynamic selection strategies of tabu tenure are as follows.
The range of tabu tenure
Trial solutions
Repeat the following steps for
Set
Update the chosen positions by the rule
If
The main roles of diversification strategy are to direct the search process to new solution regions and to accelerate escaping from local optima. ITSAR defines a vector
Generate random numbers
Repeat the following step for
If
If the search still cannot find any improvement during some iterations after generating
Construct the set
Repeat the following steps for
Delete the attribute
Update
The complete algorithm is as follows.
Let the Tabu List (TL) contain the two extreme solutions: solution of all ones and solution of all zeroes; set
Generate neighborhood trials
Set
If the number of iterations exceeds
If the number of iterations without improvement exceeds
If the number of iterations without improvement exceeds
A heuristic algorithm based on knowledge granulation for value reduction, which is used to generate decision rules of group evacuation decisionmaking, is described as follows.
Examine the condition attribute of each decision rule by the column; if removing a condition attribute, three possible cases are as follows:
if there are conflicting decision rules, then retain the dropped attribute value of conflicting decision rules, which means the value cannot be eliminated;
if there are duplicate decision rules, then mark the dropped attribute value of duplicate decision rules as “
if there are no conflicting and duplicate decision rules, then mark the dropped attribute value as “?”, which means whether the value can be eliminated is pending.
Delete possible duplicate decision rules. If all the condition attributes of a decision rule are marked, then change the attribute value marked with “?” to the original attribute value.
Examine the attribute value marked with “?” of each decision rule.
If there is only one “?”, go to (3); if there are more than one “?”, calculate the significance of all attribute values marked with “?” according to Definition
Select the attribute value marked with “?” and maximum of the significance in the decision rule
If the decision can be made only by the attribute value without the mark, go to (4); otherwise, go to (5).
Change the attribute value marked with “?” to “
Change the attribute value marked with “?” to the original attribute value, and go to (2).
Delete decision rules in which all the condition attributes are marked as “
If there are two decision rules which satisfy the following two conditions: (a) only one condition attribute value is different, (b) one of different attribute values is marked as “
Calculate the confidence of each rule; export the rules.
In this study, examples were scarce; thus, crossvalidation (CV) procedure [
We evaluated the performance of the approach by applying 10 times 5fold crossvalidation tests. The performance of the approach was measured by the hit rate of decision rule with maximum value of confidence
This section presents our tests on group evacuation decisionmaking. We firstly develop the decision table in Section
The first step is to develop decision table for group evacuation decisionmaking. As discussed previously, we have used the dataset from evacuation behavior survey in Wuchang Railway Station area. The decision table includes 523 objects or samples. For each record, six conditional attributes are registered.
Table
An example of decision table with eight objects.
Objects 








1  2  1  2  2  1  2  2 
2  2  1  1  3  1  1  3 
3  2  2  2  2  2  1  4 
4  2  1  1  2  1  3  1 
5  3  2  1  3  1  3  1 
6  1  2  1  2  2  1  2 
7  2  2  2  4  2  3  1 
8  1  2  1  2  2  3  3 
The algorithms for attribute reduction and value reduction were programmed in MATLAB and applied to the decision table of group evacuation decisionmaking. The parameter values used in ITSAR were set to the following values:
After attribute reduction by applying 10 times 5fold crossvalidation tests, some reducts can be obtained. Table
Reducts and their frequency.
Reducts  Frequency 


8 

2 

14 

11 

6 

5 

3 

1 
Based on reducts obtained in the previous step, decision rules can be generated from the decision table by value reduction. For the reduct with the highest frequency, rules are obtained from the corresponding training set and shown in Table
Decision rules of the corresponding sample.
Decision rules  Confidence 

Rule 1: If ( 
1 
Rule 2: If ( 
1 
Rule 3: If ( 

Rule 4: If ( 

Rule 5: If ( 

Rule 6: If ( 

Rule 7: If ( 

Rule 8: If ( 

Rule 9: If ( 

Rule 10: If ( 

Rule 11: If ( 

Rule 12: If ( 

Rule 13: If ( 

Rule 14: If ( 

Rule 1 means that if condition attribute values satisfy the following conditions, that is, gender is male and temperament is choleric, and group relationship is lover, then group decisionmaking mode chosen by individual is choosing the route approved by the one doing things reasonably. The confidence of this rule is 1.
Rule 3 means that if condition attribute values satisfy the following conditions, that is, gender is female and temperament is choleric, and group relationship is lover, then group decisionmaking mode chosen by individual has three possibilities, that is, choosing the route approved by self (with the confidence of 0.125), or choosing the route approved by the one familiar with the route (with the confidence of 0.5), or choosing the route approved by the one doing things reasonably (with the confidence of 0.375).
Decision rules generated from the training set are applied to the corresponding testing set in order to harvest a performance estimate. The results from 10 times 5fold crossvalidation tests show that the range of
Performance of rough set theory.
To get a better picture of the power of rough set theory, a comparison with other techniques using the same training and testing samples would prove useful. For the purpose of comparison, we chose tabu search for attribute reduction (TSAR) [
In the TSAR algorithm, the dependency degree of decision attribute is used to measure the quality of a solution, and fixed tabu tenure is used. We set fixed tabu tenure as 8 in our study. TSAR and ITSAR could obtain the same reducts in this paper. The solution times of two methods for 50 runs are displayed in Figure
Solution times of ITSAR and TSAR.
Multinomial logistics regression can be used when a categorical dependent variable has more than two categories. For the implementation of the multinomial logistic regression model, the backward elimination procedure was performed by using SPSS software in this study. The performance of multinomial logistics regression model was determined by crossvalidation procedure described in Section
The results from 10 times 5fold crossvalidation test show that the range of
Goodnessoffit measures of the best logistic regression model.

DF  Sig.  

Pearson  401.191  360  0.066 
Deviance  385.701  360  0.168 
Performance of multinomial logistics regression.
Table
Performance comparison.




Rough set theory  0.421  0.663 
MLR  0.362  0.651 
On the other hand, the fluctuation of the curve in Figure
In this paper, we focus on the analysis of group evacuation decisionmaking in the face of disagreement among decision makers in passenger transport hub area. Rough set theory is applied to analyze group evacuation decisionmaking. Based on evacuation behavior survey, we develop the decision table of group evacuation decisionmaking. An improved tabu searchbased attribute reduction (ITSAR) is proposed to find a minimal reduct of decision table, and then a heuristic algorithm based on knowledge granulation for value reduction is introduced for rule extraction of decision table. According to the presented research, rules of group evacuation decisionmaking are generated in a readily understandable form (a set of simple ifthen statements). By using 10 times 5fold crossvalidation tests, we compare the proposed method with other methods in performance. The results show that ITSAR outperformed TSAR in terms of solution time, and rough set theory has the advantage over multinomial logistics regression for the analysis of group evacuation decisionmaking. It can be concluded that rough set theory can quickly obtain more simple decision rules of group evacuation decisionmaking and provide a new way for evacuation behavior analysis.
Further research mainly includes two aspects. First, it is worthwhile to develop effective update method for rule database after increasing new samples. Second, this model could be integrated with a larger set of behavioral models into an agentbased simulation framework to comprehensively model the evacuation process, which would help public agencies develop evacuation plans that align with evacuee choices and behavior.
The authors declare that there is no conflict of interests regarding the publication of this paper.
Research for this study was supported by the National Natural Science Foundation of China (51208400, 51108362, and 51078299) and the Fundamental Research Funds for the Central Universities of China (no. 2011IV125).