Inf Syst Front (2014) 16:953–977 DOI 10.1007/s10796-013-9407-z
A new methodology to support group decision-making for IoT-based emergency response systems Ni Li & Minghui Sun & Zhuming Bi & Zeya Su & Chao Wang
Published online: 26 January 2013 # Springer Science+Business Media New York 2013
Abstract An emergency response system (ERS) can assist a municipality or government in improving its capabilities to respond urgent and severe events. The responsiveness and effectiveness of an ERS relies greatly on its data acquisition and processing system, which has been evolved with information technology (IT). With the rapid development of sensor networks and cloud computing, the emerging Internet of things (IoT) tends to play an increasing role in ERSs; the networks of sensors, public services, and experts are able to interact with each other and make scientific decisions to the emergencies based on real-time data. When group decision making is required in an ERS, one critical challenge is to obtain the good understanding of massive and diversified data and make consensus group decisions under a high-level stress and strict time constraint. Due to the nature of unorganized data and system complexity, an ERS depends on the perceptions and judgments of experts from different domains; it is challenging to assess the consensus of understanding on the collected data and response plans before appropriate decisions can be reached for emergencies. In this paper, the group decision-making to emergency situations is formulated as a multiple attribute group decision making (MAGDM) problem, the consensus among experts is modeled, and a new methodology is proposed to reach the understanding of emergency response plans with the maximized consensus in course of decision-making. In the implementation, the proposed methodology in integrated with computer programs and encapsulated as a service on the N. Li (*) : M. Sun : Z. Su : C. Wang School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China e-mail:
[email protected] Z. Bi Department of Engineering, Indiana University-Purdue University Fort Wayne, Fort Wayne, IN 46805-1499, USA
server. The objectives of the new methodology are (i) to enhance the comprehensive group cognizance on emergent scenarios and response plans and (ii) to accelerate the consensus for decision making with an intelligent clustering algorithm, (iii) to adjust the experts’ opinions without affecting the reliability of the decision when the consensus cannot be reached from the preliminary decision-making steps. Partitioning Around Medoids (PAM) has been applied as the clustering algorithm, Particle Swarm Optimization (PSO) is deployed to adjust evaluation values automatically. The methodology is applied in a case study to illustrate its effectiveness in converging group opinions and promoting the consensus of understanding on emergencies. Keywords Emergency response system (ERS) . The Internet of Things (IoT) . Multiple attribute group decision making (MAGDM) . Consensus modeling . Partition around medoid (PAM) . Particle swarm optimization (PSO)
1 Introduction High-tech hardware and software infrastructures, such as air transportation systems, bullet trains and the Internet, make humans and any objects interacting with each other more and more closely and tightly (Chen et al. 2011; Li et al. 2012a; Wang and Xu 2008; Xu et al. 2012a; Yin et al. 2012). The abrupt and unanticipated events happened at one place can affect the other places widely and rapidly. Emergence response systems (ERSs) are essential to respond the emergencies correctly and promptly to avoid severe losses (Li et al. 2008; Li 2011; Xie et al. 2011, 2012; Shan et al. 2012a, b; Xu and Xu 2011; Xu et al. 2012b). It is particular true when an emergence relates to natural disasters such as earthquake, flood, and tsunami (Luo et al. 2007). An ERS relies heavily on the information technology (IT) to collect
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and analyze real-time data and make scientific decisions. Therefore, the emerging internet of things (IoT) is playing a very important role in developing new ERSs. In this section, the progresses on IoT, its applications and the methodologies for decision-making in ERSs are introduced, and the organization of the paper is outlined. 1.1 Internet of things The Internet of Things aims at bringing intelligent interconnections of objects in the physical world through sensors and networks; objects are connected together to form a global network with heterogamous communication protocols and IT tools. The objects can communicate and interact with other objects and with humans. Despite of its short history, IoT has shown its great impact on logistic systems, manufacturing systems, business environments, and our daily lives (Fu et al. 2011; Xu 2011a, b). IoT consists of a very large number of smart objects capable of producing and consuming data, and it can be viewed as a highly dynamic and radically distributed networked system. Two types of device in IoT are sensors and actuators. Sensor device perceives an object and translates the result into understandable information; while an actuator device triggers actions to respond the changes or collected data. When an IoT has a large number of objects and system’s behaviors are highly dynamic (Li et al. 2012c; Bi et al. 2008; Bi and Kang 2010, 2011), enabling technologies should be advanced for the implementation of autonomous capabilities and self-management of IoT. The applications of IoT can be classified into the applications in business systems and these in personal systems. Personal IoT systems assist living, learning, e-health, and entertainment; while business IoT systems have been implemented for manufacturing and assembly, supply chain management, process management, and public transportation (Atzori et al. 2010). Enabling technologies of IoT have been under development stably and gradually. At its infant stage, the communication infrastructure such as Radio Frequency Identification (RFID) was adopted for various applications (Michahelles et al. 2007; Kumar et al. 2011); IoT was then evolved by integrating new technologies such as wireless sensor networks (Akyilidiz et al. 2002; Li et al. 2012b) and service-oriented architectures (SoA); the SoA approach does not require a specified platform for the implementation of service (Pasley 2005; van Sinderen and Almeida 2011). Nowadays, the capabilities of an IoT have been expanded to the Web-based services (Ghezzi and Pacifici 2008); it makes possible to decompose a monolithic and complex systems into manageable systems modules and brings the benefits of reusing hardware and software components (Atzori et al. 2010). In this paper, MAGDM has been developed as a system module on the web-server.
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1.2 IoTs for data acquisition in ERSs In this paper, a crisis refers to a sudden change in the course of severe and adverse events or natural disasters. The common natures of the sequences of crises are destructions and losses. A crisis leaves little time for one to make decisions and take actions. A typical example is the flood in Beijing, China, occurred in July 2012, which killed 79 people (Wikipedia 2012). To minimize the destructions and losses, an emergency response system (ERS) is required to collect realtime data, make prompt decisions and actions based on experts’ perceptions and wisdoms (Sinha 2005). Wickens (1992) discussed the correlations of decision-making factors and the possibility of correct decision, and identified that the source of information is one of the most important factors in decision making. Baumgart and Bass (2008) proved that an innovation in weather broadcasting could facilitate the administrations effectively to make the prompt decisions and protect the public with their best effort. In contrast, insufficient or unavailable information about emergencies will place additional great stress on decision-makers, and in turn paralyzing their capabilities of judgments in critical situations (Kowalski and Trakofler 2003). For the data acquisition and distribution, conventional approaches such as questionnaire or decision-making models (Baumgart and Bass 2008) are not able to provide the experts with sufficient onsite and real-time data, which many cause potential safety hazards especially when crises are highly time-sensitive. IoT provides a vital solution to acquire real-time data about any objects and transmit the data to experts promptly for decision-making. Chen (2011) developed a real-time assessment system for earthquake disasters using the IoT. Gluhak and van Kranenburg (2012) discussed how the pervasively deployed IOT can be integrated with new signal processing technologies to implement the decentralized governance. Bai and Yan (2011) adopted the IoT in their hospital information system with the capability of emergency response. Researchers argued that the function of IoT can even be expanded from post-disaster relief gradually mainly to early-warning. IoT has shown its great potential in addressing severe social problems, especially in the situations where sufficient and real-time data is essential to prompt decision making. 1.3 Decision factors, MAGDM and their roles in ERSs For some ill-defined and unorganized problems such as emergence responses, human experts are involved in complex decision making. Two important factors are metal stress level and the complexity of decision-making problem. Metal stress of experts under a critical situation will affect their capabilities of decision making (Kowalski and Trakofler 2003). Kowalski (1995) and Kowalski and Podlesny (2000)
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explored the issues related to the traumatic incident stress in mine disasters; Vaught et al. (1997) and Vaught (2000) discussed the influence of the burnout stress on the evacuation behaviors in drilling and underground mine fires. With an appropriate level of knowledge and experience, human decision-makers are able to make right decisions to respond emergencies; however, the correctness of a decision from a human expert is not quarantined (Streufert 2005). Taking an example of airplanes, the majority of disasters are caused by human factors instead of mechanical failures. Regarding human factors, mental stress level plays a critical role in emergency response; in the example of the Three Mile Island accident, the investigation has shown that the level of stress on human operators has exceeded significantly the average level of stress for one to respond emergency appropriately (Belanger 2001). Another important factor is the complexity of decision making. Decision making on multi-disciplinary problems requires experts to work together (Kim et al. 1999; Li and Liu 2012; Liu and Wang 2012; Ren et al. 2012; Xu et al. 2008b; Wang 2012; Wang and Xu 2012); the team effort from experts is necessary to generate better solutions to cope with complex problems. To take into consideration of the high-level of stress and the complexities under emergent situations, multiple attribute group decision making (MAGDM) is proposed to (i) share the responsibilities of decision-making among experts and (ii) mitigate the stress of expert individuals to avoid biased decisions. MAGDM provides a platform where experts with different experiences could discuss even debate with each other to achieve consensus decisions to the emergencies. MAGDM refers to the decision situations where a group of experts express their perceptions and judgments based on multiple attributes with the objective to find common solutions (Xu and Wu 2011). Multiple attributes represent the goal of decisions and corresponding actions, the attributes should be quantified so experts from different fields can assign certain values on the attributes. It is rare that a group of diversified experts have the similar understanding on a complex problem from beginning (Ben-Arieh et al. 2009; Bordogna et al. 1997; Cabrerizo et al. 2010a, b; Hahn 2010; Rosello et al. 2010). Therefore, it is important of achieving consensus before a decision can be finalized. Since the revision of the opinions could undermine the decision result, it is critical to develop a consensus model to quantify experts’ opinions and, more importantly, to ensure the reliability of understanding on critical situations for decision making. Some interesting results have been reported on the measure of consensus and the procedures to maximize the consensus. A few of the renowned consensus models include those models developed by Dong et al. (2010), Saaty (1994), Chiclana et al. (2008), Herrera-Viedma et al. (2007), and Kacprzyk et al. (1992) are available, while Ben-Arieh and Chen (2006), Herrera et al. (1997), Herrera-Viedma et al. (2005), and Xu (2005)
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proposed the linguistics based approaches to measure the consensus. Chen and Fan (2006, 2007) took into consideration of the experts’ positions and ranks in defining the consensus. A variety of decision making methodologies have been proposed. Xu and Chen (2007) introduced an interactive method for decision making, DMs were allowed to provide and modify their preferences gradually along with the decision making process to formulate a more reasonable group decision at end. Fu and Yang (2010) defined the consensus using an evidential reasoning approach; in their work, consistency measures between each pair of experts were applied and a group consensus was reached after group analysis and negotiation within a specified time. Parreiras et al. (2010) applied linguistic assessments for a flexible consensus scheme; the weights of experts’ opinions are optimized to maximize the consensus. Xu and Wu (2011) developed a discrete model to support the process of finding the maximized consensus on MAGDM, a convergent algorithm was used to guide the group to reach a predefined consensus level. Interactions in the group of experts are also important to reach consensus decisions. Researchers have studied the methodologies in promoting group interactions in the course of decision making. Anandaligam (1989) employed the multiple attribute utility functions within a Nash’s bargaining model. Salo (1995) developed an interactive method to aggregate the preferences of group members based on the representation of an evolving value. Kim and Ahn (1997) suggested that individual optimal results can assist in building group consensus, and thus considered strict or weak dominance values as the inputs for an aggregation procedure. Park and Kim (1997) proposed a dominance graph approach and the corresponding algorithm based on the information of pairwise dominance. Kim et al. (1999) presented an interactive procedure particularly for the MAGDM under insufficient information; they applied separable linear programming technique to express the relations between group’s pairwise dominance and utility ranges by using. Despite the fact that noticeable progresses have been made on the methodologies of consensus modeling and the procedure to maximize the consensus, little work has been found to ensure the reliability of the decisions under complex circumstances such as emergency responses. In a group settings, all experts do not have equal expertise on the problem domain (Ramanathan and Ganesh 1994); a DM often needs to interact with group members to reach consensus with others; the interactions allow group members to improve their incomplete preference information iteratively (Xu and Chen 2007). As a summary, the ultimate goal of group decision making process is to reach consensus; which reflects the culmination of a successful decision making process. The primary objective of MAGDM is to produce a reliable and reasonable outcome from the decision making process. Note that a bad decision is far worse no decision; it is imperative to
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guide experts with specific guidelines, so that they can reasonably adjust their opinions during the decision making process. One has to be careful since any revision of the opinion brings a risky compromise of individuals to the group consensus; inappropriate adjustments could undermine the reliability of the attained result. 1.4 Organization of the paper The presented work is motivated to (1) build an IoT-based framework to collect real-time data and make scientific decisions based on the sufficient and reliable data, (2) develop a consensus model and the procedure to achieve the consensus group decision promptly, and (3) when the consensus can be not achieved without the adjustment, propose an efficient adjustment method to converge the decisionmaking process. To achieve these objectives, the rest of the paper is organized as follows. In Section 2, the proposed approach is outlined, the background information of ERS is introduced, and IoT and sensor networks are applied to collect real-time information and support experts to achieve consensus efficiently. In Section 3, some basic concepts and definitions of MAGDM are proposed; PAM and PSO methodologies are applied in the implementations of these concepts. In Section 4, a new pragmatic procedure of group decision making is provided. In Section 5, an example has shown the effectiveness of the proposed procedure. Finally in Section 6, the concluding remarks are provided with some identified future works.
2 System architecture When an emergent event happens, it is highly possible that experts capable of handling the emergence are located in different places around the country even the world. Even though experts may be reached in other ways, enabling experts to make decisions at the distributed locations over the Internet is the best option to save precious time, which is crucial to respond emergent situations. Besides the availability of experts, an ERS must also be capable of acquiring sufficient real time data from the emergent circumstances, various sensors are needed to collect dynamic data from objects, sensors are networked so the collected data can be delivered for decision making promptly. Moreover, experts understand the same emergent situation from different perspectives to reach a group consensus of experts by the MAGDM. The application scenario of an ERS has been depicted in Fig. 1. The description of an ERS in Fig. 1 can be extended to other situations where a group of decision makers work together to achieve the consensus in a very short time and under a high-level stress caused by potential severe consequence of inappropriate decisions.
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When the scales and complexities of emergent events increase, the implementation of the ERS is very challenging. The cutting-edging IT and related methodologies and tools have to be integrated to fulfill the functions of an ERS satisfactorily. In Fig. 2, system architecture of an IoTbased ERS has been described; the system components and their relations are described in details in this section. To simplify the explanation, the emergent situation similar to the flood happened in Beijing in July 2012 is used as an example. 2.1 Sensors network Sensors are essential to acquire real-time data from objects in emergent situations. Sufficient data must be collected from anything, anywhere, and anytime. The IoT is the best IT infrastructure to fulfill such type of functions. When emergence situations related to flood, the data on the following sources are extremely important, and the sensors have to be activated to acquire data from these sources under the rainfall situation. Meteorological Phenomena:
Weather Forecasting:
Municipal Sewer System:
Transportation Condition:
Infrastructure:
Street Ponding:
Public Service:
Sensors are used to monitor meteorological phenomena-related variables such as temperature, wind speed and direction, rainfall density, barometric pressure, and visibility. Local meteorological agency has its own resources and tools to forecast the weather; the results of the predicted weather conditions may be updated with an interval period of time but can be directly used in an ERS. Flood closely relates to municipal sewer systems, sensors are applied in the systems to acquire real-time data of water flow rates and speeds to predict the moment when a regional sewer system reaches its full capacity. Flood affects surface transportations as well. Sensors are deployed to monitor peak cell rates, sustainable cell rates, maximum burst sizes, maximum frame sizes, maximum cell rates, the reports of traffic accidents. Municipal infrastructure can be destroyed by flood. Local critical infrastructure facilities, such as water plant, power plant and gas plant, must be monitored to update the statuses of the system operations. Street conditions are another major indicator of flood. Sensors are applied to upload the ponding conditions of streets under surveillance. Public services are critical to maintain normal lives of citizens. The information relates to the operation statuses of local public service agencies, such as hospitals, police stations, and fire stations, has to be collected.
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MAGDM Sensor A
Expert D Expert E
Expert F Sensor B
Sensor A Expert C Presenter Expert B Sensor C
Expert A
Fig. 1 Application scenario of an ERS
2.2 Data processing All of the collected data from the sensors network and reports are transmitted to a centralized service controller by various communication media. For example, the
information related to the statuses of municipal infrastructure can be transmitted by a Local Area Network or an interface of Wide Area Network; the information of the municipal sewer system can be collected and transmitted by an integrated wireless sensors network. As shown in
Communication Layer GPRS/ WAN
GPRS/WiFi/ WAN
Real-time Sensor Data
Decision Making Interaction
ZigBee/ LAN/WAN Sensors Network
Meteorological Phenomena
Experts Network
Service Controller Weather Forcast Municipal Sewer System Sensors
Middleware
Sensor Data Processor
Transportation Condition
MAGDM
Critical Infrastructure Database Street Ponding Raw Data Public Service
Fig. 2 System architecture of IoT-based ERS
Situation Report
Experts Set Evaluation Attributes
Contingency plans
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Inf Syst Front (2014) 16:953–977 Sensor data report Meteorological phenomena
Critical infrastructure 25% 25%
Weather forecast
100% 90% 80%
Street ponding
25% 25%
Sensor Data Processor Municipal sewer system
Public service
Transportation condition
Fig. 3 Processing and synthesizing, and visualization of sensor data
Fig. 3, those collected raw data will be processed, synthesized and visualized into an integrated form such as histograms, pie charts, tables and curve charts, serving as a situation report presented to experts. 2.3 Database As shown in Fig. 2, Evaluation Attributes and Experts Set, are two important components to be considered in the decision making process. In the emergent situation of flood, nine specified attributes (Gao 2008) are Procedure Validity, Content Validity, Coordination, Resource Availability, Logistic Capacity, Resource Distribution, Rationality of Response, Feasibility of Response and Agency Response Capacity. The corresponding design factors will be discussed in Section 5. The experts set includes the information of experts and several contingency plans. It is maintained in the database as a part of the strategic precautionary measure for an ERS. Under the proposed system architecture, a typical task of decision making is for the experts set to select the best contingency plan based on the Data Report from the sensors network. For the implementation of an ERS, the database is extremely crucial and must be developed before the real world emergency happens. However, how to establish the database is beyond the scope of the paper. The structure of the Experts Set has been described in Fig. 4, and the major components in the set are explained as follows. Personal Info:
The basic information of every expert is logged in the data table of the Personal Info, where each expert maintains a unique ID number. A Trust Degree Factor represents his/her influence weight contributed to the experts group; it is a critical component for the group to assess the consensus, and the details are provided in Section 4. Activated field includes a Boolean value to indicate whether or not the expert is invited as a member of the current experts group.
Decision Status:
The Decision Status table tells the connection status of an expert; the table would be set ‘valid’ only when the
Decision Data:
Activated field in the Personal Info is set as ‘true’. Two fields of Online are ‘Completed’ and ‘Processing’, which describe whether or not the expert has completed the task in the current round of the group evaluation. The Decision Data table is closely related to MAGDM. It maintains the data of an expert’s decisions, which is critical in assessing the consensus in the experts group. Its application has been described in Section 4.
2.4 Integrated MAGDM service Experts are usually geographically distributed around the country even the world. Traditional face to face meetings are virtually impossible in particular under emergent situations. Modern information technologies provide vital tools to support the group decision making over the Internet. Experts can be interacted and organized remotely through GPRS/WAN/WiFi by a service controller. After the decision group is initialized, experts are able to log into the system for the involvement in the decision making process; the participation will be guided by an MAGDM web service module. Conventional MAGDM approaches lack the solutions to two major problems: (i) long and time-consuming iterative process and (ii) individual experts easily be compromised. Neither of them is desirable in seeking time-sensitive and effective solutions to emergency situations. To address these problems, a new pragmatic scheme has been proposed and illustrated in Fig. 5. Firstly, the experts are divided into small groups based on the similarity of their understandings found from the first round evaluation. Secondly, a new procedure is applied to accelerate the convergence of the group opinions by promoting a better understanding of group divergences of attributes and contingency plan. Thirdly, if an expert is found to have an extremely biased opinion, the specified approach is applied to disregard the opinion. Finally, if a consensus is still not achievable, a particle swarm optimization (PSO) is applied to adjust experts’
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Fig. 4 The structure of the Experts Set
Offline Decision Status
Completed Online Processing ID/Name Affiliation & Position Contact Info
Experts Set
Personal Info
Expertise Trust Degree Factor Activated Evaluation Vector
Decision Data
isCenter
isIsolated
opinions reasonably to increase the success rate of reaching the group consensus (Wang et al. 2011b). As shown in Fig. 6, MAGDM is one part of the middleware in the ERS. Other two modules in the middleware are dataProcessor and serviceController. The serviceController interacts with the modules of dataBuffer and dataAccesssor. The dataBuffer is the container of the data to be processed by the
Start
Collecting sensor data
First round evaluation
Disposing isolated experts
Experts clustering
Adjusting evaluation values with PSO
Processing sensor dara
Accelerating opinions converging
Selecting the best solution
Forming data report
Second round evaluation
Aggregating the final result
Experts starting decision making
Experts clustering
End
Fig. 5 Main steps in the procedure of MAGDM
service modules. The MAGDM module, as the defining feature of this framework, is to interact with other modules through serviceController to guide the whole decision process. Lastly, the dataAccessor is to respond all the requests to the database to simplify and unify the database accessing. To ensure the smooth interactions among the system modules, a set of interfaces have been developed; these interfaces have been described in Tables 1, 2, 3 and 4. As shown in Table 1, the serviceController is responsible for controlling the overall process of an ERS, the functions Sensors Network
Middleware
dataProcessor
Experts Set
dataBuffer
serviceController
dataAccessor
Databsae Fig. 6 Major functional modules of an ERS
MAGDM
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Table 1 Main interfaces in serviceController
Name
Parameters
Description
triggerSensorNet readData
sensorID sensorRawData evaluationData sensorRawData sensorDataReport evaluationData expertsID expertID
Selecting sensors that need to be activated Reading data from the dataBuffer Two overrides: data from sensors and data from experts’ evaluation Writing data into database Three overrides: raw data from the sensors, data report from the dataProcessor module and data from experts’ evaluation Contacting the selected experts and setting up meeting Sending the sensor data report to the selected expert
writeData
setupMeeting sendReport
Table 2 Main interfaces in dataProcessor
Name
Parameters
Description
processData generateReport
sensorRawData Histogram pieChart Tables curveChart
Processing and reorganizing sensor raw data Generating data reports from the collected raw data Four overrides: presenting the processed source data into four forms, which are histogram, pie chart, table and curve chart
Table 3 Main interfaces in MAGDM Name
Parameters
Description
planConsensus attributeConsensus clusterExpert
evaluationData attEvaluationData expertsSet, evaluationData,
centerExpert
expertsSet, evaluationData
Calculating overall group consensus Calculating group consensus on a specified attribute Clustering the experts by PAM algorithm into group according to their evaluation data Finding the expert whose opinion is the center of the group
isolatedExpert disposeExpert psoAdjustment
expertsSet, evaluationData expertsSet, evaluationData psoParameter, evaluationData, acceptableBound
Aggregate
evaluationData
Table 4 Main interfaces in dataAccessor
Finding the isolated experts Disposing the isolated experts Automatically adjust the evaluation data by PSO algorithm in the range that the experts group can accept Aggregating the final result of the contingency plan
Name
Parameters
Description
Add
sensorRawData sensorDataReport evaluationData evaluationData evaluationData sensorRawData sensorDataReport evaluationData
Adding new data into the database Three overrides: raw data from the sensors, data report generated by the dataProcessor and experts’ evaluation data Expert deleting his own evaluation data from the database Expert modifying his own evaluation data from the database Checking data from the database Three overrides: raw data from the sensors, data report generated by the dataProcessor and experts’ evaluation data
Delete Modify Check
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include triggering the sensors network, setting up a decision making group, and interacting with other modules in the system. As shown in Table 2, the dataProcessor module is for processing raw data and generating data reports. As shown in Table 3, the MAGDM is the core module in the middleware, it provides a number of interfaces with the implementations of the algorithms and procedures detailed in Section 4. As shown in Table 4, the dataAccessor facilities data access and maintenance.
3 MAGDM implementation MAGDM is the most critical functional module in the ERS. In this section, the theory and methodologies for the implementation of MAGDM have been introduced, and the procedure of applying MAGDM will be explained. 3.1 Linguistic term sets for vague preferences Data from the emergent situations is highly unstructured and it cannot be easily perceived by experts to draw firm and concrete conclusions. DMs often have vague preferences on their choices; in particular, it is hard for them to reflect their choices in discrete numbers. Therefore, a linguistic method is proposed in this section (Xu 1990; Guo et al. 2012; Ren and Quan 2012). n o Let S l ¼ sl0 ; sl1 . . . slTi denotes the l-th pre-defined linguistic term set with odd cardinality, element sli in the set represents the i-th linguistic term, and Tl+1 is the cardinality of set Sl. In addition, the set Sl should possess the following characteristics and functions (Herrera et al. 1996; Herrera and Herrera-Viedma 2000):
good’. In the applications, experts often experience the difficulty in distinguishing similar terms. For examples, one expert may think ‘fair’ and ‘slightly good’ are both suitable, and another expert may express an ambivalent opinion on ‘poor’ and ‘slightly poor’ due to the difference of the perspectives. Therefore, the above defined has been expanded to provide a finer resolution of the terms as S1 = {sl0 for ‘very poor-inferior’, sl0þ for ‘very poorsuperior’, sl1 for ‘poor-inferior’, sl1þ for ‘poor-superior’, sl2 for ‘slightly poor-inferior’, sl2þ for ‘slightly poor-superior’, sl3 for ‘fair-inferior’, sl3þ for ‘fair-superior’, sl4 for ‘slightly goodinferior’, sl4þ for ‘slightly good-superior’, sl5 for ‘goodinferior’, sl5þ for ‘good-superior’, sl6 for ‘very good-inferior’, sl6þ for ‘very good-superior’, sl7 for ‘perfect’}. The new definition of linguistic set is expected to reduce the vagueness of experts’ choices. Take an example of the dilemma of selecting ‘fair’ or ‘slightly good’, the expert can narrow his/her inconclusive qualitative assessment down to ‘fairsuperior’ or ‘slightly good-inferior’, which reflects closely for the vague opinion. To quantify the evaluation values from experts’ qualitative knowledge, an index table as shown in Table 5 is used to interpret their uncertainty knowledge into a set of specific choices, i.e., total fifteen terms in the set < sl0þ ; sl0þ ; sl1 ; sl1þ ; sl2 ; sl2þ ; sl3 ; sl3þ ; sl4 ; sl4þ ; sl5 ; sl5þ ; sl6 ; sl6þ ; sl7 > can be interpreted to corresponding values as . 3.2 Consensus modeling in MAGDM In the formulation of MAGDM, the following elements are given: an experts group E = {e1,e2⋯em}, (m≥2), a set of plan alternatives X = {x1,x2⋯xt}, (t≥2), and a set of criteria C = {c1,c2⋯cn}, (n≥2). Besides, the following parameters
(1) The linguistic terms in the set should be ordered so that sli > slj if i > j;
Table 5 Index table
(2) A negation operator Neg Sli is defined as Neg Sji ¼ STl l i;
Linguistic terms
Value range
(3) A maximization operator is defined as max sli ; slj ¼ sli , if sli slj ;
(4) A minimization operator is defined as min
sli ; slj
Very poor
¼
sli, if sli. Poor
Definition 1 Let Sl be the l-th pre-defined finite and totally ordered linguistic term set with odd cardinality. An uncertain l linguistic term is expressed as S ¼ slm ; sln , where n ≥ m, slm and l sln are the members of S and are lower and upper limits, respectively. The difference of n and m implies the level of uncertainty, the larger the difference is, the more the uncerl l tainty of S is. As a special case when m = n, S is reduced to a certain linguistic term slm or sln (Fan and Liu 2010; Xu 2004). Fan and Liu (2010) proposed a linguistic set with seven terms: 1 for ‘very poor’, 2 for ‘poor’, 3 for ‘slightly poor’, 4 for ‘fair’, 5 for ‘slightly good’, 6 for ‘good’ and 7 for ‘very
Slightly poor Fair Slightly good Good Very good
Inferior Superior Inferior Superior
[0, 0.5) [0.5, 1) [1, 1.5) [1.5, 2)
Inferior Superior Inferior Superior Inferior Superior Inferior Superior Inferior Superior
[2, 2.5) [2.5, 3) [3, 3.5) [3.5, 4) [4, 4.5) [4.5, 5) [5, 5.5) [5.5, 6) [6, 6.5) [6.5, 7]
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are used: (i) l = (l1,l2,…lm)T denotes the weights of P experts, where li ≥ 0 (i=1,2,…,m) and mi¼1 li ¼ 1 ; (ii) W = T (w1,w2…wn) represents the weight vector of the attributes, Pn where wk ≥0, (k=1,2,…,n) and k¼1 wk ¼ 1 , and (iii) the minimum acceptable level of consensus expectation is δ. δ is a value predefined prior to the commencement of the evaluation process. Let vector Aij = (a1ij, a2ij…anij)T denotes expert i’s opinion on an alternative plan xj, (j=1,2,…,t), where Aij is based on Table 5. Furthermore, the evaluation values Aij are nor0 malized into [0, 1] as Aij; U and L represent upper and lower bounds of the evaluation values, respectively; which are fixed in Table 5, therefore 0
Aij ¼
0
Aij U L
¼
Aij 7
ð1Þ
For the simplicity, Aij is used to substitute the normalized
Aij in [0, 1].
Definition 2 Let λhl represents the comprehensive weight of expert h and expert l as follows: lhl ¼
lh þ ll 2
ð2Þ
3.3 k-medoid clustering The k-medoid is a clustering algorithm which divides the datasets into groups (Zhou et al. 2012; Duan and Xu 2012; Zeng et al. 2012a, b; Liu et al. 2011; Wetzstein et al. 2011; Duan et al. 2011; Ingvaldsen and Gulla 2012; Chiang et al. 2011; Duan et al. 2007). In its implementation, vectors are clustered into several clusters; each cluster is represented by a vector called “medoid”, which corresponds to the central point of the cluster. Within a cluster, any vector is closer to its medoid than to the medoids of other clusters. A k-Medoid algorithm divides the data into k groups; the constraints of partition are: each group must contain at least one object and each object must belong to exactly one group (Theodoridis and Koutroumbas 2006). Let N elements to be clustered be X and β be the set of the medoids for all clusters. Iβ is denoted as the set of the indices of the points in X that constitute β, and IX−β is the set of the indices of the points that are not medoids (Theodoridis and Koutroumbas 2006). The quality of the clustering associated with a given set β, of medoids, is assessed by the following cost function, Jðb; UÞ ¼
X X i2IX
As a special case, when h = l, lhl equals to lh or ll.
b
uij d xi ; xj
ð7Þ
j2Ib
where Definition 3 Let D (Ahj, Alj) represents the dissimilarity of the opinions on alternative xj between experts h and l; it can be determined by, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 D Ahj ; Alj ¼ w1 a1hj a1lj þ w2 a2hj a2lj þ . . . þ wn anhj anlj
ð3Þ
Definition 4 The similarity of opinions on alternative xj between experts h and l is defined as, S Ahj ; Alj ¼ 1
D Ahj ; Alj :
ð4Þ
Definition 5 The group consensus on alternative xj is defined as, m P m P
Fj ¼
m P m P
μðh; l Þ
h¼1 l¼1 m P m P
λhl
¼
μðh; l Þ
h¼1 l¼1
m
ð5Þ
h¼1 l¼1
where μðh; lÞ ¼
1hl 0
S Ahj ; Alj % S Ahj ; Alj < %
and μ(l, l) = 11 Definition 6 Let Aj = [A1j, A2j…Amj], j = (1,2,…,t), denotes the group evaluation values of xj and Pj represents the aggregation of group opinion on alternative xj, then Pj ¼ ðw1 ; w2 . . . wn Þ A1j ; A2j . . . Amj ð11 ; 12 . . . 1m ÞT ¼ W T Aj 1
ð6Þ
uij ¼
1 0
if d xi ; xj ¼ minq2Ib d xi ; xq otherwise
ð8Þ
Therefore, obtaining the set of medoids β that best represents the data set X, is equivalent to minimizing J(β, U). 3.3.1 Partition around medoid (PAM) When partitioning a set of objects into clusters, the main objective is to find clusters. The objects in the same cluster show a high degree of similarity; while the objects in one cluster should be different from the objects in another cluster as much as possible. Numbers of the methods are available to divide a set into a group of clusters. In the developed ERS, the partition around medoid (PAM) is used. The basic idea in the PAM is to find k representative objects in the data set; these objects are called medoids of the clusters (Kaufman and Rousseeuw 1987), which represent the data structure in the set. After k representative objects are found, the clusters can be constructed by assigning other objects to their closest representative objects (Kaufman and Rousseeuw 1990). Some algorithms, such as Clustering LARge Application (CLARA) and Clustering Large Applications based on RANdomized Search (CLARANS), are extended from PAM. These algorithms illustrate a higher efficiency when a data set has a large scale (Kaufman and Rousseeuw 1990).
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However, in our application of MAGDM for the decision making in flooding, the number of experts is limited. Therefore, the basic PAM algorithm is sufficient to cluster experts based on their evaluation values. 3.3.2 Clustering experts with PAM The step of clustering experts closes the decision making process as an iterative loop and allows necessary negotiation and fine-tuning. It is indispensable in guiding experts to comprehensively learn and exchange each other’s perceptions on the alternatives based on the specified attributes. In applying PAM, the medoids are robust representations of the cluster centers that are less sensitive to outliers than other cluster profiles, such as the cluster means of k-means. This robustness is particularly important in the common context that many elements do not belong to any cluster (van der Laan et al. 2002). A distance matrix is mapped into a specified number of clusters. The procedure of clustering experts is explained in this section (Theodoridis and Koutroumbas 2006). Recalling that Aj = [A1j, A2j…Amj] consists of m of ndimensional vectors. Each vector represents the evaluation values of a certain expert with respect to an alternative xj. Aj as a whole is the set of the objects that needs to be clustered, which corresponds to X as defined in Section 3.2. Definition 7 Suppose β and β’ are two medoids, each consisting of m elements; if they share m-1 elements, β and β’ are called neighbors. If β has l elements, the number of neighbors β can have is l*(m-l). Also, let βhk denote the neighbor of β when Akj, k 2 IAj b replaces Ahj, h ∊ Iβ. The procedure of applying PAM is as follows. Step 1: a set β with m medoids is selected randomly from Aj and the distances of the clusters are calculated as ΔJhk = J(βhk, Uhk) − J(β, U). Step 2, among all m neighbors, βhk, h ∊ Iβ, k 2 IAj b, in the set β, βqr is selected based on the condition of r ∊ IX−β, q ∊ Iβ, and ΔJqr = minhkΔJhk. Step 3, if ΔJqr is negative, then β is replaced by βqr and goes back to step 2; otherwise, if ΔJqr ≥ 0, it indicates that the algorithm has reached a local minimum, and the procedure can be terminated. Once the set β that best represents the data has been determined, each element in Aj − β is assigned to the cluster represented by the closest to its medoid. Therefore, ΔJhk is critical in the determination of whether or not an element should be chosen as a medoid. ΔJhk is quantified as (Theodoridis and Koutroumbas 2006), ΔJhk ¼
X r2IAj
Crhk
ð9Þ
b
where Crhk is the difference in J when Arj ∊ Aj − β is assigned and Ahj ∊ β is replaced by Akj ∊ Aj − β. To calculate Crhk, the Euclidean distance is used to measure the distance between any
two vectors of Aj − d(Ahj, Alj), and the following four cases are considered. Case 1: Arj belongs to cluster represented by Ahj. Let Ar2j ∈ β denote the second closest to Arj representative. If d(Arj, Akj) ≥ d(Arj, Ar2j), after Ahj is replaced by Akj in β, Arj will be represented by Ar2j. Then, Crhk ¼ d Arj ; Ar2j
d Arj ; Ahj 0
ð10Þ
Case 2: Arj belongs to the cluster represented by Ahj. Let Ar2j ∈ β denote the second closest to Arj representative. If d(Arj, Akj) ≤ d(Arj, Ar2j), after Ahj is replaced by Akj in β, Arj will now represented by Akj. Then, Crhk ¼ d Arj ; Akj
d Arj ; Ahj
ð11Þ
Case 3: Arj is not represented by Ahj. Let Ar1j be the closest to the medoid Arj. If d(Arj, Ar1j) ≤ d(Arj, Akj), then Arj will continue to be represented by Ar1j and, Crhk ¼ 0
ð12Þ
Case 4: Arj is not represented by Ahj. Let Ar1j be the closest to the medoid Arj. If d(Arj, Ar1j) > d(Arj, Akj), then Crhk ¼ d Arj ; Akj
d Arj ; Ar1j < 0
ð13Þ
Alternatively, the PAM algorithm can be described in Table 6 with a total of computation of O(k(m−k)2). 3.3.3 Selection of cluster number One important issue in applying the PAM algorithm is the selection of cluster number-k. Since the organizer is difficult to know in advance how many sub-groups of experts should be, while k is an essential input to PAM. One has to find a way to determine k. Kaufman and Rousseeuw (1990) proposed the method to determine k automatically by maximizing “average silhouette”. Silhouette refers to a method of interpretation and validation of the clusters of data. Such a method provides a concise graphical representation of how well each object lies within its cluster (Rousseeuw 1987). Each cluster is represented by one silhouette; a silhouette shows the objects within the cluster and the object at an intermediate position. The clustering result can be visualized by plotting all silhouettes into a single diagram, allowing the user to compare the quality of clustering. Silhouettes are especially useful when the dissimilarities are on a ratio scale (such as Euclidean distances) and when one seeks compact and widely separated clusters (Kaufman and Rousseeuw 1990). However, during the experimentation, it is found that the automatic selection of k was influenced by the randomly selection of medoids at step 1 if multiple runs of PAM are necessary. In other words, k could not be converged to one
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Table 6 PAM Algorithm Input: the experts’ evaluation dataset A j and the clusters number k. Output: k groups, in each of which every member is nearer to its own medoid than medoids in other groups; Randomly select k vectors from Aj as medoids, denoted by{ O1 , O2 ...Ok }, thus the remaining (m-k) vectors are described by { R1 , R2 ...Rm-k }; Let i=1, j=1; While (i
