Consensus-based non-cooperative behaviors management in large-group emergency decision-making considering experts’ trust relations and preference risks

Journal Pre-proof Consensus-based non-cooperative behaviors management in large-group emergency decision-making considering experts’ trust relations and preference risks Xuanhua Xu, Qianhui Zhang, Xiaohong Chen

PII: DOI: Reference:

S0950-7051(19)30480-0 https://doi.org/10.1016/j.knosys.2019.105108 KNOSYS 105108

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Knowledge-Based Systems

Received date : 17 June 2019 Revised date : 8 October 2019 Accepted date : 9 October 2019 Please cite this article as: X. Xu, Q. Zhang and X. Chen, Consensus-based non-cooperative behaviors management in large-group emergency decision-making considering experts’ trust relations and preference risks, Knowledge-Based Systems (2019), doi: https://doi.org/10.1016/j.knosys.2019.105108. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Consensus-based Non-cooperative Behavior Management in Largegroup Emergency Decision-making Considering Experts’ Trust Relations and Preference Risks

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Consensus-based non-cooperative behaviors management in large-group emergency decision-making considering experts’

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trust relations and preference risks Xuanhua Xu, Qianhui Zhang, Xiaohong Chen

(School of Business, Central South University, Changsha, 410083, China)

Abstract: Consensus-based large-group emergency decision-making (LGEDM) is a dynamic and iterative process, in which some experts may show non-cooperative behaviors because they have different knowledge backgrounds and represent different stakeholders. Non-cooperative behaviors greatly affect the efficiency and results of decision-making. Time is of the essence in an emergency situation, and thus rational treatment of non-cooperative behaviors is required. In addition, in traditional group

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decision-making (GDM), the decision model is based on the premise that decision makers are independent. However, with the development of online social networks, the objective trust relationships between experts should be considered. Hence, this paper proposes a consensus model that considers the experts’ trust relations based on

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social network analysis and preference risks based on interval-valued intuitionistic fuzzy numbers. The trust risk, preference risk, and an approach for analyzing and managing non-cooperative behaviors are proposed. An illustrative example and a comparison are provided to verify the feasibility and effectiveness of the proposed method.

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Keywords: non-cooperative behaviors; social network analysis; risk; large group; emergency decision-making

1. Introduction

In recent years, major and extraordinary emergencies have taken place frequently in the world, such as devastating earthquake in Japan, the major explosion at Tianjin Port in China [1].GDM is an important method to manage emergencies [2]. Traditional GDM problems normally consider only a few numbers of decision-makers

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(DMs) [3-4]. Emergency decision-making involves a wide range of issues, and the experts involved in decision-making often come from different fields and have different professional backgrounds and different decision-making capabilities. Emergency decision-making groups have the complex characteristics of a large group [5-6]: (1) the group is large (generally more than 11 DMs), (2) the problems under 1

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consideration are multi-dimensional, and (3) the consensus threshold is relatively high. Large-group emergency decision-making (LGEDM) is more complicated than traditional GDM, and thus it is difficult to solve LGEDM problems with traditional

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GDM models [7-8]. Three processes are commonly used for solving LGEDM problems [9-15], namely a clustering process, a consensus reaching process (CRP), and an alternative selection process. Among them, the CRP is most often implemented and has thus received the most attention.

Traditional consensus, called hard consensus, has only two indicators, namely 0 (no consensus reached) or 1 (consensus reached). However, unanimity may be difficult to achieve. It is also unrealistic to adjust the consensus level from 0 to 1 in a real word decision-making process [16-17].Therefore, soft consensus [18-19] has been proposed and is widely used in large group decision models. Many models have

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been proposed for achieving group consensus based on mathematical reasoning [20-25]. For example, Zhang et al. [20] developed a consensus-based multi-attribute GDM approach and proposed a failure model. Tang et al. [23] investigated the CRP in a heterogeneous large-scale group decision-making environment, and proposed an

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ordinal consensus measure with an objective threshold based on preference orderings. Liu et al. [25] purposed a consensus model that focuses on LGEDM based on fuzzy preference relations with overconfidence behaviors. Importantly, in traditional CRP of GDM, the decision models are based on the premise that decision-making experts are independent, neglecting the objective trust

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relationships between experts [26]. However, with the development of online social network, this premise rarely holds. GDM is often carried out under the framework of a social network, with personal opinions often supported by relatives and friends or people with similar views [27-29]. Under the conditions of social network, individuals have trust relationships. Research on this topic has mainly focused on three aspects: (1) trust propagation, (2) incomplete preference value estimation based on trust relationships, and (3) feedback guided by trust relationships [30]. Studies have shown that the use of social network analysis (SNA) can help reduce the complexity of GDM

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and improve the decision-making quality [31-32]. For example, Wu et al. [33] studied the trust relationships between experts based on SNA and proposed a trust-based consensus model. Ding et al. [34] presented a SNA-based conflict relationship investigation process for detecting conflict relationships among DMs. Wu et al. [35] 2

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proposed an interval binary fuzzy TOPSIS model based on social network information, and used social network methods to cluster experts. However, in these studies, the degree of experts’ trust relationships is reflected by a mutual evaluation matrix created

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by the experts themselves, which is a subjective scoring method. Moreover, few studies have been conducted on the psychological behavior of experts based on SNA. Decision-making problems cannot be studied simply using a mathematical model. The psychological behaviors and performance of decision-making experts also require consideration [16]. In LGEDM, the experts come from different domains and have different interests, and are thus likely to exhibit non-cooperative behaviors [10, 36-38]. For example, some experts refuse to modify their preference values during the CRP, or do not express their preferences truly. A few studies have considered non-cooperative behaviors. Francisco et al. [39] proposed a method for measuring the

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degree of non-cooperation using uninorm cluster operators. Xu et al. [10] defined a subjective adjustment coefficient and an objective adjustment coefficient to calculate the degree of non-cooperation, and adjusted the cluster weights and cluster preference values according to the degree of non-cooperation. Zhang et al. [16] developed a

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consensus framework based on SNA to deal with non-cooperative behaviors. Some of these studies classified non-cooperative behaviors into three categories [16, 37]: (1) disobedient behavior, (2) divergent behavior, and (3) dishonest behavior. Some other studies instead defined uniform criteria to measure the degree of non-cooperation [10, 38, 50]. Although the former is more specific and the latter is more abstract, all

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studies defined non-cooperative behaviors according to preference expression and consensus level. However, only some existing methods [10, 36-37] can be directly extended to deal with non-cooperative behaviors in LGEDM problems, because the high time pressure makes it impractical to identify individual experts who exhibit non-cooperative behaviors, and the most methods do not conform to the idea of cluster analysis in LGEDM. Moreover, even the applicable methods [10,36-37] ignore the social network relationships between experts. It is thus necessary to research non-cooperative behaviors based on experts’ objective trust relationships in LGEDM.

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In addition, because of the inherent uncertainty and ambiguity of human thinking and the urgency of decision-making, it is difficult for experts to give accurate decision-making preferences in LGEDM. The concept of fuzzy set was proposed in 1965, which can be used to mathematically express uncertainty. Various extended 3

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forms of fuzzy sets have been proposed, such as intuitionistic fuzzy sets, linguistic fuzzy sets, and interval-valued intuitionistic fuzzy sets (IVIFS) [40-42]. Fuzzy sets are intuitive, concise, and easy to express, and are thus widely used to express the

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preferences of experts in GDM. For example, Ding et al. [43] proposed an intuitionistic fuzzy clustering method based on a sparse representation for GDM clustering problems. Li et al. [44] used the score function of interval-valued intuitionistic fuzzy numbers (IVIFN) to locate earthquake emergency service points. Xu et al. [45] proposed a multi-stage conflict LGEDM method based on IVIFN. IVIFN can reflect uncertainty of preference and indirectly reflect decision risk. Therefore, this paper uses IVIFN to express expert preferences. The concept of preference risk is proposed to reflect the degree of unreliability of expert preferences. To resolve the aforementioned issues, this paper proposes a consensus-based

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non-cooperative behavior management model in LGEDM that considers the experts’ trust relations and preference risks. First, the experts’ trust relationship matrix is obtained according to the experts’ social network relationships and the experts are clustered using the Louvain algorithm to obtain the preference matrices and weights

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for each cluster. Second, the preference risk, trust risk, and comprehensive risk are defined, and a consensus adjustment model for non-cooperative behaviors is established. Finally, the ranking of alternatives is determined according to the score function and exact function to select the best alternative. The rest of this paper is organized as follows. Section 2 introduces SNA and

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IVIFN. In Section 3, we describe the LGEDM problems and propose a method for solving it based on SNA. Section 4 presents the proposed consensus-based non-cooperative behavior management model. A mechanism for identifying and managing non-cooperative behaviors is described. An illustrative example is provided to investigate the feasibility and validity of the proposed method in Section 5. Finally, conclusions are drawn in Section 6.

2. Preliminaries

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In this section, we will introduce the basic knowledge of SNA and IVIFN.

2.1. Social network analysis SNA is a useful tool for the study of relationships between enterprises and other

social entities [25]. It can be used to study the location attributes and structural 4

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balance [28], including centrality, prestige and trust. There are three common forms of SNA [32], as shown in Table 1. In this paper, the network graph is used, in which a social network is a social structure consisting of a group of nodes E and a group of

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edges L .The nodes represent individuals or organizations. In this paper, node i represents the decision-making expert ei , and the directed edges represent trust relationships. For example, the edges from e1 pointing to e2 , e3 , and e4 indicates that expert e1 trusts e2 , e3 , and e4 .

Table 1 Common representation schemes in SNA

Sociometric 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0

Graph

0  0 0  1 1  0 

Algebraic

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0  0 0 A=  0 0  0 

To measure the quality of partitions formed, a method based on the idea of

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modularity, called Louvain algorithm, is employed [46].The algorithm can discover hierarchical community structures and is computationally efficient. Its optimization goal is to maximize the modularity of the entire community network. The Louvain algorithm is widely used in social network clustering. Definition 1 [46] Modularity Q is an indicator used to assess the quality of

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community network detection. It indicates the closeness of the community, and is defined as follows:

Q

ki k j   1   Aij   (ci , c j ) 2m i j  2m 

(1)

where m denotes the sum of the weights of all edges and Aij represents the weights of the edges between nodes i and j . When the network is not a weighted graph, the weights of all edges are 1. k i represents the sum of the weights of all edges

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connected to node i and ci represents the cluster that node i belongs to. If i and

j both belong to the same cluster c , then  (ci , c j )=1 ; otherwise,  (ci , c j )=0 . Definition 2 [46] The amount of change in modularity, Q , is defined as 5

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follows:   

2

       in    tot   2m  2m  

(2) where



in

2   ki 2         2m  

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   2ki,in    tot  ki Q   in  2m 2m   

denotes the sum of the weights of all edges in cluster c ,



tot

represents the sum of the weights of edges connected to the points in cluster c , k i represents the sum of the weights of the edges connected to point i , and ki ,in denotes the sum of the weights of edges of i connected to the points in cluster c .

Centrality is a useful tool for analyzing the importance of nodes in social networks. It includes point centrality and individual proximity centrality.

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Point centrality includes point-in degree and point-out degree. The former indicates the degree of trust by other nodes, and the latter indicates the degree of connection with other nodes.

i Definition 3 Let Pini and Pout indicate the standardization point-in and

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point-out degrees of expert ei , respectively:

Pini =

(3)

Nini L

(4)

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i Pout =

i N out L

i where N ini represents the number of edges pointing to ei , N out represents the

number of edges from ei and L represents the total number of edges in the social network graph.

Definition 4 Let L(ei , e j ) represent the shortest distance between ei and e j .

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Then, the individual proximity centrality of expert ei is C (ei ) M

C ( ei )  [ L (ie , ej 1) ]

(5)

j 1

Individual proximity centrality [47] represents the distance (proximity) between

a node and the other nodes. A node that is closer to other nodes will have greater 6

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individual proximity centrality.

2.2. Interval-valued intuitionistic fuzzy numbers (IVIFN)

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Definition 5 [48] A set of fields is a non-empty finite set, and

a  { x, a ( x), a ( x) | x  X } is called an IVIFS. a ( x)  [ aL ( x), aU ( x)] and  a ( x)  [ aL ( x), aU ( x)] respectively

denote

non-membership

element

degree

of

the

the

x

membership

belonging

degree

a ,

to

and

where

0   ( x)  ( x)  1 , a ( x)  [  ( x),  ( x)]  [0,1] ,  a ( x)  [ ( x), ( x)]  [0,1] . U a

U a

L a

L a

U a

U a

When  aL ( x)   aU ( x) and  aL ( x)   aU ( x) , the IVIFN becomes an intuitionistic fuzzy number.

Let  a ( x)  ( aL ( x),  aU ( x)) ,  aL ( x)  1  aU ( x)  aU ( x) ,  aU ( x)  1   aL ( x)  aL ( x) .

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 a ( x) is the hesitant degree interval of element x belonging to a . For simplicity, the IVIFN is usually expressed as a  ([a, b],[c, d ]) , and the hesitant degree interval is

 a  [e, f ]  [1  b  d ,1  a  c] .

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Definition 6 [48] Let a1  ([a1 , b1 ],[c1 , d1 ]) and a2  ([a2 , b2 ],[c2 , d 2 ]) be any two interval fuzzy numbers, then:

a1  a2  ([a1  a2  a1a2 , b1  b2  b1b2 ],[c1c2 , d1d 2 ]) (6)

(7)

c)1 c]2 , d[ 1 d 2 ,

])

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 a1  ( [ (1 ( 1a1  ) , 1 b(11

Definition 7 [48] Let a  ([a, b],[c, d ]) be an IVIFN,  ( a ) be the score function of a , and H ( a ) be an exact function of a , where (a)  [1,1] and H (a)  [0,1] .

(a)  (a  c  b  d ) / 2

(8)

H (a )  (a  b  c  d ) / 2

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(9)

Definition 8 [48] Let a1 and a2 be any two IVIFNs. According to the score

function and exact function, the ranking rule of IVIFN is as follows: (i)

If (a1 )  (a2 ) ,then a1  a2 ; 7

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(ii)

If (a1 )=(a2 ) ,then i) if H (a1 )  H (a2 ) ,then a1 =a2 ;

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ii) if H (a1 )  H (a2 ) ,then a1  a2 . Definition 9 [49] Let d (a1 , a2 ) be the hamming distance between two interval intuitionistic fuzzy sets, and E ( a ) be the fuzzy entropy of a .

1 d (a1 , a2 )  [| a1  a2 |  | b1  b2 |  | c1  c2 | + | d1  d 2 |  | e1  e2 |  | f1  f 2 |] (10) 4

E (a ) 

min{d (a, p), d (a, q)} max{d (a, p), d (a, q)}

(11)

where p  { x,[1,1],[0, 0] | x  X } , q  { x,[0, 0],[1,1] | x  X } , and E ( a ) satisfies the following properties:

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(i) E (a )  0 if and only if a  b  0 and c  d  1. or a  b  1 and c  d  0 ; (ii) E (a)  1 if and only if [a, b]  [c, d ] ; (iii) E (a )  [0,1] .

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3. Large-group emergency decision-making based on social network analysis

An LGEDM problem can be defined as a situation where a large number of decision-making experts have to make a high-quality and timely decision in response to an emergency by choosing viable alternatives. The main elements of a typical

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LGEDM problem are as follows : E  e1 , e2 , e3 ,..., eM  ( M  11 ) [8] is a set of experts. The weight vector of the experts is   (1 , 2 , 3 ,..., M )T , where i  0 (i  1, 2,3,...M ) and



M

i 1

i  1 . X  x1 , x2 , x3 ,..., xP  ( P  2) is a set of emergency

alternatives , that represents possible solutions to the problem. The set of criteria is

C  c1 , c2 , c3 ,..., cN  , and the weight vector of the criteria is W  ( w1 , w2 , w3 ,..., wN )T , where w j  0 ( j  1, 2,3,...N ) and



N j 1

w j  1 . V i  (alji ) PN is the decision matrix

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given by expert ei  E , where a ilj is an accurate value representing the opinion value for alternative xl  X with respect to criterion c j  C .

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3.1. Opinion clustering based on large group social network relationships

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LGEDM typically uses the consistency degree of experts’ preferences as a clustering standard. This method clusters experts based on group viewpoints, but it ignores the internal relationships between experts. In the context of a social network, some experts may have the same viewpoint because of certain connections or interests, and thus clustering based on expert relationships is more objective. Therefore, this paper applies the Louvain algorithm to LGEDM based on the idea of modularity in a social network and the connection between decision experts to cluster experts. The Louvain algorithm has the following two steps:

(1) According to the expert social network relationship, the directed graph with

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nodes is converted into an undirected graph. Each point is taken as a cluster, the cluster’s neighbor nodes are merged it and then Q is calculated using equation (2). Loop iteration is conducted until each cluster’s Q no longer change. (2) The obtained cluster is regarded as a node. The weight of the edge between

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nodes is given by the sum of the weights of the edges between the nodes in the corresponding two clusters. Then, step (1) is repeated until the overall modularity does not change. Through the above two steps, the experts E  e1 , e2 , e3 ,..., eM  are clustered into K clusters. The k -th cluster is denoted as C k , and the number of

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members in cluster C k is nk .

3.2. Weights of experts and clusters In a social network, centrality is an important indicator for judging the importance of experts. Therefore, the weights of each expert and each cluster can be determined according to the position and the interconnection of the experts in the social network.

Definition 10 According to the expert’s point centrality and individual proximity

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centrality, the weight of expert ei is i : 1 2

i = (



i Pini  Pout M i

i ( Pini  Pout )

(12)

9



C (ei )



M i

C (ei )

)

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The weight of cluster C k is  k :

k = iC i k

where, 0  k  1 and

K

 k 1

k

 1.

The preference matrix of cluster C k is: 1 nk

Gk =

(14) The group preference matrix R is:

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(13)



iC k

vlji

R   k 1 k Gk K

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(15)

3.3. Consensus measure

In real-word LGEDM, there is a threshold  . When the consensus level of the

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group reaches the threshold, it is considered that the consensus level of the group is high enough, and the consensus adjustment can be ended. To ensure the timeliness of emergency decision-making, the maximum number of iterations is set to T . When the number of iterations t  T , the regulation model is automatically withdrawn. The consensus measure includes two aspects, namely the consensus level of each cluster

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and the consensus level of the large group.

Definition 11 The consensus level of cluster C k is: CT (C k ) 

1 P N

1

1

P

N

 (1  d (G

k

, R))

(16)

The consensus level of the large group is:

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GCT 

1 K

K

 CT (C k 1

10

k

)

(17)

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4. Consensus-based non-cooperative behaviors management model

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4.1. Non-cooperative behaviors The decision-making experts in LGEDM come from different fields, have different knowledge backgrounds, and may represent different stakeholders. This complexity leads to the non-cooperative behaviors commonly observed in CRP of LGEDM. Non-cooperative behaviors greatly affect the quality of emergency decision-making. Therefore, in the LGEDM process, a mechanism for the identification and management of non-cooperative behaviors should be established.

Experts who exhibit non-cooperative behaviors can be divided into the following

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four types [50]: (1) those who insist that their views are correct; (2) those who are senior leaders and have mastery of the overall situation; (3) those with a maverick personality who express their opinions and generally do not have a herd mentality; (4) those who represent stakeholders who have some interest in the decision result. The treatment method depends on the type of non-cooperative experts. The opinions of the

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first and second types of non-cooperative expert should be highly valued, whereas those of the third and fourth types should be carefully considered. Non-cooperative behaviors mainly manifest as little to no willingness to modify subjective opinions or deviation from the group opinion for some personal benefit.

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4.2. Non-cooperative behaviors analysis and management Based on the consensus, degree of subjective modification preference, and degree of objective suggestion modification, this paper analyzes non-cooperative behaviors, quantifies the degree of non-cooperation, and proposes management methods for different degrees of non-cooperative behaviors. 4.2.1. Non-cooperative behaviors identification Through clustering and a consensus measure, the consensus levels of clusters and

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the consensus level of the large group can be obtained. If the consensus level of the large group is smaller than the threshold, the clusters whose consensus level is smaller than the consensus level of the large group need to appropriately modify their cluster preferences. The objective suggestion modification coefficient for a cluster is  kO 11

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[10]:

 kO =[ (1CT1(CCT))(C(1) GCT ) , (1CT1(CTC ())C(1)  ) ] k

k

k

(18)

k

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The cluster gives a subjective preference modification range  kS =[ kSl ,  kSu ] combined with modification suggestions and the degree of consensus deviation. The actual adjustment coefficient of the preference is  kt .

Definition 12 [50] a  [al , au ] and b  [bl , bu ] are two interval numbers. The probability of a  b is:

     bu  a l  p(a  b)  max 1  max  u , 0 , 0 l u l ( a  a )  ( b  b )      

(19)

The probability degree is often used to determine the order of two interval numbers. It can be applied to measure the non-cooperation degree based on two

subjective

preference

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interval numbers, namely objective suggestion modification coefficient  kO and modification

 kS [10,

coefficient

50].

Hence,

the

non-cooperation degree  (C k ) of cluster C k is:

(20)

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 (C k )=1  p( kS   kO )

The non-cooperation degree is introduced to measure the degree to which a cluster is unwilling to modify its opinion to reach consensus. Based on the properties of the probability degree presented in [51], it is obvious that  (C k ) [0,1] .

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(1)  (C k )=0 indicates that cluster C k is not exhibiting non-cooperative behavior;

(2) 0   (C k )  1 indicates that cluster C k

is exhibiting non-cooperative

behavior.

For (2), some experts or clusters are not willing to modify their opinions. Cluster C k may have performed the preference modification according to the suggestions,

but the degree of modification was lower than the objective suggestion modification degree. This will slightly changes the consensus level of the group, and thus many

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times of consensus adjustments may be required to reach the threshold. 4.2.2. Non-cooperative behaviors management For the management of non-cooperative behaviors, given the complexity of

decision-making experts, it is difficult to accurately grasp the real reasons for their 12

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non-cooperation. In this situation, SNA can provide us a solution. The links between the experts reflect the level of trustworthiness. In addition, the uncertainty of preferences and the consensus level can reflect the risk level of the preferences.

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Considering experts’ trust degrees and preference risks can help us manage non-cooperative behaviors.

Definition 13 The trust risk of cluster C k is bC : k

bC =1  iC Pini k

(21)

k

bC represents the degree of untrustworthiness of the experts in the cluster C k , k

which reflects the overall level of trust risk of the cluster.

Definition 14 The preference risk of cluster C k is  pC k

k 1 P N E (Gk )  (1   )(1  CT (C ))  P  N l 1 j 1

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 pC  

k

(22)

The preference risk of cluster C k is determined by the preference fuzzy entropy that reflects the uncertainty of the cluster preference, and the consensus level of the

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cluster that reflects the degree of deviation from the group preference. The preference risk can be used to reflect the unreliability of expert preference. This paper considers that the cluster preference fuzzy entropy and the cluster consensus level have the same effect on the cluster preference risk, and thus take   0.5 . Based on the analysis of the social network and experts’ preferences, this paper

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considers the objective trustworthiness level of experts and the clusters’ preference risk to define the comprehensive risk. Definition 15 The comprehensive risk of the cluster C k is:

 C = pC +(1   )bC k

k

k

(23)

The comprehensive risk reflects the comprehensive risk level of trust risk and preference risk of the experts that may exist in the decision-making process. This paper considers that trust risk and preference risk are equally important, and thus

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 =0.5 .

(1) For a cluster without non-cooperative behaviors, the average value of its

subjective modification range is directly used as the final preference adjustment coefficient  kt = kS =( kSl + kSu ) / 2 ; 13

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(2) For a cluster with non-cooperative behaviors, the standards for non-cooperative behaviors management should depend on the degree of non-cooperation. Therefore, based on the degree of non-cooperation, this paper

and serious non-cooperative behaviors.

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divides non-cooperative behaviors into two types: general non-cooperative behaviors Let  denote the division threshold of non-cooperative behaviors. When

0   (C k )   ,

cluster

   (C k )  1 .Cluster C k

C k has

general

non-cooperative

behaviors.

When

has serious non-cooperative behaviors. Different

management methods are given for these two types of behaviors. 1) General non-cooperative behaviors

The degree of non-cooperation for general non-cooperative behaviors is small,

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that is, the degree of subjective modification of the cluster is less than that of the modification of the objective suggestion. The cluster itself is trustworthy, and the main risk of the decision is derived from its preference risk. Although the revision of the subjective preferences of the experts in the cluster leads to the continuous improvement of the group consensus, the small-scale revision of the experts in each

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round makes it necessary to carry out consensus adjustment many times. To improve the efficiency of decision-making, the subjective modification coefficient is modified by the preference risk. The preference adjustment coefficient  kt is:

 kt = kS + kS  pC

k

(24)

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2) Serious non-cooperative behaviors

The degree of non-cooperation for serious non-cooperative behaviors is high. In addition, the degree of subjective modification differs greatly from that of objective suggestion modification, which means that it is more difficult to adjust the subjective degree of the cluster. A higher degree of non-cooperative behaviors leads to a lower level of trustworthiness. Therefore, the trust risk and preference risk in the cluster should be considered. This paper adopts the comprehensive risk coefficient to adjust the subjective modification coefficient. To ensure the timeliness of decision-making,

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between the objective adjustment coefficient and the improved subjective modification coefficient, the larger one is selected as the final preference adjustment coefficient.

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



 kt = max  kS + kS  C , (1CT1(CTC ())C(1)  ) ) k

k

k

(25)

After the final preference adjustment coefficient is obtained, the following preference adjustment equation is used:

G k  (1   kt )G k   kt R

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'

(26)

4.3. Algorithm of proposed consensus model for LGEDM problems

This paper proposes a management model of non-cooperative behaviors in LGEDM based on consensus in a social network environment. The framework is shown in Fig. 1.

Expert preferences

Consensus measurement

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Temporary preference set

Experts

Clustering

SNA

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Serious non-cooperative behavior

Adjust preference

General non-cooperative behavior No non-cooperative behavior

Y

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Identify Non-cooperative behaviors

N

? NN

? Y

Y

Attribute weights Alternative selection

Fig. 1. Flow chart of non-cooperative behavior management in LGEDM based on consensus under a social network environment

The steps for the management of non-cooperative behaviors in LGEDM based

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on consensus under a social network environment are as follows: Input: experts E  e1 , e2 , e3 ,..., eM  , preferences of expert V i  (alji ) PN , criteria

weight W  ( w1 , w2 , w3 ,..., wN )T , the max number of iterations T , and  ,  ,  . 15

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Output: clustering results C k , the preference adjustment coefficient  kt , the number of iterations t , consensus level GCT , and the final ordering of alternatives. Step 1: Acquisition experts’ preferences and social network relationships.

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The experts score each attribute of each alternative according to the available information, the score is an IVIFN. Then, SNA is used to analyze the social network relationships of experts, and the social network relationship graph is constructed. Step 2: Large group clustering.

With the use of the social network Louvain algorithm, the experts are clustered into K clusters according to the connections between them. Then, the weight of each expert and each cluster, as well as each cluster’s preference and the group preference are obtained. Step 3: Consensus measurement.

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Equations (10), (16), and (17) are used to calculate the consensus level of each cluster and the consensus level of the group. To ensure the quality and timeliness of decision-making, this paper sets the group consensus threshold level to  =0.85 and the maximum number of iterations to T  4 . If the group conflict level GCT   , the

Step4.

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algorithm moves to Step5; otherwise, t  t  1 is set and the algorithm moves to

Step 4: Non-cooperative behavior management. Non-cooperative behaviors are identified according to a comparison of the subjective modification degree of each cluster and the degree of revision of the

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objective suggestion. The cluster with non-cooperative behaviors is managed according to the degree of non-cooperation. The algorithm returns to Step 3 after the new cluster’s preference in this round is obtained. Step 5: Selection of the optimal alternative. The final group preference matrix R is obtained using equation (15). The score and accuracy of each alternative are calculated by using the alternatives’ attribute weights W and equations (8) and (9). The alternatives are sorted according to the

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rules in Definition 7.

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5. Case analysis 5.1. Case background

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At 14:11 on April 25, 2015, an earthquake with magnitude 8.1 occurred in Nepal with a focal depth of 20 km. This strong earthquake triggered a 5.9-magnitude earthquake at 17:17 on the same day in Dingri County, Shigatse Prefecture, Tibet Autonomous Region, China. This is the largest earthquake that has occurred in Tibet in over 80 years. In Tibet, 31 people were killed, 865 people were injured, 2,511 houses collapsed, 24,797 houses were damaged, and 82 temples were damaged. The direct economic loss was 34.84 billion yuan and the indirect economic loss was 47.117 billion yuan. After the earthquake, the Party Committee of the autonomous region quickly took measures, made saving people a priority, and quickly launched

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the second-level response of the earthquake emergency plan. Relevant leaders in the command area, city, and county, and relevant earthquake, civil affairs, health, transportation, communications, armed police, fire protection, border defense, and other departments hurried to the earthquake zone to witness the damage and organize

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earthquake relief work. An emergency command department composed of 16 experts was established. After analysis, three alternatives were initially determined:

X  x1 , x2 , x3

x1 : Build up a task force, go deep into the disaster area, examine the specific situation of the disaster area, and guide the people in the disaster area to save

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themselves. At the same time, dispatch the armed police to the rescue roads, dispatch external relief resources, and organize a rescue team to repair communications and power facilities. After information is received from the assault squad, deploy further rescue work.

x2 : Organize medical rescue teams to enter the disaster area together with the task force and quickly rescue the victims in need. At the same time, dispatch the armed police to the rescue roads, dispatch external relief resources, and organize a

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rescue team to repair communications and power facilities. After information is received from the assault squad, deploy further rescue work.

x3 : Quickly dispatch a large number of armed police officers and medical rescue

teams to the disaster area to rescue the injured and organize the transfer of affected 17

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people. At the same time, dispatch the armed police to the rescue roads, dispatch external relief resources, and organize rescue teams to repair communications and power facilities.

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The decision-making experts decided to use cost effectiveness, program timeliness, and casualty control as attribute indicators for the evaluation of these three alternatives according to the rescue target and rescue environment. After deliberation, the weights of the attributes were determined as W  0.2,0.35,0.45 .

5.2. Method steps

Step 1: Acquisition of experts’ preferences and social network relationships.

Considering the emergency environment and the incompleteness of the decision information, the decision-making experts scored the alternatives in the form of IVIFN.

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The preferences matrix is shown in Table 2.

Table 2 Preferences matrix for case study experts

x3

casualty control

cost

experts

effectiveness

timeliness

casualty control

([0.3,0.3],[0.4,0.7]) ([0.4,0.5],[0.4,0.5]) ([0.1,0.2],[0.6,0.7])

2

([0.3,0.4],[0.5,0.5])

([0.2,0.3],[0.5,0.6]) ([0.2,0.4],[0.5,0.5])

3

([0.1,0.2],[0.2,0.3]) ([0.3,0.3],[0.2,0.2]) ([0.2,0.3],[0.3,0.4])

4

([0.5,0.6],[0.2,0.3])

([0.4,0.4],[0.3,0.5]) ([0.4,0.5],[0.3,0.4])

…

…

…

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1

13

x2

timeliness

…

…

…

14

15

([0.6,0.6],[0.3,0.3]) ([0.2,0.6],[0.3,0.4]) ([0.3,0.5],[0.2,0.4])

16

([0.5,0.7],[0.1,0.2)

([0.4,0.5],[0.3,0.4]) ([0.5,0.6],[0.3,0.3])

1

([0.6,0.6],[0.2,0.3]) ([0.6,0.7],[0.1,0.2]) ([0.2,0.3],[0.3,0.4])

2

([0.7,0.8],[0.1,0.2])

([0.5,0.7],[0.3,0.3]) ([0.5,0.5],[0.5,0.5])

3

([0.2,0.4],[0.1,0.2]) ([0.2,0.3],[0.3,0.4]) ([0.2,0.3],[0.1,0.2])

4

([0.5,0.6],[0.2,0.3])

([0.4,0.5],[0.3,0.4]) ([0.5,0.7],[0.2,0.2])

…

…

13

([0.4,0.5],[0.3,0.4])

15

([0.6,0.7],[0.2,0.3])

([0.5,0.6],[0.3,0.3]) ([0.5,0.6],[0.3,0.4])

1

([0.8,0.9],[0.1,0.1]) ([0.8,0.8],[0.1,0.2]) ([0.7,0.8],[0.2,0.2])

3

([0.3,0.3],[0.2,0.2]) ([0.2,0.3,[0.2,0.3])

…

…

…

…

([0.5,0.7],[0.1,0.2]) ([0.4,0.6],[0.2,0.3])

…

([0.4,0.4],[0.5,0.5])

…

([0.4,0.5],[0.3,0.5]) ([0.4,0.5],[0.2,0.4]) ([0.4,0.6],[0.3,0.4])

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x1

cost effectiveness

…

14

([0.1,0.2],[0.2,0.2])

([0.5,0.6],[0.3,0.3]) ([0.2,0.3],[0.6,0.6])

…

…

([0.5,0.5],[0.3,0.4])

([0.4,0.6],[0.3,0.4]) ([0.6,0.6],[0.3,0.4])

16

([0.3,0.4],[0.3,0.5])

([0.5,0.6],[0.4,0.4]) ([0.5,0.5],[0.4,0.5])

2

([0.7,0.8],[0.1,0.2])

([0.5,0.7],[0.1,0.3]) ([0.5,0.6],[0.2,0.3])

4

([0.7,0.8],[0.1,0.2])

([0.6,0.8],[0.1,0.1]) ([0.5,0.6],[0.2,0.3])

…

…

…

…

13

([0.6,0.6],[0.1,0.3]) ([0.5,0.5],[0.5,0.5]) ([0.7,0.7],[0.1,0.2])

14

([0.8,0.8],[0.1,0.2])

([0.7,0.8],[0.1,0.1]) ([0.5,0.7],[0.1,0.2])

15

([0.5,0.5],[0.4,0.5]) ([0.5,0.6],[0.2,0.3]) ([0.6,0.6],[0.3,0.3])

16

([0.5,0.7],[0.3,0.3])

([0.7,0.8],[0.1,0.2]) ([0.6,0.9],[0.1,0.1])

At the same time, SNA was used to analyze the social network relationships of decision-making experts, and the social network relationship graph was constructed.

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The social network relationships are shown in Fig. 2.

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Fig. 2. Graph of experts’ social network relationships

Step 2: Large group clustering.

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The social network Louvain algorithm was used to cluster the experts. The

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clustering structure diagram is shown in Fig. 3.

Fig. 3. Network structure of experts cluster

The clustering results are shown in Table 3. Table 3 Clustering results

Ck

k

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0.28

0.29

0.19

ei

preference matrices

([0.30,0.32],[0.02,0.03])

([0.30,0.40],[0.01,0.01])

([0.20,0.32],[0.02,0.03])

([0.57,0.61],[0.00,0.01])

([0.46,0.59],[0.00,0.01])

([0.49,0.53],[0.00,0.00])

([0.66,0.69],[0.00,0.00])

([0.63,0.69],[0.00,0.02])

([0.61,0.67],[0.00,0.00])

([0.46,0.57],[0.00,0.00])

([0.37,0.44],[0.00,0.01])

([0.39,0.51],[0.00,0.01])

([0.51,0.59],[0.00,0.00])

([0.44,0.57],[0.00,0.00])

([0.49,0.64],[0.00,0.00])

([0.61,0.67],[0.00,0.00])

([0.44,0.59],[0.00,0.00])

([0.51,0.64],[0.00,0.00])

([0.13,0.23],[0.00,0.01])

([0.20,0.23],[0.00,0.01])

([0.23,0.29],[0.01,0.02])

([0.26,0.35],[0.00,0.01])

([0.17,0.26],[0.01,0.02])

([0.23,0.32],[0.00,0.00])

([0.23,0.29],[0.00,0.00])

([0.17,0.29],[0.00,0.00])

([0.10,0.20],[0.01,0.01])

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0.07

([0.48,0.55],[0.01,0.02])

([0.38,0.53],[0.01,0.02])

([0.35,0.51],[0.00,0.01])

([0.49,0.56],[0.00,0.01])

([0.46,0.55],[0.01,0.01])

([0.46,0.51],[0.01,0.02])

([0.51,0.57],[0.01,0.02])

([0.53,0.59],[0.00,0.01])

([0.49,0.59],[0.00,0.00])

([0.10,0.18],[0.15,0.24])

([0.14,0.18],[0.02,0.10])

([0.18,0.32],[0.06,0.13])

([0.14,0.22],[0.04,0.10])

([0.19,0.26],[0.06,0.13])

([0.22,0.38],[0.05,0.08])

([0.19,0.26],[0.04,0.08])

([0.14,0.22],[0.06,0.08])

([0.18,0.26],[0.03,0.10])

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0.17

Step 3: Consensus measurement.

Equations (10), (16) and (17) were used to calculate the consensus level of each cluster and the consensus level of the group. The initial consensus levels are shown in Table 4. To ensure the quality and timeliness of decision-making, the group consensus threshold was set to  =0.85 , the maximum number of iterations was set to T  4 . Table 4 Initial consensus levels

0.85

0.79

0.88

0.67

0.81

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0.87

Table 4 shows that the level of group consensus was lower than the threshold, and thus it was necessary to modify the preferences for clusters with a low consensus level.

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Step 4: Non-cooperative behaviors management.

Because the consensus levels of clusters C 3 and C 5 were both smaller than the group consensus level, the objective suggestion modification coefficient was given according to the consensus of two clusters. The range of subjective adjustment coefficients was given by the experts in the two clusters through consultation. The

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degrees of non-cooperation between the two clusters were obtained by comparing the two coefficients, as shown in Table 5. Table 5 Non-cooperation degrees of clusters C 3 and C 5

[0.10,0.29]

[0.20,0.25]

0.375

[0.42,0.54]

[0.30,0.50]

0.75

Table 5 shows that cluster C

3

exhibited general non-cooperative behaviors and

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that cluster C 5 exhibited the serious non-cooperative behaviors. Equations (11) and (22) were respectively used to calculate the preference risk of cluster C 3 as

 pC =0.49 , and the final preference adjustment coefficients of cluster C 3 as  31 =0.33 . k

Equations (11) and (21), (22), (23) were used to calculate the comprehensive risk of 20

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cluster C 5 as  C =0.78 and the final preference adjustment coefficients of cluster k

C 5 as  51 =0.71 . The adjusted preferences are shown in Table 6.

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Table 6 Preference matrices for clusters C 3 and C 5 after the first adjustment

([0.19,0.27],[0,0])

([0.22,0.26],[0,0])

([0.23,0.30],[0,0])

([0.26,0.32],[0,0])

([0.25,0.31],[0,0])

([0.24,0.33],[0,0])

([0.30,0.37],[0,0])

([0.22,0.31],[0,0])

([0.27,0.34],[0,0])

([0.35,0.41],[0,0])

([0.30,0.40],[0,0])

([0.33,0.40],[0,0])

([0.29,0.34],[0,0])

([0.24,0.34],[0,0])

([0.20,0.28],[0,0])

([0.39,0.44],[0,0])

([0.34,0.42],[0,0])

([0.34,0.42],[0,0])

From equation (15), a new group preference was obtained. Then, equations (16) and (17) were respectively used to obtain the consensus of each aggregation and the group consensus. The results are shown in Table 7.

Table 7 Consensus levels after the first adjustment

0.92

0.83

0.93

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0.91

0.90

0.90

As shown in Table 7, the level of consensus was higher than the consensus threshold. The process thus moved to Step 5.

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Step 5: Selection of the optimal alternative.

Equation (8) was used to score each alternative. The results were:

( x1 )  0.32, ( x2 )  0.46 and ( x3 )  0.52 . According to the rules in Definition 7, the alternatives were ranked as: x3

x2

x1 , x3 was thus the optimal alternative.

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5.3. Method comparison and discussion To illustrate the rationality and advantages of the proposed method, it is compared with a previous method in Ref. [10] in terms of timeliness and improvement of consensus. The previous management method of non-cooperative behaviors in Ref. [10] was applied to the case study in this paper. The results are shown in Table 8.

Table 8 Results obtained using a previous method in Ref. [10]

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Ck

k

 kt

CT (C k )

0.30 0.32 0.17 0.19

0 0 0.3 0

0.91 0.91 0.81 0.94 21

GCT (C k )

0.88

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0.02

0.45

0.82

First, the consistency of alternative ranking shows the rationality of the proposed

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method. Second, in terms of the number of iterations, the previous method in Ref. [10] needed two iterations, whereas the proposed method needed only one iteration, which is more in line with the timeliness requirements of emergency decision-making. Third, the final group consensus level obtained using the proposed method was 0.90, which is larger than that obtained using the previous method.

To sum up, the proposed method has three main advantages over the previous method in Ref. [10]. (1) The trust relationship among experts based on SNA and the uncertainty of experts’ preferences based on IVIFN are considered. Then, the preference adjustment coefficient is objectively calculated by combining trust risk and

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preference risk, which is more objective than the previous method. (2) The proposed method increases the level of group consensus, which reduces decision-making time and meets the timeliness requirements of emergency decision-making. (3) Louvain clustering is used to reduce the complexity of decision-making. Unlike the traditional preference clustering method, the inherent relationship between experts is considered.

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Considering the widespread use of online social networks and public participation in decision-making environments, the proposed method is more practical.

6. Conclusion

This paper proposed a management model of non-cooperative behaviors based

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on consensus that considers the experts’ trust relations and preference risks in LGEDM under a social network environment. The main contributions of this study are as follows:

(1) In real-life LGEDM, trust relationships among experts play a key role. We focused on the objective trust relationships among experts rather than a subjective trust scoring mechanism. The trust value in this paper was calculated based on the trust relationship and the position of experts in a social network. By taking objective trust relationships into account, we proposed a consensus reaching framework based

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on SNA in LGEDM.

(2) A mechanism for addressing non-cooperative behaviors was proposed. We

defined two kinds of non-cooperative behaviors, according to the degree of non-cooperation. For different types of non-cooperative behaviors, the different 22

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methods for determining cluster preference adjustment coefficients were proposed. (3) The decision-making risk in LGEDM was considered. We carried out a quantitative analysis of decision-making risk based on the social network

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relationships among experts, the uncertainty degree and consensus level of expert preference. And we defined the concepts of trust risk and preference risk. Meanwhile, there still exist the following limitations:

(1) There are many types of non-cooperative behaviors. Future research should consider a detailed classification of non-cooperative behaviors.

(2) The alternative indicators and attribute weights are important in LGEDM. It could be meaningful to explore attributes of public concern based on SNA to provide a reference for the determination of attribute indicators for experts.

(3) The study of decision-making risk was not extensive. The elimination of risks

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in decision-making is a future research goal.

Acknowledgments

This work was supported by grants from the National Natural Science Foundation of China (No. 71671189, No. 71971217), the Major Project of the Natural

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Science Foundation of China (No. 71790615), the Integrated Project of Natural Science Foundation of China (No. 91846301), and the Independent Exploration of Innovation

Project

(2018zzts300).

Postgraduate

of

Central

South

University,

China

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References

for

[1] L. Zhou, X.H. Wu, Z.S. Xu, H. Fujita, Emergency decision-making for natural disasters: An overview, Int. J. Disast. Risk Re. 27 (2018) 567-576.

[2] J. Cosgrave, Decision-making in emergencies, Disast Preven. Manage. 5(4) (1996) 28-35.

[3] Z.W. Gong, H.H. Zhang, J. Forrest, Two consensus models based on the minimum cost and maximum return regarding either all individuals or one individual, Eur. J. Oper. Res. 240(1) (2015) 183-192.

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[4] Z.W. Gong, X.X. Xu, H.H Zhang, The consensus models with interval preference opinions and their economic interpretation, Omega, 55 (2015) 81-90.

[5] X.H. Xu, D. Liang, X.H. Chen, A risk elimination coordination method for large group decision-making in natural disaster emergencies, Hum. Ecol. Risk Assess. 23

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An Inter. J. 21(5) (2015) 1314-1325. [6] X.H. Xu, L.L. Wang, X.H Chen, B.S. Liu, Large group emergency decision-making method with linguistic risk appetites based on criteria mining,

pro of

Knowl.-Based Syst. (2019), https://doi.org/10.1016/j.knosys.2019.07.020. [7] Á. Labella, Y. Liu, R.M. Rodríguez, Analyzing the performance of classical consensus models in large scale group decision-making: A comparative study, Appl. Soft Comput. 67 (2018) 677-690.

[8] T. Wu, K. Zhang, X. Liu, A two-stage social trust network partition model for large-scale group decision-making problems, Knowl.-Based Syst. 163 (2019) 632-643.

[9] R. Efremov, D.R. Insua, A. Lotov, A framework for participatory decision support

Res. 199(2) (2009) 459-467.

re-

using Pareto frontier visualization, goal identification and arbitration, Eur. J. Oper.

[10] X.H. Xu, Z.J. Du, X.H. Chen, Consensus model for multi-criteria large-group emergency decision-making considering non-cooperative behaviors and minority opinions, Decis. Support Syst. 79 (2015) 150-160.

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[11] X. Jing, J. Xie. Group buying: A new mechanism for selling through social interactions, Manage. Sci. 57(8) (2011) 1354-1372. [12] Y.J. Xu, X.W. Wen, W.C. Zhang, A two-stage consensus method for large-scale multi-attribute group decision-making with an application to earthquake shelter selection, Comput. Ind. Eng. 116 (2018) 113-129.

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[13] Z.B. Wu, J.P. Xu, A consensus model for large-scale group decision-making with hesitant fuzzy information and changeable clusters, Inf. Fusion.41 (2018) 217-231.

[14] X.H. Xu, X.Y. Zhong, X.H. Chen, A dynamical consensus method based on exit-delegation mechanism for large group emergency decision-making, Knowl.-Based Syst. 86(C) (2015) 237-249. [15] H.J. Zhang, J. Xiao, I. Palomares, Linguistic distribution-based optimization approach for large-scale GDM with comparative linguistic information. An

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application on the selection of wastewater disinfection technology, IEEE Trans. Fuzzy Syst. (2019). DOI 10.1109/TFUZZ.2019.2906856.

[16] H.J. Zhang, I. Palomares, Y.C. Dong, Managing non-cooperative behaviors in consensus-based multiple attribute group decision-making: An approach based 24

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on social network analysis, Knowl.-Based Syst. 162 (2018) 29-45. [17] H.J. Zhang, Y.C. Dong, F. Chiclana, Consensus efficiency in group decision-making: A comprehensive comparative study and its optimal design,

pro of

Eur. J. Oper. Res. 275(2) (2019) 580-598. [18] E. Herrera-Viedma, F.J. Cabrerizo, J. Kacprzyk, A review of soft consensus models in a fuzzy environment, Inf. Fusion. 17(1) (2014) 4-13.

[19] Y.C. Dong, H.J. Zhang, E. Herrera-Viedma, Consensus reaching model in the complex and dynamic MAGDM problem, Knowl.-Based Syst. 106(C) (2016) 206-219.

[20] H.J. Zhang, Y.C. Dong, I. Palomares, H.W. Zhou, Failure mode and effect analysis in a linguistic context: A consensus-based multiattribute group decision-making approach, IEEE Trans. Reli. 68(2) (2018) 566-582.

re-

[21] J. Wu, Q. Sun, H. Fujita, An attitudinal consensus degree to control the feedback mechanism in group decision making with different adjustment cost, Knowl.-Based Syst. 164 (2019) 265-273.

[22] H.J. Zhang, Y.C. Dong, V.E. Herrera. Consensus Building for the Heterogeneous

lP

Large-Scale GDM with the Individual Concerns and Satisfactions, IEEE Trans. Fuzzy Syst. 26(2) (2018) 884-898.

[23] M. Tang, X.Y. Zhou, H.C. Liao, H. Fujitad, Ordinal consensus measure with objective threshold for heterogeneous large-scale group decision-making, Knowl.-Based Syst. 180 (2019) 62-74.

urn a

[24] Z.W. Gong, H. Zhang, J. Forrest, Two consensus models based on the minimum cost and maximum return regarding either all individuals or one individual, Eur. J. Oper. Res. 240(1) (2015) 183-192. [25] X. Liu, Y. Xu, F. Herrera, Consensus model for large-scale group decision-making based on fuzzy preference relation with self-confidence: Detecting and managing overconfidence behaviors, Inf. Fusion. 52 (2019) 245-256.

[26] J. Wu, F. Chiclana, H. Fujita, A visual interaction consensus model for social

Jo

network group decision-making with trust propagation, Knowl.-Based Syst. 122 (2017) 39-50.

[27] Q. Liang, X. Liao, J. Liu,

A social ties-based approach for group

decision-making problems with incomplete additive preference relations, 25

Journal Pre-proof

Knowl.-Based Syst. 119 (2016) 68-86. [28] L.G. Pérez, F. Mata, F. Chiclana, Modelling influence in group decision-making, Soft Comput. 20(4) (2016) 1653-1665.

pro of

[29] I.J. Perez, F.J. Cabrerizo, S. Alonso, A new consensus model for group decision-making problems with non-homogeneous Experts, IEEE trans. Man Cybern. 44(4) (2014) 494-498.

[30] Y. Dong, Q. Zha, H. Zhang, H. Fujita, Consensus reaching in social network group decision-making: Research paradigms and challenges, Knowl.-Based Syst. 162 (2018) 3-13.

[31] L.G. Pérez, F. Mata, F. Chiclana, Social network decision-making with linguistic trustworthiness–based induced OWA operators, Int. J. Intell. Syst. 29(12) (2015) 1117-1137.

re-

[32] J. Chu, X. Liu, Y. Wang, Social network analysis based approach to group decision-making problem with fuzzy preference relations, J. Intell. Fuzzy Syst. 31(3) (2016) 1271-1285.

[33] J. Wu, F. Chiclana, A social network analysis trust–consensus based approach to

lP

group decision-making problems with interval-valued fuzzy reciprocal preference relations, Knowl.-Based Syst. 59 (2014) 97-107. [34] R.X. Ding, X. Wang, K. Shang, Social network analysis-based conflict relationship investigation and conflict degree-based consensus reaching process for large scale decision-making using sparse representation, Inf. Fusion. 50

urn a

(2019) 251-272.

[35] T. Wu, X. Liu, F. Liu, An interval type-2 fuzzy TOPSIS model for large scale group decision-making problems with social network information, Inf. Sci. 432 (2018) 392-410.

[36] I. Palomares, L. Martinez, F. Herrera, A consensus model to detect and manage non-cooperative behaviors in large-scale group decision-making, IEEE Trans. Fuzzy Syst. 22(3) (2014) 516-530. [37] Y.C. Dong, S.H. Zhao, H.J. Zhang, F. Chiclana, A self-management mechanism

Jo

for noncooperative behaviors in large-scale group consensus reaching processes, IEEE Trans. Fuzzy Syst. 26(6) (2018) 3276-3288.

[38] C.C. Li, Y.C. Dong, F. Herrera, A consensus model for large-scale linguistic group decision-making with a feedback recommendation based on clustered 26

Journal Pre-proof

personalized individual semantics and opposing consensus groups, IEEE Trans. Fuzzy Syst. 27(2) (2018) 221-233. [39] J. Francisco, F. Quesada, I. Palomares, L. Martínez, Managing expert’s behavior

Appl. Soft Comput. 35(C) (2015) 873-887.

pro of

in large-scale consensus reaching processes with uninorm aggregation operators,

[40] Z.N. Hao, Z.S. Xu, H. Zhao, H. Fujita, A dynamic weight determination approach based on the intuitionistic fuzzy Bayesian network and its application to emergency decision-making, IEEE Trans. Fuzzy Syst. 26(4) (2017) 1893-1907.

[41] H.C Liao, G.S. Si, Z.S. Xu, H. Fujita, Hesitant fuzzy linguistic preference utility set and its application in selection of fire rescue plans, Int. J. Environ. Res. Public Health, 15(4) (2018) 664.

re-

[42] X.Y. Zhou, L.Q. Wang, H.C. Liao, A prospect theory-based group decision approach considering consensus for portfolio selection with hesitant fuzzy information,

Knowl.-Based Syst. 168 (2019) 28-38.

[43] R.X. Ding, X.Q. Wang, K. Shang, B.S. Liu, F. Herrera, Sparse

lP

representation-based intuitionistic fuzzy clustering approach to find the group intra-relations and group leaders for large-scale decision-making, IEEE Trans. Fuzzy Syst. 27(3) (2019) 559-573.

[44] Y.Y. Li, Z.H. Zhou, Y. Fan, Z.Z. Jiang, Seismic emergency service point location model based on interval intuitive fuzzy number, J. Disast. Preven. Miti. Eng.

urn a

33(6) (2013) 725-729.

[45] X.H. Xu, C.G. Cai, X.H. Chen, A multi-attribute large group emergency decision-making method based on group preference consistency of generalized interval-valued trapezoidal fuzzy numbers, J. Syst. Sci. Sys. Eng. 24(2) (2015) 211-228.

[46] V.D. Blondel, J.L. Guillaume, R. Lambiotte, Fast unfolding of communities in large networks, J. Stat. Mech.-Theory Exper. 10 (2008) 105-118. [47] Y. Chen, X.Y. Liu, Identification of opinion leaders based on social network

Jo

analysis, Intell. Sci. 33(4) (2015) 13-19. [48] Z.S. Xu, Integration method of interval intuitionistic fuzzy information and its application in decision-making, Control. Decis. 02 (2007) 215-219.

[49] Z.H. Gao, C.P. Fan, An interval intuitionistic fuzzy entropy formula and its 27

Journal Pre-proof

application, Comput. Eng. Appli. 48(2) (2012) 53-55. [50] X.H. Xu, Z.J. Du, X.H. Chen, Confidence consensus-based model for large-scale group decision-making: A novel approach to managing non-cooperative

pro of

behaviors, Inf. Sci. 477 (2019) 410-427. [51] Z.S. Xu, Dependent uncertain ordered weighted aggregation operators, Inf.

Jo

urn a

lP

re-

Fusion. 9(2) (2008) 310-316.

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Highlights (for review)

Highlights： (1) By taking the objective trust relationships in to account, we propose a new consensus reaching framework based on SNA in LGEDM.

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(2) A novel mechanism for addressing non-cooperative behaviors is proposed.

(3) The decision-making risk in LGEDM is considered, the concepts of trust risk

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and preference risk are proposed.

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*conflict of Interest Statement

Dear editors: We would like to submit the revised manuscript entitled “Consensus-based non-cooperative behavior management in large group emergency decision

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making considering the experts’ trust relations and preference risks”, which we wish to be reconsidered, and manuscript is approved by all authors for submission.

The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a

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conflict of interest in connection with the work submitted.