Scientific Programming

Scientific Programming / 2020 / Article
Special Issue

Intelligent Decision Support Systems Based on Machine Learning and Multicriteria Decision-Making

View this Special Issue

Research Article | Open Access

Volume 2020 |Article ID 1631869 | https://doi.org/10.1155/2020/1631869

Xue-Feng Ding, Li-Xia Zhu, Mei-Shun Lu, Qi Wang, Yi-Qi Feng, "A Novel Linguistic Z-Number QUALIFLEX Method and Its Application to Large Group Emergency Decision Making", Scientific Programming, vol. 2020, Article ID 1631869, 12 pages, 2020. https://doi.org/10.1155/2020/1631869

A Novel Linguistic Z-Number QUALIFLEX Method and Its Application to Large Group Emergency Decision Making

Academic Editor: Rahman Ali
Received24 Nov 2019
Revised17 Mar 2020
Accepted10 Jun 2020
Published26 Jun 2020

Abstract

After an unconventional emergency event occurs, a reasonable and effective emergency decision should be made within a short time period. In the emergency decision making process, decision makers’ opinions are often uncertain and imprecise, and determining the optimal solution to respond to an emergency event is a complex group decision making problem. In this study, a novel large group emergency decision making method, called the linguistic Z-QUALIFLEX method, is developed by extending the QUALIFLEX method using linguistic Z-numbers. The evaluations of decision makers on the alternative solutions are first expressed as linguistic Z-numbers, and the group decision matrix is then constructed by aggregating the evaluations of all subgroups. The QUALIFLEX method is used to rank the alternative solutions for the unconventional emergency event. Besides, a real-life example of emergency decision making is presented, and a comparison with existing methods is performed to validate the effectiveness and practicability of the proposed method. The results show that the proposed linguistic Z-QUALIFLEX can accurately express the evaluations of the decision makers and obtain a more reasonable ranking result of solutions for emergency decision making.

1. Introduction

Emergency decision making is a human activity based on cognitive information, especially in the large group context. How to effectively express human cognitive information and perform cognitive computation in the large group emergency decision making is a highly challenging task and issue. Recently, a lot of studies have been carried out for cognition information representation and computation in solving various decision making problems, which include location evaluation [1, 2], enterprise resource planning system selection [3, 4], doctor selection [5], medical inquiry application evaluation [6], and others [79]. These research studies have proposed many effective methods and algorithms for using cognitive information in practical decision making processes. In this paper, we will pay attention to the large group emergency decision making problem based on human cognitive information.

Over the past several years, different unconventional emergency events occurred frequently all over the world. Examples include the Indian Ocean tsunami in 2004, Hurricane Katrina in the US in 2005, the 9.0 magnitude earthquake in Japan in 2011, and the Tianjin Port explosion in China in 2015, among others. These emergency events are difficult to predict and often impossible to control. They not only bring painful disasters and huge losses of life and properties but also cause serious social panic and potential secondary derivative hazards. When an emergency event happens, to reduce casualties and property losses and to eliminate various potential derivative hazards, decisions of reasonable and effective emergency relief solutions need to be made within a short time period [10]. However, because of their complexity, inadequate precursors, and devastating and potential secondary derivatives, it is difficult to deal with unconventional emergency events by conventional emergency management methods [11]. Therefore, the emergency decision making problem has gained increasing attention from both scholars and practitioners over recent years [1221].

Previous works in solving emergency decision making problems involve only a small number of decision makers. However, such problems are usually large group emergency decision making (LGEDM) problems. Emergency management often involves many different organizations and departments, and the decision making team often includes a large number of experts from various professional backgrounds [12]. The large team, or large group, decision making problems have the following characteristics [21, 22]: (a) the team may have 20 or more members, and the members cooperate but may also have conflicts; (b) the various decision criteria may be incommensurate although related; and (c) the opinions of the team members may change over time. The large group decision making problem aims to support decision makers in making the best choice from all the alternatives or solutions while considering multiple criteria effectively and efficiently. Therefore, it is preferred to address emergency decision making problems in the environment of the large group.

Owing to the uncertainty and complexity of the emergency situations, it is hard for decision makers to express their judgments with accuracy, especially under time pressure [23]. Various theories, such as fuzzy sets, intuitionistic fuzzy sets, and hesitant fuzzy sets, have been proposed to deal with imprecise decision information. However, these theories are inefficient in expressing the reliability of decision makers’ assessments [24]. This study uses linguistic Z-numbers [6] to represent inaccurate judgments of the decision makers. Compared with other methods such as fuzzy sets, intuitionistic fuzzy sets, and hesitant fuzzy sets, the linguistic Z-numbers can not only describe the cognition of the decision makers better but also consider the reliability of the cognitive information so as to represent the evaluations of decision makers more accurately.

The QUALIFLEX (Qualitative Flexible Multiple Criteria) method was developed by Paelinck [25] for group decision making using cardinal and ordinal information under uncertainty and fuzzy circumstance. Compared with other outranking methods such as SAW (simple additive weighting method), WP (weighted product method), LA (liner allocation method), TOPSIS, and ELECTRE, the QUALIFLEX method is a more flexible sorting method. In the QUALIFLEX method, a concordance/discordance index is first determined for each pair of alternatives through pairwise comparisons of the alternatives with respect to each criterion for all possible permutations of the alternatives. A weighted concordance/discordance index is then calculated for each pair of alternatives in each permutation. Finally, a comprehensive concordance/discordance index is calculated for each possible permutation of the alternatives. The permutation with the maximal value of the comprehensive concordance/discordance index is determined to be the best permutation, and the alternative ranked on the top of the best permutation is identified as the optimal alternative [26].

In order to describe the decision maker’s assessment more accurately under the emergency circumstance and make an effective emergency decision as quickly as possible, this study develops an extended QUALIFLEX method using linguistic Z-numbers, called the linguistic Z-QUALIFLEX method, for solving LGEDM problems. Linguistic Z-numbers are first used to represent the decision makers’ evaluations of the alternative solutions over various criteria, and the decision makers are divided into several subgroups according to the similarities of their evaluations. A group linguistic decision matrix is then constructed by aggregating the evaluations of all subgroups. The QUALIFLEX method is finally used to rank the alternative emergency solutions. Besides, an empirical example is provided to verify the applicability and the effectiveness of the proposed method. The proposed linguistic Z-QUALIFLEX method can accurately express the evaluations of the decision makers, characterize the similarities of their evaluations, and can also help decision makers get the best solution quickly and effectively.

The remainder of this paper is organized as follows. Previous related works are briefly reviewed in Section 2. Section 3 briefly introduces the basic concepts of Z-numbers and the QUALIFLEX method. Section 4 presents the linguistic Z-QUALIFLEX method for LGEDM problems. In Section 5, a numerical example is presented, and a comparative analysis is provided to illustrate the feasibility and validity of the proposed method. Conclusions and suggestions for future research are presented in Section 6.

2. Literature Review

Nowadays, a variety of methods have been proposed for EDM in the literature. For example, Ding et al. [27] proposed a new EDM approach by using picture fuzzy sets and an axiomatic design technique for determining the optimal rescue plan to reduce the damages of emergencies. Ding and Liu [28] presented an integrated approach based on prospect theory and the VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje) method for EDM with 2-dimension uncertain linguistic information, and Ding and Liu [29] solved the EDM problem by the use a combined approach of Pythagorean fuzzy uncertain linguistic variables and zero-sum game theory. Li and Cao [30] provided a risk decision analysis method by extending the TODIM method with interval numbers to solve multiattribute risk decision making problems in emergency response. Peng et al. [31] introduced a deviation-based method with q-rung orthopair fuzzy number (q-ROFN) to deal with EDM problems. In [32], a consistency-based EDM method was designed by extending the incomplete probabilistic linguistic term set in an incomplete probabilistic linguistic preference relation (InPLPR). In [33], a method combining probabilistic linguistic term sets (PLTSs) and the D-S evidence theory is applied to the EDM problem.

In addition, there are a few research studies that focused on EDM on the situation of the large group in recent years. Song and Li [34] proposed a consensus process of the large group EDM by using multigranular probabilistic fuzzy linguistic preference relations (MGPFLPRs) to represent subgroup’s preferences information. Xu et al. [35] presented a framework for the LGEDM problem in a linguistic environment by considering decision makers’ risk appetites. Xu et al. [36] found a LGEDM model for determining the severity of emergencies based on a decision paradigm obtained from the analysis of similar cases. Xu et al. [37] established a consensus model for the effective management of opinion differences and noncooperative behaviors in LGEDM environment. Cai et al. [16] suggested a multistage LGEDM model based on the preference information expressed as interval numbers and the similarity measures of decision makers. Aiming at the lower consensus and the urgency of LGEDM, Xu et al. [10] described a preference consensus model by taking into account the noncooperative behaviors and minority opinions of decision makers, and Xu et al. [38] proposed a dynamical consensus method based on exit-delegation mechanism considering consistency and consensus measures simultaneously.

The above literature review shows that various theories, such as interval numbers, 2-dimension uncertain linguistic variables, and probabilistic linguistic term sets, have been employed to deal with imprecise cognitive information in the EDM process. However, these theories are inefficient in expressing the reliability of decision makers’ cognitive assessments. Moreover, no or little attention has been paid to the large group EDM problems under the context of linguistic Z-numbers. In addition, various MCDM methods have been proposed to deal with EDM problems. To the best of our knowledge, no previous studies have investigated EDM problems with the QUALIFLEX method yet. Therefore, in this paper, we fill the above gaps by developing a novel, integrated cognitive approach based on linguistic Z-numbers and an extended QUALIFLEX method to solve the EDM problem within the large group environment. The developed method in this paper can not only express the subjective cognitive evaluation information of decision makers more precisely but also support the rescue team in finding the optimal response to an emergency event effectively.

3. Preliminaries

3.1. Linguistic Z-Numbers

Combining Z-numbers [39] and linguistic variables [40], Wang et al. [6] introduced the concept of linguistic Z-numbers to address the reliability of information as a significant dimension in a decision making process.

Definition 1 (see [41]). An uncertain variable is a measurable function from an uncertainty space to the set of real numbers.

Definition 2 (see [6]). Suppose that is a finite universe of discourses. and are two finite and totally ordered discrete linguistic term sets, where and are the positive odd integers. Let and . A linguistic Z-number set in is expressed aswhere represents the fuzzy restriction on the domain of the uncertain variables, and is a measure of reliability of .
Normally, and represent different preference information and, hence, are not always consistent. For simplicity, is called a linguistic Z-number, where and are the two linguistic terms.

Definition 3 (see [6]). Let and be two linguistic Z-numbers and and be the possible functions of , , , and where , , , and are strictly monotonically increasing functions. Then, the operational laws of Z-numbers are defined as follows:(1)(2) (3)(4), for (5), for

Definition 4. (see [6]). Suppose that is a linguistic term set and is a linguistic Z-number; then, the score function of is defined asand the accuracy function of is defined as

Definition 5. (see [6]). Let and be two linguistic Z-numbers. Then, the comparison laws of and are defined as follows:(1)When and , then is strictly greater than , expressed as (2)When and , then is greater than , expressed as (3)When and , then equals , expressed as (4)When and , then is less than , expressed as

Definition 6. (see [6]). Let and be two linguistic Z-numbers and and be two linguistic scale functions. Then, the distance between and is defined asTo aggregate the evaluations expressed by linguistic Z-numbers, the linguistic Z-number weighted averaging (LZNWA) operator is proposed.

Definition 7. Suppose is a collection of linguistic Z-numbers , and LZNWA: , then the LZNWA operator is given bywhere is the same operator defined in Definition 3, is the weight of , satisfying , for , and . If , the LZNWA operator becomes the linguistic Z-number arithmetic mean (LZAM) operator.

3.2. QUALIFLEX Method

The QUALIFLEX method, proposed by Paelinck [25], is a useful outranking technique for solving multiple attribute decision making problems with exact values for the evaluations given by the decision makers [42, 43]. The QUALIFLEX method treats cardinal and ordinal information simultaneously in the process of decision making. In the QUALIFLEX method, pairwise comparisons of the alternatives with respect to each criterion under all possible alternative permutations are made, and the optimal alternative(s) can be determined by maximizing the value of the comprehensive concordance/discordance index [44] among all possible alternative permutations. Let be a set of alternatives, be a set of criteria, and be the weights of the criteria satisfying , for , and . There are permutations of the rankings of the alternatives. The decision process of the QUALIFLEX method is described step by step as follows [25, 45]:Step 1: list all permutations of the rankings of the alternatives. Suppose , as shown in equation (6), is the th permutation:where , and the ranking of is higher or equal to that of .Step 2: determine the concordance/discordance index by using equation (7) for each pair of alternatives , and measure the similarity between and , in each permutation with respect to each criterion :Step 3: calculate the weighted concordance/discordance index by using equation (8) for each pair of alternatives and in each permutation :Step 4: determine the comprehensive concordance/discordance index by using equation (9) for each permutation and determine the optimal alternative:

The best ranking of the alternatives is the one with the maximum value of the comprehensive concordance/discordance index . The alternative ranked on the top of the corresponding ranking is the optimal alternative.

4. The Proposed LGEDM Approach

In this section, the linguistic Z-QUALIFLEX method, an extended QUALIFLEX approach with linguistic Z-numbers, is proposed to solve emergency decision making problems when a large group of decision makers is involved. The evaluations of the alternatives with respect to the criteria, represented by Z-numbers, are given by the large group of decision makers. The major steps of the proposed approach are shown in Figure 1. The decision makers are first divided into several subgroups according to the similarities of their evaluations. The evaluations represented by linguistic Z-numbers given by the decision makers in each subgroup are then aggregated into a group linguistic Z-number decision matrix using the LZAM operator. The best ranking of the alternatives is finally identified by using the QUALIFLEX method.

In the QUALIFLEX method, let be a set of emergency solutions, i.e., alternatives, be a set of criteria, be the weights of the criteria satisfying , for , and , and with be a set of decision makers in an LGEDM problem. Each decision maker gives his/her judgment of with respect to using linguistic Z-numbers, represented by . The linguistic Z-number evaluation matrices , with and for , are then obtained. Each element of is given by , where is the linguistic evaluation of alternative with respect to criterion given by the decision maker using the linguistic term set , and is a measure of reliability of using the linguistic term set . The evaluations of decision makers are assumed to be independent of each other. The linguistic Z-QUALIFLEX method used to solve LGEDM problems is presented step by step in three phases in the following.Phase 1: cluster the decision makers into subgroupsStep 1.1: normalize the linguistic Z-number evaluation matrix by using

The normalized linguistic Z-number evaluation matrix is represented by .Step 1.2: calculate the similarity degrees between decision makers’ linguistic Z-number evaluations. Let denote the normalized linguistic evaluation vector for alternative , for , by decision maker , for . The similarity degree between and is given byStep 1.3: divide decision makers into subgroups for each alternative. Suppose is the clustering threshold of alternative obtained by usingwhereand are the evaluation vectors of all decision makers for alternative .For alternative , if , then and are put into the same subgroup. Let denote the number of subgroups after clustering for alternative , be the decision makers in subgroup , be the corresponding assessment vectors of , and be the number of decision makers in . The requirement is needed. If there is a , for any , such that , needs to be modified. The method proposed by Cai et al. [16] is used for modification.Phase 2: construct the group linguistic decision matrixStep 2.1: aggregate the linguistic Z-number evaluation vectors of the decision makers in each subgroup into a subgroup linguistic Z-number evaluation vector by the LZAM operator. For each alternative , the linguistic Z-number evaluation vectors , for , of decision makers in subgroup are aggregated into the subgroup linguistic evaluation vector by using the LZAM operator:where is the weight of .Step 2.2: construct the group linguistic evaluation matrix . Using the subgroup linguistic evaluation vectors , for , the group linguistic evaluation vector can be obtained by using the LZAM operator:where . The group linguistic evaluation vectors , for , form the group linguistic evaluation matrix .Phase 3: rank the alternatives by using the QUALIFLEX methodStep 3.1: list all permutations of the rankings of the alternatives:where is the th permutation, , and is ranked higher or equal to in the permutation.Step 3.2: calculate the concordance/discordance index of each pair of alternatives in each permutation by considering every criterion usingStep 3.3: calculate the weighted concordance/discordance index of each permutation by usingStep 3.4: determine the comprehensive concordance/discordance index by using

The best ranking of the alternatives is with the maximum value of the comprehensive concordance/discordance index , i.e., . The alternative ranked on the top of is the optimal solution for the LGEDM problem.

5. A Numerical Example

In China, from June to July, there are often persistent rainstorms in the middle and lower reaches of the Yangtze River, which are of long duration, wide area, and heavy rainfall. July to August is the main rainstorm season in northern provinces, and the rainstorm intensity is very high. These torrential rains often lead to floods, which may cause river levee breach incidents, resulting in great harm to people and public property.

In order to reduce the huge damage to people and public property caused by these accidents and provide scientific support for the emergency management of such emergencies, in this section, an LGEDM problem of a river levee breach incident is used as the illustrative example to demonstrate the effectiveness and practicability of the proposed linguistic Z-QUALIFLEX method.

5.1. Decision Process and Results

In the morning of June 21, 2017, a severe thunderstorm watch with red color warning of possible heavy rainfall in the next three days was issued by the meteorological department in area C in Hubei province of China. According to weather report, the probabilities of moderate, heavy, and violent rainfalls are 0.30, 0.50, and 0.20, respectively. A riverbank breach will cause a wide range flooding disaster and a large number of casualties, seriously affecting the lives of people in the surrounding area. 20 experts from the emergency management department, the meteorological department, the water conservancy department, and the transportation department were invited to choose the best emergency solution within a short period of time. There are three emergency solutions for the decision makers to choose from. : strengthen the riverbank, keep close monitoring, and expand the emergency force of inspection and rescue. : strengthen the riverbank, keep close monitoring, send the villager rescue team to the site, and transfer the villagers in low-lying areas to safe areas. : strengthen the riverbank, keep close monitoring, and send the villager rescue team and medical team to the site, allocate a large quantity of relief supplies, and transfer the nearby villagers to safe areas. Four criteria are considered for each emergency solution: C1—number of victims, C2—public satisfaction, C3—property loss, and C4—rescue cost. The weights of these criteria are supposed as (0.30, 0.25, 0.30, and 0.15). Suppose that all decision makers DM = {D1, D2,…, D20} have the same weights and are required to give their linguistic Z-number evaluations for the solutions over each criterion. Note that is a benefit, i.e., maximization, criterion, while , , and are cost, i.e., minimization, criteria.

The evaluations given by the 20 decision makers on three solutions by considering the four criteria are represented by linguistic Z-numbers. The linguistic term set for used by the decision makers isand the linguistic term set for is

The decision process and the results of the proposed linguistic Z-QUALIFLEX method of selecting the best solution for this example LGEDM problem are summarized as follows:Phase 1: divide the decision makers into subgroupsThe linguistic Z-number evaluation matrices are obtained first from all the decision makers. By using equation (10), the linguistic Z-number evaluation matrices of the decision makers are normalized. As a result, a normalized linguistic evaluation matrix composed of the evaluation vectors of 20 decision makers is constructed for each alternative. Due to space limitation, only , for , i.e., the normalized linguistic evaluation vectors by the 20 decision makers for alternative , are listed, which are shown in Table 1.The similarity degrees between the decision makers’ linguistic evaluation vectors of each alternative are then calculated by using equation (11). The result for alternative is shown in Table 2. By using equation (12) and the steps of modification, the decision makers for each alternative are divided into several subgroups, and the clustering results of are shown in Table 3.Phase 2: construct the group linguistic decision matrixFor each alternative , for i = 1, 2, 3, the linguistic Z-number evaluation vectors in , for , of the decision makers in subgroup are aggregated into the subgroup linguistic evaluation vector by using equation (14). By aggregating the subgroup linguistic evaluation vectors of all alternatives based on equation (15), the group linguistic evaluation matrix is obtained as shown in Table 4.Phase 3: rank the alternatives using the QUALIFLEX method


DMC1C2C3C4

D1
D2
D3
D4
D5
D6
D7
D8
D9
D10
D11
D12
D13
D14
D15
D16
D17
D18
D19
D20


DMD1D2D3D4D5D6D7D8D9D10D11D12D13D14D15D16D17D18D19D20

D11.0000.5720.2390.6460.2880.5170.1860.2270.2330.4130.1610.2960.2060.3420.2370.4020.2770.2890.2520.643
D20.5721.0000.2960.3010.3330.3130.1820.2330.2280.2710.1820.2960.2120.2320.2100.4840.3010.3380.2500.513
D30.2390.2961.0000.1810.3730.1920.2740.4550.4940.1730.2460.2270.2880.1770.2420.2710.2800.2000.1740.439
D40.6460.3010.1811.0000.5080.6670.1560.1790.1820.5170.1380.3500.1720.4440.1870.2650.2320.4460.3350.346
D50.2880.3330.3730.5081.0000.5080.2100.2860.2550.4250.2060.6000.2750.3180.2720.3220.2810.6250.5140.272
D60.5170.3130.1920.6670.5081.0000.1580.1850.1840.6420.1400.4170.1740.4440.1940.2580.2130.4580.5020.383
D70.1860.1820.2740.1560.2100.1581.0000.3920.3470.1780.3290.2340.3380.1150.5750.2650.2560.1870.5710.236
D80.2270.2330.4550.1790.2860.1850.3921.0000.6330.2320.5000.3310.8330.1320.3830.5040.5080.2460.2440.275
D90.2330.2280.4940.1820.2550.1840.3470.6331.0000.2310.2720.2660.4670.1310.3010.3300.3420.2420.2540.340
D100.4130.2710.1730.5170.4250.6420.1780.2320.2311.0000.1540.4380.2240.5670.2110.2900.2510.5420.4880.291
D110.1610.1820.2460.1380.2060.1400.3290.5000.2720.1541.0000.2490.5830.1150.3170.4030.5270.1710.2010.187
D120.2960.2960.2270.3500.6000.4170.2340.3310.2660.4380.2491.0000.3210.3980.3260.3540.3070.5630.5300.267
D130.2060.2120.2880.1720.2750.1740.3380.8330.4670.2240.5830.3211.0000.1240.3560.4700.6750.2380.2340.254
D140.3420.2320.1770.4440.3180.4440.1150.1320.1310.5670.1150.3980.1241.0000.1320.1970.1540.5020.4250.200
D150.2370.2100.2420.1870.2720.1940.5750.3830.3010.2110.3170.3260.3560.1321.0000.3740.2650.2450.3100.263
D160.4020.4840.2710.2650.3220.2580.2650.5040.3300.2900.4030.3540.4700.1970.3741.0000.6750.2830.2850.308
D170.2770.3010.2800.2320.2810.2130.2560.5080.3420.2510.5270.3070.6750.1540.2650.6751.0000.2330.2400.259
D180.2890.3380.2000.4460.6250.4580.1870.2460.2420.5420.1710.5630.2380.5020.2450.2830.2331.0000.4130.304
D190.2520.2500.1740.3350.5140.5020.5710.2440.2540.4880.2010.5300.2340.4250.3100.2850.2400.4131.0000.220
D200.6430.5130.4390.3460.2720.3830.2360.2750.3400.2910.1870.2670.2540.2000.2630.3080.2590.3040.2201.000


AlternativesSubgroups

E1{D8, D13}; {D1, D4, D5, D6, D10, D18, D20}; {D16, D17}; {D3, D7, D9, D12, D14, D19}; {D2, D11, D15}.
E2{D1, D2, D4, D6, D7, D11, D13, D14, D16, D17, D18, D19}; {D3, D8, D15, D20}; { D5, D9, D10, D12}.
E3{D1, D2, D4, D5, D6, D10, D12, D13, D14, D15, D16, D17, D18, D19, D20}; {D3, D8}; {D7, D9, D11}.


AlternativesC1C2C3C4

E1(A3.400, B3.997)(A5.119, B2.145)(A4.633, B4.337)(A5.346, B4.221)
E2(A1.118, B0.889)(A2.264, B1.521)(A1.056, B0.708)(A1.014, B0.826)
E3(A0.991, B0.880)(A4.168, B2.636)(A1.093, B1.084)(A0.920, B0.622)

By equation (16), there are 6 (=3!) permutations of the rankings for the three candidate emergency solutions, i.e.,

By using equation (17), the concordance/discordance index of each pair of solutions , for , in each permutation , for , is calculated by considering each criterion. Because of space limitation, only the concordance/discordance indices of permutation are presented in Table 5. The weighted concordance/discordance indices of each permutation are obtained by using equation (18), and the results of permutation are listed in Table 6. Finally, the comprehensive concordance/discordance indices are calculated by using equation (19), and the results are , , , , , and , respectively. Hence, the best ranking of the alternatives is . Therefore, is the best emergency solution.


P1

C12.8983.005–2.8980.127–3.0050.127
C2–2.855–3.0052.855–1.9043.0051.904
C33.6083.570–3.608–0.038–3.5700.038
C44.3504.444–4.3500.094–4.444–0.094



P13.3123.391–3.312–0.435–3.3910.435
P23.3182.877–3.318–0.435–2.8770.435
P33.3122.877–3.3120.073–2.877–0.073
P43.3122.877–3.312–0.435–2.8770.435
P53.3122.877–3.312–0.435–2.8770.435
P63.3122.877–3.312–0.435–2.8770.435

5.2. Comparative Analysis

To demonstrate the effectiveness and practicability of the proposed linguistic Z-QUALIFLEX method, a comparative analysis is conducted. Four typical large group decision making methods at present including the interval type-2 fuzzy TOPSIS method [12], the preference conflict method [16], the large group EDM method considering experts’ hesitation preference [46], and the large group decision making method based on expert’s consensus [47] are used for comparison. The ranking results of the three emergency solutions obtained by these three methods are shown in Figure 2.

From Figure 2, it can be seen that the rankings of the emergency solutions obtained by the proposed method are the same as those of the interval type-2 fuzzy TOPSIS method and the large group EDM method considering experts’ hesitation preference, but the rankings are different from those of the preference conflict method and the large group decision making method based on experts’ consensus. Compared with the interval type-2 fuzzy TOPSIS method and the large group EDM method considering experts’ hesitation preference, the calculation process is simpler by the proposed method.

The ranking result obtained with the proposed method is more practical. The reasons are as follows: in this example, first, the best solution selected by the proposed method not only ensures public safety but also saves cost. The probability of a violent rainfall causing collapse of the riverbank in area C is 0.20, which means that the probability of collapse of the riverbank is small. The solution involves sending the villager rescue team, the medical and the health team to the site, allocating a large quantity of relief supplies, and transferring the nearby villagers, which requires large quantities of manpower, material, and financial resources. If is taken as the emergency solution under the situation of a relatively small probability of collapse of the riverbank, it may not only cause wastes of the manpower, material, and financial resources but also lead to the discontent of the transferred villagers, which can minimize casualties but costs the most. cannot minimize casualties or improve personnel satisfaction, and it needs more material consumption compared with . Therefore, it is more reasonable for the emergency management office to inform all kinds of emergency organizations and villagers in advance to prepare for the emergency and the transfer, and to strengthen the riverbank, keep close monitoring, and expand the emergency force of inspection and rescue at the same time just as what the alternative will do. Once a breach of the riverbank happens, the villagers will be transferred immediately, and less manpower, material, and financial resources are needed. Besides, in reality, a river levee breach occurred in Matou village in the afternoon of June 23, 2017. The whole village was in danger of flooding, and the lives and property of 2,600 people in the village were threatened. The emergency solution is also in agreement with the emergency measure taken in reality by the emergency management office to the river levee breach incident occurred in area C.

Comparing with the existing LGEDM methods, the linguistic Z-QUALIFLEX method has the following advantages: (1) the linguistic Z-numbers can describe the inherent thoughts of the decision makers more precisely and practically, ensuring the accuracy of the final results. (2) The similarity degrees and the LZAM operator are used for dividing the large group of decision makers into subgroups and for aggregating subgroups, which not only takes the conflicting nature of large group decision preferences into account but also considers the subgroup opinions under different preferences. (3) The QUALIFLEX method based on preference relation similarities is used to rank the emergency solutions. This method can handle cardinal and ordinal information in the process of decision making at the same time and can well express the complexity of the LGEDM problem. (4) Many existing large group decision making methods need to constantly recalculate expert weights or other parameters to classify expert groups, and the initial subgroups of experts or the value of some thresholds are mostly set artificially, which not only increases the calculation complexity but also may cause the decision results change due to different parameter values. The proposed method adopts an automatic threshold determination method to classify decision makers. The calculation is relatively simple and helps to reduce and eliminate the decision making risk caused by subjectivity.

6. Conclusions

This study proposed an extended QUALIFLEX method using linguistic Z-numbers, called the linguistic Z-QUALIFLEX method, to deal with the LGEDM problem. Linguistic Z-numbers are first used to express the evaluations of the decision makers, which can more precisely express the inherent opinions of the decision makers. The similarity degrees between the decision makers’ linguistic evaluation vectors of each alternative are then calculated and used to divide the large group of decision makers into several subgroups. The evaluations of the decision makers in each subgroup are aggregated, and the group linguistic decision matrix is constructed by the LZAM operator. The QUALIFLEX method is finally used to rank the emergency solutions. To demonstrate the effectiveness and practicability of the proposed linguistic Z-QUALIFLEX method, a real-life example of a river levee breach incident is presented, and the obtained ranking result is compared with those of the existing LGEDM methods.

There are some improvements to be made in future studies. (1) The proposed method should be extended to support LGEDM problems by considering more complex influencing factors. (2) The complex psychological behaviors of the decision makers in the decision making process under uncertain or emergency circumstances should be considered. (3) More linguistic expression techniques should be investigated for reducing the subjectivity in the decision making process. (4) More reasonable and effective approaches for dividing a large group of decision makers into subgroups need to be developed.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China (No. 71502098), the Soft Science Research Support Project of Shanghai Science and Technology Development Fund (No. 19692109000), and the Training program of School of management of Shanghai University (2020-SDGY-KZ-003).

References

  1. L. Wang, Y.-M. Wang, and L. Martínez, “A group decision method based on prospect theory for emergency situations,” Information Sciences, vol. 418-419, pp. 119–135, 2017. View at: Publisher Site | Google Scholar
  2. P. Ji, H.-Y. Zhang, and J.-Q. Wang, “A projection-based outranking method with multihesitant fuzzy linguistic term sets for hotel location selection,” Cognitive Computation, vol. 10, no. 5, pp. 737–751, 2018. View at: Publisher Site | Google Scholar
  3. Z.-P. Tian, J. Wang, J.-Q. Wang, and H.-Y. Zhang, “A likelihood-based qualitative flexible approach with hesitant fuzzy linguistic information,” Cognitive Computation, vol. 8, no. 4, pp. 670–683, 2016. View at: Publisher Site | Google Scholar
  4. P. Liu and X. Zhang, “A novel picture fuzzy linguistic aggregation operator and its application to group decision making,” Cognitive Computation, vol. 10, no. 2, pp. 242–259, 2018. View at: Publisher Site | Google Scholar
  5. J. Hu, L. Pan, and X. Chen, “An interval neutrosophic projection-based VIKOR method for selecting doctors,” Cognitive Computation, vol. 9, no. 6, pp. 801–816, 2017. View at: Publisher Site | Google Scholar
  6. J.-Q. Wang, Y.-X. Cao, and H.-Y. Zhang, “Multicriteria decision making method based on distance measure and Choquet integral for linguistic Z-numbers,” Cognitive Computation, vol. 9, no. 6, pp. 827–842, 2017. View at: Publisher Site | Google Scholar
  7. B. Farhadinia and Z. Xu, “Distance and aggregation-based methodologies for hesitant fuzzy decision making,” Cognitive Computation, vol. 9, no. 1, pp. 81–94, 2017. View at: Publisher Site | Google Scholar
  8. F. Meng, C. Wang, and X. Chen, “Linguistic interval hesitant fuzzy sets and their application in decision making,” Cognitive Computation, vol. 8, no. 1, pp. 52–68, 2016. View at: Publisher Site | Google Scholar
  9. H.-Y. Zhang, P. Ji, J.-Q. Wang, and X.-H. Chen, “A neutrosophic normal cloud and its application in decision making,” Cognitive Computation, vol. 8, no. 4, pp. 649–669, 2016. View at: Publisher Site | Google Scholar
  10. X.-H. Xu, Z.-J. Du, and X.-H. Chen, “Consensus model for multicriteria large group emergency decision making considering non-cooperative behaviors and minority opinions,” Decision Support Systems, vol. 79, pp. 150–160, 2015. View at: Publisher Site | Google Scholar
  11. Y. Liu, Z.-P. Fan, and Y. Zhang, “Risk decision analysis in emergency response: a method based on cumulative prospect theory,” Computers & Operations Research, vol. 42, pp. 75–82, 2014. View at: Publisher Site | Google Scholar
  12. Z. Wu and J. Xu, “A consensus model for large scale group decision making with hesitant fuzzy information and changeable clusters,” Information Fusion, vol. 41, pp. 217–231, 2018. View at: Publisher Site | Google Scholar
  13. A. Pagano, I. Pluchinotta, R. Giordano, A. B. Petrangeli, U. Fratino, and M. Vurro, “Dealing with uncertainty in decision making for drinking water supply systems exposed to extreme events,” Water Resources Management, vol. 32, no. 6, pp. 2131–2145, 2018. View at: Publisher Site | Google Scholar
  14. B. Sun, W. Ma, B. Li, and X. Li, “Three-way decisions approach to multiple attribute group decision making with linguistic information-based decision-theoretic rough fuzzy set,” International Journal of Approximate Reasoning, vol. 93, pp. 424–442, 2018. View at: Publisher Site | Google Scholar
  15. S. Bingzhen and M. Weimin, “An approach to evaluation of emergency plans for unconventional emergency events based on soft fuzzy rough set,” Kybernetes, vol. 45, no. 3, pp. 461–473, 2016. View at: Publisher Site | Google Scholar
  16. C.-G. Cai, X.-H. Xu, P. Wang, and X.-H. Chen, “A multistage conflict style large group emergency decision making method,” Soft Computing, vol. 21, no. 19, pp. 5765–5778, 2017. View at: Publisher Site | Google Scholar
  17. J. He, C. Feng, D. Hu, and L. Liang, “A decision model for emergency warehouse location based on a novel stochastic mcda method: evidence from China,” Mathematical Problems in Engineering, vol. 2017, Article ID 7804781, 10 pages, 2017. View at: Publisher Site | Google Scholar
  18. F. Jin, Z. Ni, H. Chen, and Y. Li, “Approaches to decision making with linguistic preference relations based on additive consistency,” Applied Soft Computing, vol. 49, pp. 71–80, 2016. View at: Publisher Site | Google Scholar
  19. Y. Xu, W. Zhang, and H. Wang, “A conflict-eliminating approach for emergency group decision of unconventional incidents,” Knowledge-Based Systems, vol. 83, pp. 92–104, 2015. View at: Publisher Site | Google Scholar
  20. Y. Xu, F. Ma, W. Xu, and H. Wang, “An incomplete multigranular linguistic model and its application in emergency decision of unconventional outburst incidents,” Journal of Intelligent & Fuzzy Systems, vol. 29, no. 2, pp. 619–633, 2015. View at: Publisher Site | Google Scholar
  21. B. Liu, Y. Shen, X. Chen, H. Sun, and Y. Chen, “A complex multiattribute large group PLS decision making method in the interval-valued intuitionistic fuzzy environment,” Applied Mathematical Modelling, vol. 38, no. 17-18, pp. 4512–4527, 2014. View at: Publisher Site | Google Scholar
  22. B. Liu, Y. Shen, W. Zhang, X. Chen, and X. Wang, “An interval-valued intuitionistic fuzzy principal component analysis model-based method for complex multiattribute large group decision making,” European Journal of Operational Research, vol. 245, no. 1, pp. 209–225, 2015. View at: Publisher Site | Google Scholar
  23. L. Zhang, Y. Wang, and X. Zhao, “A new emergency decision support methodology based on multisource knowledge in 2-tuple linguistic model,” Knowledge-Based Systems, vol. 144, pp. 77–87, 2018. View at: Publisher Site | Google Scholar
  24. S. Xian, J. Chai, and H. Guo, “Linguistic-induced ordered weighted averaging operator for multiple attribute group decision making,” International Journal of Intelligent Systems, vol. 34, no. 2, pp. 271–296, 2019. View at: Publisher Site | Google Scholar
  25. J. H. P. Paelinck, “Qualiflex: a flexible multiple criteria method,” Economics Letters, vol. 1, no. 3, pp. 193–197, 1978. View at: Publisher Site | Google Scholar
  26. A. Isik and E. Adali, “The qualiflex method for the insurance company selection problem,” European Scientific Journal, vol. 12, no. 10, pp. 348–358, 2016. View at: Google Scholar
  27. X.-F. Ding, L. Zhang, and H.-C. Liu, “Emergency decision making with extended axiomatic design approach under picture fuzzy environment,” Expert Systems, vol. 37, no. 2, 2020. View at: Publisher Site | Google Scholar
  28. X.-F. Ding and H.-C. Liu, “An extended prospect theory-VIKOR approach for emergency decision making with 2-dimension uncertain linguistic information,” Soft Computing, vol. 23, no. 22, pp. 12139–12150, 2019. View at: Publisher Site | Google Scholar
  29. X.-F. Ding and H.-C. Liu, “A new approach for emergency decision making based on zero-sum game with Pythagorean fuzzy uncertain linguistic variables,” International Journal of Intelligent Systems, vol. 34, no. 7, pp. 1667–1684, 2019. View at: Publisher Site | Google Scholar
  30. M.-Y. Li and P.-P. Cao, “Extended TODIM method for multiattribute risk decision making problems in emergency response,” Computers & Industrial Engineering, vol. 135, pp. 1286–1293, 2019. View at: Publisher Site | Google Scholar
  31. X. Peng, R. Krishankumar, and K. S. Ravichandran, “Generalized orthopair fuzzy weighted distance-based approximation (WDBA) algorithm in emergency decision making,” International Journal of Intelligent Systems, vol. 34, no. 10, pp. 2364–2402, 2019. View at: Publisher Site | Google Scholar
  32. J. Gao, Z. Xu, Z. Liang, and H. Liao, “Expected consistency-based emergency decision making with incomplete probabilistic linguistic preference relations,” Knowledge-Based Systems, vol. 176, pp. 15–28, 2019. View at: Publisher Site | Google Scholar
  33. P. Li and C. Wei, “An emergency decision making method based on D-S evidence theory for probabilistic linguistic term sets,” International Journal of Disaster Risk Reduction, vol. 37, p. 101178, 2019. View at: Publisher Site | Google Scholar
  34. Y. Song and G. Li, “Consensus constructing in large scale group decision making with multigranular probabilistic 2-tuple fuzzy linguistic preference relations,” IEEE Access, vol. 7, pp. 56947–56959, 2019. View at: Publisher Site | Google Scholar
  35. X. Xu, L. Wang, X. Chen, and B. Liu, “Large group emergency decision making method with linguistic risk appetites based on criteria mining,” Knowledge-Based Systems, vol. 182, pp. 1–13, 2019. View at: Publisher Site | Google Scholar
  36. X. Xu, Y. Huang, and K. Chen, “Method for large group emergency decision making with complex preferences based on emergency similarity and interval consistency,” Natural Hazards, vol. 97, no. 1, pp. 45–64, 2019. View at: Publisher Site | Google Scholar
  37. X.-H. Xu, Z.-J. Du, X.-H. Chen, and C.-G. Cai, “Confidence consensus-based model for large scale group decision making: a novel approach to managing noncooperative behaviors,” Information Sciences, vol. 477, pp. 410–427, 2019. View at: Publisher Site | Google Scholar
  38. X.-H. Xu, X.-Y. Zhong, X.-H. Chen, and Y.-J. Zhou, “A dynamical consensus method based on exit-delegation mechanism for large group emergency decision making,” Knowledge-Based Systems, vol. 86, pp. 237–249, 2015. View at: Publisher Site | Google Scholar
  39. L. A. Zadeh, “A note on Z-numbers,” Information Sciences, vol. 181, no. 14, pp. 2923–2932, 2011. View at: Publisher Site | Google Scholar
  40. L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning-I,” Information Sciences, vol. 8, no. 3, pp. 199–249, 1975. View at: Publisher Site | Google Scholar
  41. D. B. Liu, Uncertainty Theory, Springer Berlin Heidelberg, Heidelberg, Germany, 2007.
  42. X. Zhang, “Multicriteria Pythagorean fuzzy decision analysis: a hierarchical QUALIFLEX approach with the closeness index-based ranking methods,” Information Sciences, vol. 330, pp. 104–124, 2016. View at: Publisher Site | Google Scholar
  43. T.-Y. Chen, “Interval-valued intuitionistic fuzzy QUALIFLEX method with a likelihood-based comparison approach for multiple criteria decision analysis,” Information Sciences, vol. 261, pp. 149–169, 2014. View at: Publisher Site | Google Scholar
  44. J.-J. Peng, J.-Q. Wang, and W.-E. Yang, “A multivalued neutrosophic qualitative flexible approach based on likelihood for multicriteria decision making problems,” International Journal of Systems Science, vol. 48, no. 2, pp. 425–435, 2017. View at: Publisher Site | Google Scholar
  45. J.-Q. Wang, J.-J. Kuang, J. Wang, and H.-Y. Zhang, “An extended outranking approach to rough stochastic multicriteria decision making problems,” Cognitive Computation, vol. 8, no. 6, pp. 1144–1160, 2016. View at: Publisher Site | Google Scholar
  46. X. Xu and Y. Yu, “Incomplete information complement method based on the hesitation of experts in large group emergency decision making,” Information and Control, vol. 48, no. 6, pp. 678–686, 2019. View at: Google Scholar
  47. P. Wang, X. Xu, and S. Huang, “An improved consensus-based model for large group decision making problems considering experts with linguistic weighted information,” Group Decision and Negotiation, vol. 28, no. 3, pp. 619–640, 2019. View at: Publisher Site | Google Scholar

Copyright © 2020 Xue-Feng Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


More related articles

 PDF Download Citation Citation
 Download other formatsMore
 Order printed copiesOrder
Views206
Downloads289
Citations

Related articles