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GroupDecisionMakingArticle.pdf
Journal of Intelligent & Fuzzy Systems 37 (2019) 1513–1527 DOI:10.3233/JIFS-182934 IOS Press
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A large group decision-making method and its application to the evaluation of property perceived service quality
Wen-Jin Zuoa,b, Deng-Feng Lia,∗, Gao-Feng Yua and Li-Ping Zhanga a School of Economics and Management, Fuzhou University, Fuzhou, Fujian, China bZhejiang college, Shanghai university of finance and economics, Jinhua, Zhejiang, China
Abstract. With the development of modern property service industry, the property perceived service quality (PPSQ) evaluation data is characterized by multiple evaluation subjects, complicated data structure and large scale data. Since the traditional decision-making methods are difficult to solve the above similar problems, this paper proposes a large group decision-making (LGDM) method of generalized multi-attribute and multi-scale (MAMS) based on the linear programming technique for multidimensional analysis of preference (LINMAP). In this method, the large-scale heterogeneous data of expert preference and user evaluation is fused. The decision matrix of generalized MAMS is used to process user evaluation information. The positive ideal solution (PIS) and the attribute weights are determined by the LINMAP model. The comprehensive evaluation values are calculated and hereby the alternatives are ranked order. According to the relation between attribute weights and preset values, a mechanism for identifying invalid data is designed. This paper analyzes a set of survey data of PPSQ for the four public construction projects in the same city. The analysis results show the validity and rationality of the proposed method, and develop the property service evaluation theory.
Keywords: Large group decision-making, generalized multi-attribute and multi-scale method, linear programming technique for multidimensional analysis of preference, large-scale heterogeneous data processing, property perceived service quality
1. Introduction
Many traditional decision methods are available for data processing. The Dempster-Shafer evidence theory can be used for data fusion [1]. The rough set theory are usually used to process incomplete infor- mation [2–6]. The operator theory uses some function to transform data [7–15]. However, the above meth- ods cannot be directly applied to the complex large-scale data fusion effectively. The traditional group decision-making theory and method faces
∗Corresponding author. Deng-Feng Li, School of Economics and Management, Fuzhou University, No. 2, Xueyuan Road, Daxue New District, Fuzhou District, Fuzhou, Fujian 350108, China. Tel./Fax: +86 0591 87892973; E-mail: lidengfeng@fzu. edu.cn.
challenges with the expansion of decision-maker group. The large group decision-making (LGDM) method emerges in response to the needs of times [16]. Research on LGDM has been carried for- ward based on the theory and application of group decision-making. Collecting and processing evalua- tion information of decision-making is the basis of LGDM. There are many research results of LGDM based on various types of data processing, such as trapezoidal fuzzy numbers [17], hesitant fuzzy infor- mation [18], intuitionistic fuzzy information [19–21], interval type-2 fuzzy technique for order preference by similarity to ideal solution (TOPSIS) model [22, 23] and interval-valued intuitionistic fuzzy principal component analysis [24]. As an effective method to solve LGDM problems, the consensus reaching
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1514 W.-J. Zuo et al. / A large group decision-making method
process based on clustering has been widely used by scholars [25–29]. LGDM has been used in natu- ral disaster emergencies [30], air pollution treatment [31], energy network dispatch [32], E-commerce [33], and so on.
1.1. Review of the LGDM methods
Based on different research methods, research results of LGDM can be roughly divided into two categories: (1) According to various decision-making environments, there are many classic methods to be applied or improved in the large group decision- making [34–38], such as cluster analysis and ant colony algorithm. Decision-makers or attributes in these research results are divided into several small groups, and theirs weights are usually determined by some traditional methods. The ranking order is based on comprehensive evaluation value. This kind of research results have pioneered the research of LGDM, and these research results are the main body of research on LGDM. However, the number of decision-makers in this kind of LGDM research is usually no more than a few dozen. It is difficult for existing models to directly process large-scale evaluation data. (2) The idea of probability distribu- tion is introduced into the research of LGDM. The evaluation data is processed based on multi-attribute and multi-scale (MAMS) decision matrix. Many comprehensive methods which combine stochastic distribution function with traditional methods such as evidence inference [39] and stochastic domi- nance [40] are adopted. These research results are applied to selection of teacher appointment sys- tem [41] and commodity selection based on online evaluation information [42]. Obviously, this kind of research methods have some advantages in process- ing large-scale data, but they cannot effectively solve the problems of data redundancy and data conflict that usually exist in data processing based on multidimen- sional perspective [43]. In other word, such methods cannot process large-scale heterogeneous data.
In addition, there are some deficiencies in tra- ditional LGDM research. Their research methods are not abundant in types. The value of attribute weight is usually given in advance. The results focus on the ranking order of alternatives rather than get meaningful comprehensive evaluation value. Fur- thermore, although traditional research on group decision-making considers differences in preferences and conflicts of interests among decision-makers, different decision-makers have similar evaluation
perspectives and evaluation methods when they eval- uate on the same decision-making problems [44, 45]. However, there is a widespread difference among dif- ferent subgroups of decision-makers in real group decision-making. Take the property perceived service quality (PPSQ) as an example, experts evaluate the overall preference for the projects from macroscopic perspective, and users use scale values to evaluate different attributes of each project from micro per- spective.
1.2. Limitations of PPSQ
Property management was originated in Britain in the 1860s. It was introduced into mainland China from Hong Kong in the early 1980s. Property man- agement industry in China has developed for a short time, but it has developed rapidly and come into being a huge market scale. According to the latest statistics, national property management area is about 24.67 billion square meters, and most cities have over 90% of new residential property management coverage. The total number of property service enterprises in China has exceeded 118,000 by the end of 2017. Until now, most of large and medium-sized prop- erty service enterprises have been conducting the PPSQ survey. In the practice of PPSQ evaluation, simple weighted method is usually used to calcu- late the comprehensive score of all projects. Many property service enterprises take PPSQ as the basic means or objectives of enterprise management. Exist- ing theoretical studies [46, 47] took city or enterprise as object, used the entropy weight method or econo- metric method to explore the residential PPSQ. In conclusion, research on PPSQ in China is character- ized of insufficient theoretical analysis and widely application in practice.
In 1965, Cardozo made the first study of cus- tomer satisfaction [48]. In the early 1970s, Anderson [49], Olshavsky and Miller [50] explored the differ- ence theory of expectations and its effect on product performance. In 1982, Gronroos [51] put forward the concept of perceived service quality. Since then, scholars have conducted a great deal of research on the evaluation dimension, evaluation method, eval- uation model and its application to service quality. Evaluation dimension division is the premise of establishing evaluation index system. Scholars have proposed a variety of classification methods, among which the five-dimension classification method pro- posed by Zeithaml et al. is the most representative [52]. These results have laid a theoretical foundation
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for the practical research on service quality. As for the evaluation method of PPSQ, most property service enterprises in China evaluate property service accord- ing to service attitude, greening, cleaning, facilities and safety by the method of owner perceived ser- vice quality survey. Most of the research results on service quality evaluation are based on SERVQUAL model [53], and its empirical analysis is conducted by econometric methods. There are also many reports on the application of entropy method [46], analytic hier- archy process [54], fuzzy comprehensive evaluation method [55] and quality function deployment method [56] and so on. As for the research on macro quality evaluation methods, the evaluation model of national customer satisfaction index mainly includes SCSB, ACSI, ECSI and CCSI [57].
1.3. The motivation of the developed method
Based on the shortcomings of LGDM method and PPSQ theory in traditional research, the research motivation of this paper is as follows:
(1) Although the MAMS decision matrix has been used the LGDM problem [39, 40], the scale of each attribute are the same. What if the scale of each attribute are different? This paper extends the MAMS matrix into the general form and process the above data. Then we develop a decision method that is suitable for the gen- eralized MAMS matrix information.
(2) There are many research results which the var- ious types of data are processed respectively based on LGDM method [17–24]. However, the existing methods cannot process the basic data with multiple evaluation subjects, com- plicated data structure and large scale data. We need to develop a new method to process large- scale heterogeneous data from different types of decision-makers.
(3) Traditional decision-making methods usually focus on the ranking order of alternatives, instead of analysis of the raw data and its evaluation result. The raw data and its results analysis are of practical significance in man- agement. Therefore, we need to design an analysis mechanism which link the evaluation results with the raw data.
(4) Last, the traditional PPSQ evaluation research [46, 47] is insufficient, and the existing meth- ods of service quality are mainly econometric. The basic data in modern PPSQ evaluation
is complicated. The existing methods cannot solve the complex problem. Therefore, it is necessary to develop a new PPSQ evaluation method that meets the higher requirements.
As mentioned above, the existing LGDM research cannot realize the fusion of heterogeneous data, nor is it capable of processing large-scale raw evalua- tion data. This paper propose a LGDM method of generalized MAMS based on LINMAP, and it is a new attempt to process complex data using deci- sion model. The case study takes public construction property service projects as the research object. We designed an evaluation index system which learn from the practical experience of Vanke, Greentown and other famous property service enterprises. We collect both expert preferences and user evaluation information at the same time. The proposed method in this paper is used to calculate the weight of each index and the comprehensive score of property service projects to be evaluated. The case study verifies the proposed method and enriches the theory of PPSQ.
The content of this paper is arranged as follows. The next section uses the thought of probability dis- tribution to build decision matrix which based on describing the decision problem. In section 3, the relation of consistency and non-consistency is deter- mined by using the above decision matrix, and the LGDM method of generalized MAMS is constructed by using the LINMAP model. In section 4, four pub- lic construction property service projects in the same city are taken as the research objects, and the pro- posed method in this paper is used for the evaluation of PPSQ. In section 5, the proposed method is com- pared with the traditional method, and the advantages of new method are analyzed. Section 6 draws a brief conclusion and outlook on the research prospect.
2. Description of the generalized MAMS problem
As we know, each attribute has the same scale in the classic MAMS method. However, there are many situations in which different attributes have different scales in practice. We call the generalized MAMS decision method. In the traditional LGDM, there is an increasing difficulty of processing large group decision information with the increase of decision members. Using the generalized MAMS decision martix can enhance the efficiency of information processing. Different from the traditional decision
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methods, the generalized MAMS decision method considers the influence of both attributes and scales on the ranking order of alternatives. There are some notations used to denote the sets and variables in this paper as follows:
• A = {A1, A2, . . . , Ap}: the set of p alterna- tives, where Ak denotes the kth alternative, k = 1, 2, . . . , p.
• C = {C1, C2, . . . , Cm}: the set of m attributes, where Ci denotes the ith attribute, i = 1, 2, . . . , m.
• ω = (ω1, ω2, ..., ωm): the weight vector of m attributes, where ωi denotes the weight of the ith attribute Ci,
∑m i=1 ωi = 1, ωi ≥ 0.
• S = {S1, S2, . . . , Sm}: the scale set with respect to attribute set C, where Si denotes the ith scale set. Specially, not all attributes have the same number of scales.
• Si = {si1, si2, ..., sini }: the scale set with respect to attribute Ci, where sij denotes the jth scale of scale set Si, j = 1, 2, . . . , ni, niis a natural number. There is usually a positive correlation between the scale value and satisfaction degree. The evaluation scale and its assignment are determined by referring to the existing research results [46, 47, 52, 53, 55] before the evaluation. Equidistant scale is used in this paper.
• U = (uijk): the generalized MAMS decision matrix, where uijk denotes the standardization of the number of decision-makers that correspond to attribute Ci, scale sij and alternative Ak. The generalized MAMS decision matrix as shown in Table 1.
• Nk: the number of general decision-makers, where Nijk denotes the number of people who use scale sij of attribute Ci evaluate Ak. In order to ensure the comparability of evaluation infor- mation, the decision-makers of all alternatives are the same. Therefore, there exists N1 = N2 = · · · = Nm in this paper.
The main calculation formula is as follows
Nk = m∑
i=1
ni∑ j=1
Nijk (1)
uijk = Nijk/Nk (2) In addition to general decision-makers, there are
also special decision-makers. Let � be preference set of special decision-makers, � = {(k, l) |Ak�Al } rep- resents the preference set where alternative Ak is not inferior to alternative Al in the opinion of all special decision-makers, where k, l = 1, 2, ..., p.
The basic evaluation data comes from users of general decision-makers and experts of special decision-makers. The former evaluates each alter- native based on itemized attributes, while the latter compares alternatives based on overall preferences. The problem to be solved in this paper is how to pro- cess and fuse large-scale heterogeneous evaluation information, and realize the ranking order of alterna- tives.
3. Method for LGDM of generalized MAMS based on LINMAP
The LINMAP method was first proposed by Shocker and Srinivasan in 1973 [58]. Since then, it has been widely used in decision-making research of different types of information [59–64]. The classical LINMAP method is a pairwise comparison between alternatives given by decision-makers and generate the best compromise as the solution that has the shortest distance from positive ideal solution (PIS) [58, 61]. Determining consistency and inconsistency based PIS is the core of LINMAP method. After the LGDM model of generalized MAMS based on LIN- MAP is solved, we also design the mechanism for raw data analysis by the results of model.
3.1. The PIS matrix and its analysis
In traditional decision-making methods, the PIS are usually a row vector. As the generalized MAMS decision information belongs to three-dimensional structure. Therefore, its PIS are expressed as
PIS(u∗ij ) = (u∗iji )m×n (3) Table 1
The generalized MAMS decision matrix of the user evaluation
C C1 C2 · · · Cm S s11 s12 · · · s1n1 s21 s22 · · · s2n2 · · · sm1 sm2 · · · smnm A1 u111 u121 · · · u1n1 1 u211 u221 · · · u2n2 1 · · · um11 um21 · · · umnm 1 A2 u112 u122 · · · u1n1 2 u212 u222 · · · u2n2 2 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · Ap u11p u12p · · · u1n1 p u21p u22p · · · u2n2 p · · · um1p um2p · · · umnmp
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where u∗iji is a PIS with respect to the scale set sij of attribute Ci. For example, u
∗ 11 is the PIS of vector
(u111, u112..., u11p). If there exists n1 = n2 = · · · = nm, Equation (3) is a matrix.
When the scale value sij of attribute Ci is mini- mum, the minimum of the evaluation value of all the alternatives corresponding to the scale value is the PIS. On the contrary, the maximum of the evaluation value of all the alternatives corresponding to the scale value is the PIS. In other cases, the PIS is between the minimum and the maximum of the evaluation value of all the alternatives corresponding to scale sij and attribute Ci. Therefore, the range of PIS is as follows
p
min k=1
{uijk} ≤ u∗ij ≤ p
max k=1
{uijk} (4)
3.2. Consistency and inconsistency measurements
Based on the above analysis, the basic idea of consistency and inconsistency measurements is as follows: First, the evaluation value of each alterna- tive is determined. Second, the Euclidean distance squared value between each alternative and the PIS is calculated. Then, the consistency and inconsistency are constructed based on the above variables.
According to Table 1, the evaluation value of Ak from the general decision-makers denotes as follows
P (Ak) = (uijik)m×n×p (5)
Analogously, the evaluation value of Al from the general decision-makers denotes as follows
P (Al) = (uijil)m×n×p (6)
If there exists n1 = n2 = · · · = nm, Equations (5) and (6) are matrix.
Let Dk denotes the Euclidean distance squared value between alternative Ak and the PIS. Since the scale values represent the evaluation values of decision-makers, we consider the influence of the scale value when calculating the square value of weighted Euclidean distance. Combine to Equations (3) and (5), the square of the weighted Euclidean dis- tance Dk between the alternative Ak and the PIS is denoted as
Dk = m∑
i=1
ni∑ j=1
[ωi(sij uijk − sij u∗ij )2] (7)
Analogously, the square of the weighted Euclidean distance between the alternative Al and the PIS is denoted as
Dl = m∑
i=1
ni∑ j=1
[ωi(sij uijl − sij u∗ij )2] (8)
If Dl ≥ Dk, it indicates that the alternative Ak is closer to the PIS. At this time, the alternative Ak is not inferior to the alternative Al. Therefore, the rank- ing order between Ak and Al is determined based on (ωi, sij, u
∗ ij ) by the preferences of decision-makers.
The next discussion is how to express consistency and inconsistency by the preferences of decision- makers. The relation between Dk and Dl can be used to determine the inconsistency and consistency between the alternative Ak and the alternative Al. An index (Dl − Dk)− is defined to measure inconsis- tency of Ak and Al. The inconsistency (Dl − Dk)− is denoted as follows
(Dl − Dk)− = {
Dk − Dl(Dl < Dk) 0(Dl ≥ Dk) (9)
The above equation can be further simplified as
(Dl − Dk)− = max(0, Dk − Dl) (10) Considering the preferences of all experts, the total
inconsistency can be written as
B = ∑
(k,l)∈� (Dl − Dk)− =
∑ (k,l)∈�
max(0, Dk − Dl)
(11) Similarly, the consistency (Dl − Dk)+ is denoted
as
(Dl − Dk)+ = {
Dl − Dk(Dl ≥ Dk) 0(Dl < Dk)
(12)
The above equation can be further simplified as
(Dl − Dk)+ = max(0, Dl − Dk) (13) Considering the preferences of all experts, the total
consistency can be written as
G = ∑
(k,l)∈� (Dl − Dk)+ =
∑ (k,l)∈�
max(0, Dl − Dk)
(14)
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According to Equations (10) and (13), the differ- ence between consistency and inconsistency is
G − B = ∑ (k,l)∈�
(Dl − Dk)+ − ∑
(k,l)∈� (Dl − Dk)− =
∑ (k,l)∈�
[(Dl − Dk)+ − (Dl − Dk)−]
= ∑ (k,l)∈�
[Dl − Dk]
(15)
3.3. The LINMAP model of LGDM
In the classical LINMAP method, the attribute weight and the PIS are unknown variables in advance. The decision-makers make pair-wise comparison between on different alternatives, and it produce a set of compromise solutions which are closest to the PIS. Refer to existing research results [58, 59], the basic model of the LINMAP is as follows
min{B}⎧⎪⎪⎪⎨ ⎪⎪⎪⎩
G − B ≥ h m∑
i=1 ωi = 1
ωi > ε, i = 1, 2, ..., m
(16)
where G and B denote consistency and inconsistency respectively, which are determined on the basis of the distance between the evaluation value of each alter- native and the corresponding PIS. In addition, h > 0 and ε > 0 are given a priori by the decision-maker. h is a threshold value which ensures that consistency is greater than inconsistency. ε is sufficiently small pos- itive number which ensures that all attribute weights are not zero.
For each pair of (k, l) ∈ �, letλkl = min(0, Dl − Dk), then
λkl ≥ Dl − Dk (17)
where λkl ≥ 0. Combining Equations (3), (4), (7), (8), (15), (16)
and (17), the LINMAP model of LGDM based on the generalized MAMS decision matrix can be written as follows
min
⎧⎨ ⎩
∑ (k,l)∈�
λkl
⎫⎬ ⎭
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
∑ (k,l)∈�
m∑ i=1
ni∑ j=1
ωi[s 2 ij
(u2ijl − u2ijk ) + 2u∗ij .sij (uijk − uijl)] ≥ h m∑
i=1
ni∑ j=1
ωi[s 2 ij
(u2ijk − u2ijl) + 2u∗ij .sij (uijl − uijk )]+λkl ≥ 0
u∗ ij
≥ l
min k=1
{uijk}
u∗ ij
≤ lmax k=1
{uijk} λkl > 0((k, l) ∈ �) m∑
i=1 ωi = 1
ωi ≥ ε i = 1, 2, ..., m, j = 1, 2, ..., ni, k, l = 1, 2, ..., p
(18)
3.4. Analysis of evaluation data
By solving Equation (18), the PIS and weight value can be determined. Due to the lack of relevant empirical research, the determination of threshold h is a difficult problem. It usually is determined by decision-makers based on theirs experience in the existing researches. In this paper, we determine the value h by the sensitivity analysis results, experi- ence of decision makers and the relevant literature researches [58–65]. As ε is sufficiently small posi- tive number, we can judge whether the raw evaluation data is valid or not according to the relation between attribute value and threshold value. The criteria for determining whether invalid data exists are as follows
ωi ≤ ε (19)
When Equation (19) is true, attribute Ci and its corresponding raw evaluate data are invalid. Con- versely, Ci and its corresponding raw evaluation data are valid. There exists absolute or relative invalid evaluation data. The former refers to the situation in which the weight and its raw data are invalid when h takes any value. The latter refers to the situation in which the weight and its raw data are change between invalid and valid when h takes different values.
In addition, we also can analyze the distance between the PIS and evaluation value of each alterna- tive. The distance of alternative Ak is determined by P (Ak) and PIS. The smaller value of the distance for an alternative indicates that the alternative is closer to the PIS. On the contrary, the bigger value of the dis- tance for an alternative indicates that the alternative is further away from the PIS.
W.-J. Zuo et al. / A large group decision-making method 1519
There are maybe some valuable management enlightenment using the above two methods respec- tively combined with the analysis of the actual situation.
3.5. Calculate and rank comprehensive score of alternatives
If the scale value is corresponding to the evalua- tion score, then the comprehensive evaluation value of each alternative is the comprehensive score. At this point, the comprehensive score has comparability and economic significance.
After the weight value is determined, the invalid attribute and its evaluation data are deleted according to Equation (19). Standardizing the weights of valid attributes, the comprehensive score of each alterna- tive can be calculated. The calculation formula is as follows
V (Ak) = m′∑ i=1
n′ i∑
j=1 ω
′ is
′ iju
′ ijk (20)
Where the symbols in Equation (20) represent the corresponding variables after invalid data is deleted. See Section 2 for the meanings of each variable.
The range of V (Ak) can be expressed as follows
m′∑ i=1
(ω′i. n′
i
min j=1
s ′ ij ) ≤ V (Ak) ≤
m′∑ i=1
(ω′i. n′
i max j=1
s ′ ij ) (21)
The proof of Equation (21) is simple and has been ignored in this paper. The economic significance of the comprehensive evaluation value of each alterna- tive as follows:
– The upper limit is the sum of all product of the attribute weight and the maximum scale value corresponding to the attribute;
– The lower limit is the sum of all product of the attribute weight and the minimum scale value corresponding to the attribute.
3.6. Decision-making process
Step 1. Determine general decision-makers (large group users) and special decision-makers (some experts).
Step 2. Collect the evaluation information of gen- eral decision-makers and standardize the evaluation information according to Equations (1) and (2), and form the generalized MAMS decision matrix U = (uijk)m×ni×p.
Step 3. Collect the preference information of special decision-makers for different alternatives and deter- mine the overall preference set �.
Step 4. Calculate the PIS and its value range respec- tively by Equations (3) and (4).
Step 5. Construct the LINMAP model of LGDM based on generalized MAMS decision matrix by Equation (18).
Step 6. Solve Equation (18) by simplex method and determine all PIS and the weight of each attribute.
Step 7. According to Equation (19), judge whether the decision matrix has invalid data or not.
Step 8. Calculate the comprehensive score of each alternative by Equation (20), and determine the rank- ing order of all alternatives.
4. A real example analysis: PPSQ evaluation
The PPSQ is a comprehensive index to measure the level of property service [46], which is affected by social, economic and cultural factors. Considering the comparability among the projects to be evalu- ated, we choose four public construction projects with similar external environment, close geograph- ical location and the same evaluation group. The data in this example come from a survey on the PPSQ eval- uation of four public construction projects in the same city.
Table 2 Distribution on the number of participants in the PPSQ evaluation
C C1 C2 C3 C4 C5 S 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
A1 3 38 49 12 2 5 35 45 18 1 5 33 42 22 2 7 38 46 12 1 2 31 58 11 2 A2 12 51 32 7 2 5 50 38 8 3 7 49 38 9 1 10 48 36 9 1 4 48 43 9 0 A3 20 40 37 6 1 15 50 31 7 1 15 38 42 7 2 13 49 35 6 1 12 45 33 12 2 A4 7 25 59 12 1 6 37 39 20 2 7 19 56 20 2 6 28 46 22 2 9 22 49 19 5
1520 W.-J. Zuo et al. / A large group decision-making method
4.1. Introduction to the PPSQ evaluation
Decision-makers are composed of property man- agement experts and ordinary citizens. The four adjacent public construction projects are museum (A1), ibrary (A2), science & technology museum (A3) and grand theater (A4) respectively. The expert opin- ion method is adopted in the interview of property management experts. Three property management experts from university, industry association and government are invited. We ask experts to make the overall preference between public construction projects. By combining the evaluation information of the three experts, the results are as follows
� = {(1, 2), (2, 3), (4, 1), (4, 3)} (22) Questionnaire survey is adopted to investigate
ordinary citizens. The main content of question- naire has 5 survey items, including service attitude (C1), greening (C2), cleaning (C3), facilities (C4) and safety (C5). The evaluation value is assessed using the five-degree mark method. The evaluation results are ‘very poor’, ‘poor’, ‘indifferent’, ‘good’ and ‘very good’ respectively, and assign the scores 1, 2, 3, 4 and 5 in sequence. When the questionnaire is carried out, the ordinary citizens are asked to evaluate the PPSQ of four public construction projects.
This questionnaire survey adopts two forms: tele- phone interview and on-site intercept interview. The telephone interviewees are from the library’s reade database, and the intercept interview is carried out around each project. In order to ensure the rationality of the evaluation information, it requires that the inter- viewees are familiar with the four projects. A total of 71 questionnaires are given out and 52 telephone interviews are conducted. Finally, 104 valid question- naires are obtained, and statistical results as shown in Table 2. Using Equations (1) and (2), the distribution on number of participants involved in the evaluation under different attributes and scales of each prop- erty service project is transformed into probability distribution, as shown in Table 3.
4.2. Calculation process of PPSQ evaluation
Use the generalized MAMS decision matrix to pro- cess the user evaluation information. According to Table 3, the PIS is as follows
PIS = (u∗iji )5×5 (23)
T ab
le 3
P ro
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di st
ri bu
ti on
on th
e nu
m be
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pa rt
ic ip
an ts
in th
e P
P S
Q ev
al ua
ti on
C C
1 C
2 C
3 C
4 C
5
S 1
2 3
4 5
1 2
3 4
5 1
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4 5
1 2
3 4
5 1
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A 1
0. 02
9 0.
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0. 47
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0. 33
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46 2
0. 34
6 0.
08 7
0. 01
0 0.
03 8
0. 46
2 0.
41 3
0. 08
7 0.
00 0
A 3
0. 19
2 0.
38 5
0. 35
6 0.
05 8
0. 01
0 0.
14 4
0. 48
1 0.
29 8
0. 06
7 0.
01 0
0. 14
4 0.
36 5
0. 40
4 0.
06 7
0. 01
9 0.
12 5
0. 47
1 0.
33 7
0. 05
8 0.
01 0
0. 11
5 0.
43 3
0. 31
7 0.
11 5
0. 01
9 A
4 0.
06 7
0. 24
0 0.
56 7
0. 11
5 0.
01 0
0. 05
8 0.
35 6
0. 37
5 0.
19 2
0. 01
9 0.
06 7
0. 18
3 0.
53 8
0. 19
2 0.
01 9
0. 05
8 0.
26 9
0. 44
2 0.
21 2
0. 01
9 0.
08 7
0. 21
2 0.
47 1
0. 18
3 0.
04 8
W.-J. Zuo et al. / A large group decision-making method 1521
The scale value of each attribute in Equation (23) is the same, that is n1 = n2 = n3 = n4 = n5. Therefore, Equation (23) is a matrix, and it is a special case.
Using Equation (4) and Table 3, the value range of the PIS is determined as follows
u ∗ ij ≥ min{uij1, uij2, uij3, uij4} (24)
u ∗ ij ≤ max{uij1, uij2, uij3, uij4} (25)
min{λ12+λ23+λ41+λ43}⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
−3.048ω1 − 0.500ω∗1 u∗11 − 2.308ω∗1 u∗12+7.615ω∗1 u∗13+3.692ω∗1 u∗14 − 0.000ω∗1 u∗15 −1.113ω2 − 0.346ω∗2 u∗21 − 2.000ω∗2 u∗22+2.769ω∗2 u∗23+8.000ω∗2 u∗24 − 0.962ω∗2 u∗25 −2.488ω3 − 0.308ω∗3 u∗31 − 2.923ω∗3 u∗32+4.846ω∗3 u∗33+8.000ω∗3 u∗34 − 0.000ω∗3 u∗35 −1.602ω4 − 0.269ω∗4 u∗41 − 3.231ω∗4 u∗42+3.808ω∗4 u∗43+9.846ω∗4 u∗44+0.962ω∗4 u∗45 −1.771ω5 − 0.115ω∗5 u∗51 − 3.538ω∗5 u∗52 + 5.538ω∗5 u∗53 + 4.308ω∗5 u∗54 + 2.885ω∗5 u∗55 ≥ 1.0 λ12+0.846ω1+0.173ω∗1 u∗11+1.000ω∗1 u∗12 − 2.942ω∗1 u∗13 − 1.538ω∗1 u∗14 + 0.000ω∗1 u∗15 +0.378ω2+0.000ω∗2 u∗21+1.154ω∗2 u∗22 − 1.212ω∗2 u∗23 − 3.077ω∗2 u∗24+0.962ω∗2 u∗25 +0.382ω3+0.038ω∗3 u∗31+1.231ω∗3 u∗32 − 0.692ω∗3 u∗33 − 4.000ω∗3 u∗34 − 0.481ω∗3 u∗35 +0.453ω4+0.058ω∗4 u∗41+0.769ω∗4 u∗42 − 1.731ω∗4 u∗43 − 0.923ω∗4 u∗44 + 0.000ω∗4 u∗45 +0.831ω5+0.038ω∗5 u∗51+1.308ω∗5 u∗52 − 2.596ω∗5 u∗53 − 0.615ω∗5 u∗54 − 0.962ω∗5 u∗55 ≥ 0 λ23+0.086ω1+0.154ω∗1 u∗11 − 0.846ω∗1 u∗12+0.865ω∗1 u∗13 − 0.308ω∗1 u∗14 − 0.481ω∗1 u∗15 +0.424ω2+0.192ω∗2 u∗21 − 0.000ω∗2 u∗22 − 1.212ω∗2 u∗23 − 0.308ω∗2 u∗24 − 0.962ω∗2 u∗25 +0.112ω3+0.154ω∗3 u∗31 − 0.846ω∗3 u∗32+0.692ω∗3 u∗33 − 0.615ω∗3 u∗34+0.481ω∗3 u∗35 +0.083ω4+0.058ω∗4 u∗41+0.077ω∗4 u∗42 − 0.173ω∗4 u∗43 − 0.923ω∗4 u∗44+0.000ω∗4 u∗45 +0.621ω5+0.154ω∗5 u∗51 − 0.231ω∗5 u∗52 − 1.731ω∗5 u∗53+0.923ω∗5 u∗54+0.962ω∗5 u∗55 ≥ 0 λ41+0.593ω1 − 0.077ω∗1 u∗11+1.000ω∗1 u∗12 − 1.731ω∗1 u∗13 − 0.000ω∗1 u∗14+0.481ω∗1 u∗15 −0.246ω2 − 0.019ω∗2 u∗21 − 0.154ω∗2 u∗22+1.038ω∗2 u∗23 − 0.615ω∗2 u∗24 − 0.481ω∗2 u∗25 +0.750ω3 − 0.038ω∗3 u∗31+1.077ω∗3 u∗32 − 2.423ω∗3 u∗33+0.615ω∗3 u∗34+0.000ω∗3 u∗35 +0.265ω4+0.019ω∗4 u∗41+0.769ω∗4 u∗42 − 0.000ω∗4 u∗43 − 3.077ω∗4 u∗44 − 0.481ω∗4 u∗45 (26) −0.567ω5 − 0.135ω∗5 u∗51+0.692ω∗5 u∗52+1.558ω∗5 u∗53 − 2.462ω∗5 u∗54 − 1.442ω∗5 u∗55 ≥ 0 λ43+1.524ω1+0.250ω∗1 u∗11+1.154ω∗1 u∗12 − 3.808ω∗1 u∗13 − 1.846ω∗1 u∗14+0.000ω∗1 u∗15 +0.556ω2+0.173ω∗2 u∗21+1.000ω∗2 u∗22 − 1.385ω∗2 u∗23 − 4.000ω∗2 u∗24 − 0.481ω∗2 u∗25 +1.244ω3+0.154ω∗3 u∗31+1.462ω∗3 u∗32 − 2.423ω∗3 u∗33 − 4.000ω∗3 u∗34+0.000ω∗3 u∗35 +0.801ω4+0.135ω∗4 u∗41+1.615ω∗4 u∗42 − 1.904ω∗4 u∗43 − 4.923ω∗4 u∗44 − 0.481ω∗4 u∗45 +0.886ω5+0.058ω∗5 u∗51+1.769ω∗5 u∗52 − 2.769ω∗5 u∗53 − 2.154ω∗5 u∗54 − 1.442ω∗5 u∗55 ≥ 0 u∗11 ≤ 0.192, u∗11 ≥ 0.029, u∗12 ≤ 0.490, u∗12 ≥ 0.240, u∗13 ≤ 0.567, u∗13 ≥ 0.308, u∗14 ≤ 0.115, u∗14 ≥ 0.058, u∗15 ≤ 0.019, u∗15 ≥ 0.010, u∗21 ≤ 0.144, u∗21 ≥ 0.048, u∗22 ≤ 0.481, u∗22 ≥ 0.337, u∗23 ≤ 0.433, u∗23 ≥ 0.298, u∗24 ≤ 0.192, u∗24 ≥ 0.067, u∗25 ≤ 0.029, u∗25 ≥ 0.010, u∗31 ≤ 0.144, u∗31 ≥ 0.048, u∗32 ≤ 0.471, u∗32 ≥ 0.183, u∗33 ≤ 0.538, u∗33 ≥ 0.365, u∗34 ≤ 0.212, u∗34 ≥ 0.067, u∗35 ≤ 0.019, u∗35 ≥ 0.010, u∗41 ≤ 0.125, u∗41 ≥ 0.058, u∗42 ≤ 0.471, u∗42 ≥ 0.269, u∗43 ≤ 0.442, u∗43 ≥ 0.337, u∗44 ≤ 0.212, u∗44 ≥ 0.058, u∗45 ≤ 0.019, u∗45 ≥ 0.010, u∗51 ≤ 0.115, u∗51 ≥ 0.019, u∗52 ≤ 0.462, u∗52 ≥ 0.212, u∗53 ≤ 0.558, u∗53 ≥ 0.317, u∗54 ≤ 0.183, u∗54 ≥ 0.087, u∗55 ≤ 0.048, u∗55 ≥ 0.000 ω1> 0.001, ω2> 0.001, ω3> 0.001, ω4> 0.01, ω5> 0.001
ω1+ω2+ω3+ω4+ω5= 1 λ12>= 0, λ23>= 0, λ41>= 0, λ43>= 0
where i, j = 1, 2, 3, 4, 5. Because ε is sufficiently small positive number
which ensures that attribute weights are not zero, and the data in this example retains three decimal places, this paper determines ε = 0.001. According to the existing research literature [54–59], the expert experience and sensitivity analysis results, this paper determines h = 1.0.
Combining Equations (18), (22)–(25) and Table 3, the LINMAP model of PPSQ evaluation is deter- mined as follows
1522 W.-J. Zuo et al. / A large group decision-making method
LINGO software is used to solve Equation (26), the PIS is obtained as shown in Table 4. The optimal solution of attribute weight is as follows
ω = (ω1, ω2, ω3, ω4, ω5) = (0.239,0.001,0.376,0.010, 0.374) (27)
According to Equation (19), the attribute C2 and its evaluation information are invalid data. After deleting the invalid data, the attribute weights are standardized as follows
ω ′ = (ω′1, ω′3, ω′4, ω′5) =(0.239,0.376,0.010, 0.374)
(28) Using Table 3, Equations (20) and (28), the
comprehensive evaluation value of all projects are calculated as follows
V (A1) = 2.798 (29)
V (A2) = 2.490 (30)
V (A3) = 2.431 (31)
V (A4) = 2.869 (32) Therefore, the ranking order of the PPSQ for four
public construction projects is as follows
A4 � A1 � A2 � A3 (33)
4.3. Sensitivity analysis and identifying invalid data
According to the principle of LINMAP, there is h > 0. When h ∈ [1.50, +∞], Equation (26) has no feasible solution. To sum up, there is h ∈ (0, 1.50). In order to analyze the impact of the threshold value on the result, h takes different value in (0, 1.50) based on the gradient 0.1. We repeat to calculate Equations (26) - (33), and obtain the calculate results of attribute weight, PIS and comprehensive score. These prop- erty service projects to be evaluated are ranked order by the above comprehensive score. The calculated
Table 4 Calculation results of PIS
Symbol Value Symbol Value Symbol Value Symbol Value Symbol Value
u∗11 0.029 u ∗ 21 0.048 u
∗ 31 0.048 u
∗ 41 0.125 u
∗ 51 0.019
u∗12 0.240 u ∗ 22 0.337 u
∗ 32 0.471 u
∗ 42 0.269 u
∗ 52 0.212
u∗13 0.567 u ∗ 23 0.298 u
∗ 33 0.538 u
∗ 43 0.442 u
∗ 53 0.558
u∗14 0.115 u ∗ 24 0.192 u
∗ 34 0.212 u
∗ 44 0.212 u
∗ 54 0.183
u∗15 0.019 u ∗ 25 0.029 u
∗ 35 0.010 u
∗ 45 0.019 u
∗ 55 0.048
results are summarized in Tables 5 and 6. Accord- ing to Table 5 and Equation (19), the analysis is as follows:
– When h = 0.1 and h = 0.2, the attribute C1 and its corresponding evaluation data are invalid;
– When h takes any value, the attribute C2 and its corresponding evaluation data are invalid;
– When h takes any value, the weight ω4 = 0.010, which means that the attribute C4 and its corre- sponding evaluation data have little effect on the comprehensive score.
Specially, some invalid data is relative. The attributes and theirs evaluation data corresponding to ω1 and ω3 are invalid at some value of h. The other invalid data is absolute, the attribute and its evaluation data corresponding to w2 are invalid at any value of h. Therefore, the so-called invalid attributes and eval- uation data are associated with specific model and its threshold value. When the model and its threshold value change, there may be a transformation between invalid data and valid data.
How to determine the threshold value h? We consider three factors: sensitivity analysis, existing researches and experience of decision-makers. As we know from Table 5, the ranking order of alter- natives are the same in any value of h. There is h h = 1.0 in the existing research results of LINMAP [54–59]. We consulted several experts on the results of sensitivity analysis, and most of them believe that h = 1.0 should be determined. Therefore, this paper determine h = 1.0.
4.4. PPSQ evaluation results analysis
According to Table 6, there are the following gen- eral rules about the calculation results of PIS:
– When the scale value sij < 3, the PIS is the mini- mum evaluation value corresponding to the scale value and its attribute;
– When the scale value sij ≥ 3, the PIS is the maxi- mum evaluation value corresponding to the scale value and its attribute.
W.-J. Zuo et al. / A large group decision-making method 1523
Table 5 Calculation results under different threshold value h
Threshold Attribute weights Comprehensive score Ranking orders value h ω1 ω2 ω3 ω4 ω5 V (A1) V (A2) V (A3) V (A4)
0.1 0.001 0.001 0.827 0.010 0.161 2.830 2.507 2.457 2.910 A4 � A1 � A2 � A3 0.2 0.001 0.001 0.823 0.010 0.165 2.830 2.507 2.457 2.910 A4 � A1 � A2 � A3 0.3 0.341 0.001 0.014 0.010 0.634 2.780 2.491 2.426 2.848 A4 � A1 � A2 � A3 0.4 0.001 0.001 0.816 0.010 0.172 2.829 2.508 2.457 2.909 A4 � A1 � A2 � A3 0.5 0.030 0.001 0.775 0.010 0.184 2.826 2.505 2.454 2.905 A4 � A1 � A2 � A3 0.6 0.077 0.001 0.711 0.010 0.201 2.821 2.500 2.447 2.897 A4 � A1 � A2 � A3 0.7 0.124 0.001 0.647 0.010 0.218 2.815 2.496 2.441 2.890 A4 � A1 � A2 � A3 0.8 0.171 0.001 0.582 0.010 0.236 2.810 2.491 2.435 2.882 A4 � A1 � A2 � A3 0.9 0.209 0.001 0.480 0.010 0.300 2.804 2.490 2.432 2.875 A4 � A1 � A2 � A3 1.0 0.239 0.001 0.376 0.010 0.374 2.798 2.490 2.431 2.869 A4 � A1 � A2 � A3 1.1 0.268 0.001 0.273 0.010 0.448 2.793 2.490 2.429 2.863 A4 � A1 � A2 � A3 1.2 0.297 0.001 0.170 0.010 0.522 2.788 2.490 2.428 2.857 A4 � A1 � A2 � A3 1.3 0.326 0.001 0.066 0.010 0.597 2.783 2.491 2.427 2.851 A4 � A1 � A2 � A3 1.4 0.247 0.001 0.001 0.010 0.741 2.787 2.507 2.444 2.861 A4 � A1 � A2 � A3
Table 6 Calculation results of PIS under different threshold value h
Symbol Extreme value Threshold values h of PIS min max 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4
u∗11 0.029 0.192 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 u∗12 0.240 0.490 0.240 0.240 0.240 0.240 0.240 0.240 0.240 0.240 0.240 0.240 0.240 0.240 0.240 0.240 u∗13 0.308 0.567 0.567 0.567 0.567 0.567 0.567 0.567 0.567 0.567 0.567 0.567 0.567 0.567 0.567 0.567 u∗14 0.058 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 u∗15 0.010 0.019 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.019 0.019 0.019 0.019 0.019 0.019 u∗21 0.048 0.144 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 u∗22 0.337 0.481 0.481 0.481 0.408 0.481 0.364 0.337 0.367 0.337 0.337 0.337 0.337 0.337 0.337 0.337 u∗23 0.298 0.433 0.298 0.298 0.298 0.298 0.298 0.298 0.298 0.298 0.298 0.298 0.298 0.298 0.298 0.433 u∗24 0.067 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 u∗25 0.010 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 u∗31 0.048 0.144 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 u∗32 0.183 0.471 0.471 0.471 0.471 0.471 0.471 0.471 0.471 0.471 0.471 0.471 0.471 0.471 0.471 0.183 u∗33 0.365 0.538 0.538 0.538 0.538 0.538 0.538 0.538 0.538 0.538 0.538 0.538 0.538 0.538 0.538 0.538 u∗34 0.067 0.212 0.147 0.166 0.186 0.205 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 u∗35 0.010 0.019 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 u∗41 0.058 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 u∗42 0.269 0.471 0.269 0.269 0.269 0.269 0.269 0.269 0.269 0.269 0.269 0.269 0.269 0.269 0.269 0.269 u∗43 0.337 0.442 0.442 0.442 0.442 0.442 0.442 0.442 0.442 0.442 0.442 0.442 0.442 0.442 0.442 0.442 u∗44 0.058 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 u∗45 0.010 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019 u∗51 0.019 0.115 0.049 0.033 0.019 0.042 0.115 0.115 0.115 0.115 0.019 0.019 0.019 0.019 0.019 0.019 u∗52 0.212 0.462 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 u∗53 0.317 0.558 0.478 0.441 0.406 0.376 0.413 0.469 0.516 0.558 0.558 0.558 0.558 0.558 0.558 0.558 u∗54 0.087 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 u∗55 0.000 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048
Why are there a few cases in Table 5 that do not conform to the above rules? Noise data, computa- tional accuracy and questionnaire survey quality may all lead to the deviation of calculation results. The reasons for the above general rules are as follows:
– When the scale value sij < 3, the user has a neg- ative view of satisfaction. It shows that the less the number of user evaluate, the better the overall PPSQ;
– When the scale value sij ≥ 3, the user has a pos- itive view of satisfaction. It shows that the more the number of user evaluate, the better the overall PPSQ.
The external environment of these public construc- tion projects are similar, and they are comparable. Therefore, the following analysis focuses on the char- acteristics of each project. In order to ensure the rationality of the analysis results, we conducted field research on these four projects and consulted the
1524 W.-J. Zuo et al. / A large group decision-making method
property management experts on the above results after data analysis. Based on the calculation results of the above data, we analyze the PPSQ of the public construction project in this paper as follows:
(1) According to the attribute weight value, the effect of these factors for the PPS com- prehensive score range from large to small in sequence are as follows: cleaning, safety, service attitude, greening and facilities. The reasons for the above results can be explained as follows: On the one hand, cleaning and safety are difficulties of property service in the crowded public construction projects, and these two factors are also the most public concerned. On the other hand, as the four pub- lic construction projects are similar in space, construction time and standards, greening and facilities conditions are similar. Therefore, there is little difference in public perception of these two property services.
(2) The PPSQ comprehensive scores of four property service projects from high to low in sequence are as follows: grand theater, museum, library, and science & technology museum. It can be explained by the behavior of people. When people go to grand theater and museums, they always pay attention to decency. It maybe the power of history and art. At this time, the pressure of property ser- vices is relatively small, and PPSQ is relatively high. The library and science & technology museum are high concentration of people, and teenagers and children make up a large pro- portion of them. It brings great pressure to property service. Therefore, PPSQ is also low.
(3) There are two conclusions based on sensitivity analysis. On the one hand, although there are some factors that are difficult to control, most of the PIS can effectively explain the princi- ple of PPSQ evaluation. On the other hand, attribute weight changes frequently with the change of threshold value. In particular, ser- vice attitude, cleaning and safety factors lead to changes in the comprehensive score of each
property service project, but there is no change in the ranking order of PPSQ. Obviously, LIN- MAP is an effective method to analyze PPSQ.
5. Comparison analysis between the proposed method and the traditional method
With the increase of data scale and attribute item, the advantages of the proposed method will be fur- ther demonstrated. The outstanding advantage of the new model in the proposed method is that it can better process complex data. In this paper, the tra- ditional method in literature [39] is compared with the proposed method. We make comparative anal- ysis in terms of decision makers, evaluation scale, evaluation result and management implications. The results of comparative analysis based on data struc- ture characteristics are shown in Table 7. Specially, the evaluation result of traditional method is only the ranking order, but the proposed method provides a set of comprehensive values by which can be com- pared among all alternatives. Therefore, there are many management enlightenment by analyzing the results.
Compared with the traditional LGDM method [39–42], the proposed method has four specific advantages as follows.
(1) In this paper, the MAMS method is extended into the general form, and use the general- ized MAMS decision matrix to process the evaluation information of large group. Expert preference and user evaluation information can be fused simultaneously by using this new method. Therefore, the proposed method optimizes the information structure on which the calculation results depend, and fuses the evaluation information of the two types of decision-makers effectively.
(2) In the existing LGDM research, attribute weights are partially or entirely subjective. This paper uses the LINMAP model to cal- culate attribute weight. The objective weight method based on large-scale heterogeneous
Table 7 Comparative analysis between the proposed method and the traditional method
Decision-makers Evaluation scale Evaluation result Management implications
The method in reference [39] users single ranking order weak The method in this paper Users and experts diversity comprehensive values strong
W.-J. Zuo et al. / A large group decision-making method 1525
evaluation data is the core of the proposed method. At the same time, according to the relation between attribute weight value and model preset value, the proposed method designs an identifying mechanism for invalid evaluation data. So the proposed method opens a new idea for the traditional decision method to be used in data analysis.
(3) The existing research results use the method of stochastic dominance and evidence inference respectively. The calculate result of compre- hensive evaluation value can only be used for the ranking order. The comprehensive score by the proposed method is of practical signifi- cance. For example, V (A1) = 2.620 indicates that PPSQ of museum is 2.620, and it lies between ‘indifferent’ and ‘good’
(4) This paper proposes a new PPSQ evaluation method, which enriches the property ser- vice quality evaluation research. The proposed method uses large-scale heterogeneous evalu- ation data to determine the attribute weight. Compared with the traditional PPSQ eval- uation method, the proposed method fuses multi-type subject data to make the PPSQ eval- uation results more reasonable. Furthermore, the proposed method is a new attempt to apply the improved decision model in property ser- vice quality evaluation.
6. Concluding remarks
To sum up, we proposes a LGDM method of gen- eralized MAMS based on LINMAP, and use the method to rank the PPSQ of 4 public property service projects by simultaneously processing the evaluation data of 104 users and 3 experts. As a new method processing the data of multiple evaluation subjects, complicated data structure and large scale data, it is applicable to all cases where evaluation information can be converted into the generalized MAMS infor- mation structure. Therefore, the proposed method can be used to process both questionnaire data and online evaluation data. Since the determination of the thresh- old value h in the existing research mainly depends on the experience of the decision-maker, it is a valuable issue to conduct the future research with the empiri- cal method. In addition, we can also improve decision model combining to variable weight [66] or prospect theory [67] in practice of PPSQ.
Acknowledgments
This research is the result of the Social Science Planning Project in Zhejiang province (No.19NDJC 396YBM) and the Key Program of National Natural Science Foundation of China (No.71231003).
References
[1] P. Liu and X. Zhang, Approach to multi-attributes decision making with intuitionistic linguistic information based on Dempster-Shafer evidence theory, IEEE ACCESS 6 (2018), 52969–52981.
[2] H.B. Jiang, J.M. Zhan and D.G. Chen, Covering based variable precision (I,T)-fuzzy rough sets with applications to multi-attribute decision-making, IEEE Transactions on Fuzzy Systems (2018), 1–1.
[3] J.M. Zhan, B.Z. Sun and J.C.R. Alcantud, Covering based multigranulation (I,T)-fuzzy rough set models and applica- tions in multi-attribute group decision-making, Information Sciences 476 (2019), 290–318.
[4] L. Zhang, J.M. Zhan and Z.X. Xu, Covering-based generalized IF rough sets with applications to multi- attribute decision-making, Information Sciences 478 (2019), 275–302.
[5] K. Zhang, J.M. Zhan, W.Z. Wu and J.C.R. Alcantud, Fuzzy �-covering based (I, T)-fuzzy rough set models and appli- cations to multi-attribute decision-making, Computers & Industrial Engineering 128 (2019), 605–621.
[6] P.D. Liu and P. Wang, Multiple-Attribute decision mak- ing based on Archimedean Bonferroni operators of q-Rung orthopair Fuzzy Numbers, IEEE Transactions on Fuzzy Sys- tems 99 (2019), 1–1.
[7] P. Liu, Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making, IEEE Transactions on Fuzzy Systems 22 (2014), 83–97.
[8] P.D. Liu and P. Wang, Some q-rung orthopair fuzzy aggre- gation operators and their applications to multiple-attribute decision making, International Journal of Intelligent Sys- tems 33 (2018), 259–280.
[9] P.D. Liu and J.L. Liu, Some q-rung orthopai fuzzy Bonfer- roni mean operators and their application to multi-attribute group decision making, International Journal of Intelligent Systems 33 (2018), 315–347.
[10] R. Arora and H. Garg, Group decision-making method based on prioritized linguistic intuitionistic fuzzy aggre- gation operators and its fundamental properties, Computa- tional and Applied Mathematics (2019), 36–38.
[11] G. Kaur and H. Garg, Generalized cubic intuitionistic fuzzy aggregation operators using t-norm operations and their applications to group decision-making process, Arabian Journal for Science and Engineering 44 (2019), 2775–2794.
[12] H. Garg and D. Rani, Complex interval-valued intuitionis- tic fuzzy sets and their aggregation Operators, Fundamenta Informaticae 164 (2019), 61–101.
[13] H. Garg, New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications, International Journal of Intelligent Systems 34 (2019), 82–106.
1526 W.-J. Zuo et al. / A large group decision-making method
[14] H. Garg, Nancy, Algorithms for possibility linguistic single- valued neutrosophic decision-making based on COPRAS and aggregation operators with new information measures, Measurement 138 (2019), 278–290.
[15] H. Garg, Hesitant Pythagorean fuzzy Maclaurin symmet- ric mean operators and its applications to multiattribute decision-making process, International Journal of Intelli- gent Systems 34 (2019), 601–626.
[16] J.J. Zhu and J.G. Zheng, Theory, method and application of group decision-making: Literature review and future directions, Chinese Journal of Management 6 (2009), 1131–1136.
[17] X.H. Xu, C.G. Cai, X.H. Chen and Y.J. Zhou, A multi- attribute large group emergency decision-making method based on group preference consistency of generalized interval-valued trapezoidal fuzzy numbers, Journal of Sys- tems Science and Systems Engineering 24 (2015), 211–228.
[18] Z.B. Wu and J.P. Xu, A consensus model for large-scale group decision-making with hesitant fuzzy information and changeable clusters, Information Fusion 41 (2018), 217–231.
[19] H. Garg and K. Kumar, Linguistic interval-valued Atanassov intuitionistic fuzzy sets and their applications to group decision-making problems, IEEE Transactions on Fuzzy Systems (2019), 1–10.
[20] B.S. Liu, Y.H. Shen, X.H. Chen, et al., A partial binary tree DEA-DA cyclic classification model for decision mak- ers in complex multi-attribute large-group interval-valued intuitionistic fuzzy decision-making problems, Information Fusion 18 (2014), 119–130.
[21] H. Garg and K. Kumar, Improved possibility degree method for ranking intuitionistic fuzzy numbers and their application in multiattribute decision-making, Granular Computing 4 (2019), 237–247.
[22] T. Wu, X.W. Liu and F. Liu, An interval type-2 fuzzy TOP- SIS model for large scale group decision-making problems with social network information, Information Sciences 432 (2018), 392–410.
[23] H. Garg and K. Kumar, A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory, Artificial Intelligence Review (2018), 1–30.
[24] B.S. Liu, Y.H. Shen, W. Zhang, et al., An interval- valued intuitionistic fuzzy principal component analysis model-based method for complex multi-attribute large- group decision-making, European Journal of Operational Research 245 (2015), 209–225.
[25] Á Labella, Y. Liu, R.M. Rodrı́guez and L. Martı́nez, Analyz- ing the performance of classical consensus models in large scale group decision-making: A comparative study, Applied Soft Computing 67 (2018), 677–690.
[26] X.H. Xu, Z.J. Du and X.H. Chen, Consensus model for multi-criteria large-group emergency decision-making con- sidering non-cooperative behaviors and minority opinions, Decision Support Systems 79 (2015), 150–160.
[27] I. Palomares, L. Martinez and F. Herrera, A consensus model to detect and manage noncooperative behaviors in large- scale group decision-making, IEEE Transactions on Fuzzy Systems 22 (2014), 516–530.
[28] Y.J. Xu, X.W. Wen and W.C. Zhang, A two-stage consensus method for large-scale multi-attribute group decision- making with an application to earthquake shelter selection, Computers & Industrial Engineering 116 (2018), 113–129.
[29] Z.B. Wu and J.P. Xu, A consensus model for large-scale group decision-making with hesitant fuzzy information
and changeable clusters, Information Fusion 41 (2018), 217–231.
[30] X. Xu, D. Liang, X. Chen and Y. Zhou, A Risk Elimination Coordination Method for Large Group Decision-Making in Natural Disaster Emergencies, Human & Ecological Risk Assessment An International Journal 21 (2015), 1314–1325.
[31] X. Chen, L. Zhao and M.S., Özdemir and H. Liang, Mixed strategy to allocate resources with air pollution treatment in China: Based on the analytic network process and large- group decision-making method, Environmental Science & Pollution Research (2018), 1–15.
[32] X. Liu, Energy network dispatch optimization under emer- gency of local energy shortage with web tool for automatic large group decision-making, Energy 120 (2017), 740–750.
[33] T. Wu, X.W. Liu and J.D. Qin, A linguistic solution for double large-scale group decision-making in E-commerce, Computers & Industrial Engineering 116 (2018), 97–112.
[34] X.H. Chen Complex large group decision-making and appli- cation, Science Press 2009.
[35] X.H. Xu, Z.J. Du, X.H. Chen and Y.J. Zhou, Conflict large-group emergency decision-making method while pro- tecting minority opinions, Journal of Management Sciences in China 20 (2017), 10–23.
[36] H.C. Liu, Z. Li, J.Q. Zhang and X.Y. You, A large group decision-making approach for dependence assessment in human reliability analysis, Reliability Engineering & Sys- tem Safety 176 (2018), 135–144.
[37] X. Gou, Z. Xu and F. Herrera, Consensus reaching pro- cess for large-scale group decision-making with double hierarchy hesitant fuzzy linguistic preference relations, Knowledge-Based Systems 157 (2018), 20–33.
[38] P. Wang, X. Xu, C. Cai and S. Huang, A linguistic large group decision-making method based on the cloud model, IEEE Transactions on Fuzzy Systems 99 (2018), 1.
[39] X. Zhang and Z.P. Fan, A method for large group decision- making with multi-attribute and multi-identifier based on evidential reasoning, Operations Research and Manage- ment Science 20 (2011), 15–20.
[40] X. Zhang and Z.P. Fan, Method for multi-attribute and multi- identifier large group decision-making based on prospect stochastic dominance, Control and Decision 29 (2014), 1429–1433.
[41] Y. Liu, Z.P. Fan and X. Zhang, A method for large group decision-making based on evaluation information provided by participators from multiple groups, Information Fusion 29 (2016), 132–141.
[42] T.H. You, J. Zhang and Z.P. Fan, Method for selecting desirable product(s) based on online rating information and customer’s aspirations, Chinese Journal of Management Science 25 (2017), 94–102.
[43] L. Liu, Z.H. Yan and S.Z. Bai, Big data-divisions change the decision modes, Science and Technology Management Research 36 (2016), 224–227+242.
[44] G.R. Teng, Research on group decision-making: Origin, development and status quo, Journal of Psychological Sci- ence 6 (1988), 53–58.
[45] K. Joseph, Social choice and individual values /-second ed, Yale University Press 1963.
[46] G.X. Yang and S. Shen, Evaluation on the satisfaction of property services in urban residential areas, Research on Development 158 (2012), 156–160.
[47] T.M. Zhu, Y.Q. Zhao and T.C. Wang, Customer satisfac- tion management of service enterprises based on experience factors, Productivity Research 221 (2010), 238–240.
W.-J. Zuo et al. / A large group decision-making method 1527
[48] R.N. Cardozo and An, Experimental Study of Customer Effort, Expectation, and Satisfaction, Journal of Marketing Research 2 (1965), 244–249.
[49] R.E. Anderson, Consumer dissatisfaction: The effect of dis- confirmed expectancy on perceived product performance, Journal of Marketing Research 10 (1973), 38–44.
[50] R.W. Olshavsky and J.A. Miller, Consumer expectations, product performance, and perceived product quality, Jour- nal of Marketing Research 9 (1972), 19–21.
[51] C. Gronroos, Strategic management and marketing in the service sector, Marketing Science Institute (1983), 83–104.
[52] V.A. Zeithaml, L.L. Berry and A. Parasuraman, The nature and determinants of customer expectations of service, Jour- nal of the Academy of Marketing Science 21 (1993), 1–12.
[53] Y.B. Huo, Study on service quality evaluation of property management based on SERVQUAL, Journal of Nanjing University of Finance & Economics 88 (2010), 81–84.
[54] H.L. Guo and Y.C. Wang, Performance evaluation model and application of project department of large-scale prop- erty service companies, China Journal of Commerce (2014), 56–58.
[55] Q.Y. Liao and S.S. Hu, Research on service quality evalua- tion system of property management in residential quarters: A case study of Chongqing, Construction economy 38 (2017), 76–82.
[56] Y.F. Lu, Application of QFD theory in improveing the perceived quality of property service, Management and administration (2018), 130–133.
[57] X.Y. Liu, Y.N. Liu and H.F. Wan, The Construction of a New Customer Satisfaction Index Model Based on the Analy- sis of SCSB, ACSI and ECSI, Nankai Business Review 6 (2003), 52–56.
[58] A.D. Shocker and V. Srinivasan, LINMAP: Linear Pro- gramming Techniques for the Multidimensional Analysis of Preferences, Psychometrika 38 (1973), 337–369.
[59] D.F. Li and J.B. Yang, Fuzzy linear programming technique for multiattribute group decision-making in fuzzy environ- ments, Information Sciences 158 (2004), 263–275.
[60] H.C. Xia, D.F. Li, J.Y. Zhou and J.M. Wang, Fuzzy LINMAP method for multiattribute decision-making under fuzzy environments, Journal of Computer & System Sciences 72 (2006), 741–759.
[61] D.F. Li, Extension of the LINMAP for multiattribute decision-making under Atanassov’s intuitionistic fuzzy environment, Fuzzy Optimization & Decision-making 7 (2008), 17–34.
[62] I. Bereketli, M.E. Genevois, Y.E. Albayrak and M. Özyol, WEEE treatment strategies’ evaluation using fuzzy LIN- MAP method, Expert Systems with Applications 38 (2011), 71–79.
[63] S.P. Wan and D.F. Li, Fuzzy, LINMAP approach to hetero- geneous MADM considering comparisons of alternatives with hesitation degrees, Omega 41 (2013), 925–940.
[64] H.C. Liao, L.S. Jiang, Z.S. Xu and F. Herrera, A linear programming method for multiple criteria decision mak- ing with probabilistic linguistic information, Information Sciences 415-416 (2017), 341–355.
[65] D.F. Li, G.H. Chen and Z.G. Huang, Linear programming method for multiattribute group decision making using IF sets, Information Sciences 180 (2010), 1591–1609.
[66] G.F. Yu, W. Fei and D.F. Li, A compromise-typed vari- able weight decision method for hybrid multi-attribute decision making, IEEE Transactions on Fuzzy Systems, https://ieeexplore.ieee.org/document/8531747/authors
[67] K.A. Tversky, Prospect Theory: An Analysis of Decision under Risk, Econometric 47 (1979), 263–292.
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