Evaluation for quality regulatory capability maturity in government procurement of public service based on probabilistic linguistic term sets

Abstract

Recently, the reform practice of government procurement of public service (GPPS) in China has been promoted gradually and got great breakthrough. Meanwhile, in order to guarantee that the expected goal of this reform achieved, mature and effective regulation is of vital importance. Considering the practical demand, the capability maturity model is applied into the evaluation of quality regulatory capability in GPPS. The concept of quality regulatory capability maturity is proposed, and the evaluation model based on TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) method for probabilistic linguistic term sets (PLTSs) is provided. Taking Jiangsu Province as an example, an empirical study of its quality regulatory capability evaluation for GPPS is conducted, through which, not only comparative results of maturity levels of different cities in Jiangsu is obtained, but the improving measures are also determined. The proposed maturity evaluation model fully reflects experts’ preferences and evaluation information, and is able to point out the direction for regulatory capability’s future promotion level by level, as well as its continual improvement.

Keywords

Government procurement of public service quality supervision capability maturity evaluation probabilistic linguistic term set

1 Introduction

Government procurement of public service (GPPS) is an effective practice for government to improve the quality of public service and the efficiency of financial fund, and can transfer the provision of public service from governments themselves to social organizations. Meanwhile, the focus of governments’ function is shifting from “supplier” to “supervisor” [1]. In China, with deepening of economic system reform, providing public service in the way of government procurement from social force has become more and more important [2, 3]. Jiangsu province, launched GPPS in 2013, has established a preliminary institution system composed of promotion mechanism, top layer design and practice. In 2013, 21 projects were selected to be piloted by Jiangsu Finance, and by the end of 2015, the 61 key projects have been done. Taking projects of cities and counties in Jiangsu into account, the cumulative projects add up to 3778, with budget as high as 15.896 billion RMB. This amount reached 67.888 billion in 2016. Compared with previous years, not only the number of GPPS projects grows notably, but also the sum value increases sharply, as well as the coverage expands. Legal aid, social consultation service, community aid, shantytowns’ reconstruction and the PPP projects appear in the list for the first time. With the development of practice in GPPS, the top layer design is also strengthened in Jiangsu province, and the institution system is continuously being improved [4]. Jiangsu Finance and Civil Affairs Departments have jointly made and issued several normative documents such as ‘Implementation guidelines for GPPS’, ‘Management of the fund for GPPS’ and ‘Performance evaluation method for GPPS’, which actually regulate and promote the work of GPPS in Jiangsu.

Meanwhile, to ensure the effect and efficiency of public service provision under government procurement, a comparatively perfect regulatory system is being established. At present, there are three critical transformations in constructing the supervision system of GPPS. The first one is the transformation from static regulatory capability building to dynamic capability improving. A certain foundation has been built in quality supervision for GPPS nationwide. Therefore, it is essential to improve the general communication and coordination capability of regulatory capability. There is an urgent need in improving such capabilities as quality control, resource distribution and collaborative supervision between different interest groups, all of which should face dynamic process [5]. The second transformation is to transform from passive supervision to active supervision. Through establishing a quality supervision system covering the whole process, active measures are taken to identify, reduce and stop the quality risks and potential quality problems in the whole process of GPPS, which will strengthen prior forecast and in-process quality control. The third transformation is to transform from fragmentation to systemized supervision. The supervision should be transformed from single evaluation to omnibus quality supervision, which is multi-agent, multi-link and multi-way, thus constructing a perfect network of quality control system step by step [6]. For these transformations, the focus of quality regulation in GPPS should be better controlling and coordinating the process, as well as improving the degree of scientific and standardization [7]. Therefore, it is necessary to explore a regulatory capability evaluation method for GPPS, which is able to identify the governments’ capability level of quality regulation in public service procurement, timely detect weak points and areas to be improved. Through that, targeted measures are taken to improve the quality regulatory capability in public service procurement, as well as to promote further development of China’s reform in GPPS. The purpose of this paper is to provide a regulatory capability evaluation method for GPPS. Our contributions include: (1) Constructing evaluation criteria for quality regulatory capability in GPPS based on capability maturity model (CMM); (2) Proposing an evaluation model based on TODIM method for PLTSs, which better reflects the experts’ preferences and evaluation information in evaluating quality regulatory capability in GPPS.

When evaluating quality regulatory capability maturity in GPPS, experts may feel comfortable to express their opinions with linguistic terms, such as good, perfect or poor, rather than quantitative evaluations because some criteria are difficult to describe with crisp numbers. Owing to the uncertainty of evaluation problems in real life, the evaluation process needs more than one expert to make it more reasonable. Different experts may express different opinions on the same evaluation object. To cope with this issue, Rodriguez et al. [8] proposed the definition of hesitant fuzzy linguistic term sets by continuous linguistic terms (HFLTSs). However, the method of HFLTS did not consider the situation that the number of experts expressing different opinions may be different. For example, there are 10 experts to evaluate a car. We assume that there are 4 experts thinking it is good and 6 perfect. The method of HFLTS can’t describe such situation. Zhang et al. [9] (2014) proposed the linguistic distribution (LD). Dong et al. [10] generalized the LD and proposed the multi-granular unbalanced linguistic distribution with interval symbolic. Numerical scale model [11, 12] and personalized individual semantics model [13 –15] are the main types of methods for LD problems. Additionally, Pang et al. [16] expanded the HFLTS to probabilistic linguistic term sets (PLTSs) by using two dimensions: linguistic term and probability of the linguistic term. For the aforementioned example, we can use the PLTS to describe the situation: L (p) = {(s₁, 0.4) , (s₃, 0.6)} (Here we assume that the number of language granularity is 7). The difference between PLTS and LD is minor. The sum of symbolic proportions in PLTSs can be smaller than 1, while that in LD is 1. What is more, PLTS can be transformed into linguistic distributions.

The PLTS has attracted lots of researchers owing to its strong practicality. There are many studies concerning the PLTS from theories and applications. Zhang et al. [17] proposed novel probabilistic linguistic preference relations and analyzed the consensus process of group decision making problems. Yu et al. [18] put forward a new multiple criteria decision making (MCDM) method for PLTS and applied it to hotel selection. Wu and Liao [19] designed a new way to deal with the problem of selecting innovative product design through quality function deployment and PLTS. Peng et al. [20] established a cloud decision support model using PLTS to select hotels according to online reviews. Bai et al. [21] proposed a new possibility degree formula by a diagram method to compare different PLTSs. Gou and Xu [22] proposed some basic operational laws for PLTs and studied the relations of PLTS and HFLTS. The above studies focus more on theory study on PLTSs. There is little research on evaluation model for quality regulatory capability maturity in GPPS. In this paper, we will propose a TODIM method for PLTSs and apply it to the evaluation of quality regulatory capability maturity in GPPS.

The remainder of the paper is structured as follows. Section 2 is a literature review. Section 3 develops the evaluation criteria for quality regulatory capability in GPPS based on CMM, and the establishment of the evaluation model based on TODIM method for PLTSs is described in Section 4. Section 5 provides a case study to illustrate and verify our proposed evaluation model. A conclusion is provided in Section 6.

2 Literature review

2.1 Evaluation of regulatory capability

Regulatory capability, as one of governments’ capabilities, mainly focuses on implementing supervising policies, and ensuring supervisory quality through executing these policies. Supervisory capability is different from supervisory performance. However, sound supervisory performance needs powerful regulatory capability as a guarantee. All factors should be comprehensively taken into consideration to evaluate the regulatory capability, such as the building of regulatory organizations, application of supervisory tools, and policy making for regulation [23]. Scientific and logical evaluating index system is necessary to make a precise assessment, so that weak links and relative gaps in the regulation system can be found out. The regulation level will be increased through implementation of effective improving measures, which are to the point. In 1995, the Organization for Economic Co-operation and Development (OECD) issued the first international standard on construction of regulation system and evaluation of regulatory capability, which made it clear that regulatory capability should composite of three ingredients: organizations, policies and tools for regulation. There are plenty of studies on composition and evaluation of regulatory capability in recent academic world. According to current literature, evaluation of regulatory capability may stick to one specific organization, or to one certain area or industry. Subjects and matters to be evaluated are generally set from their composition, including extent of resources’ abundance, relationship between subjects and objects in supervision, establishment and implementation of regulation policies, relative independence of regulation organizations. Kjekshus and Veggeland [24] suggested that supervision capability is the capability for formal regulation organizations to carry out a series of measures to ensure that the goal of supervision correspondence to a nation’s decision-making. Therefore, performance of regulation policies’ implementation should be an important constitutive of regulatory capability. Yadav [25] showed that firms used a systematic process to build capabilities for managing regulations, and offered a process model for firms to build regulatory capabilities. Mcallister [26] proposed that the extent of resources’ abundance is the base for regulatory capability evaluation. Rooij [27] suggested that the extent of resources’ abundance restricted improvement of local governments’ environmental regulatory capability, as well as the improvement of supervision performance. Liu et al. [28] established a graduated measurement indicator system on regulatory capability which includes the building of regulatory institution, the using of regulatory tools and quality of regulatory policies. The Ministry of Environmental Protection (MEP), China Food and Drug Administration (CFDA) and the Center of Inspection and Supervision of National Health and Family Planning Commission (CISNHFPC) were chosen to be measured and graduated by their proposed system. Aiming at the regulatory capability of urban public utility, Li [29] summarized the enlightenment and reference of American evaluation system of urban public utilities regulation. Yang [30] suggests learning from the idea of responsive regulation that emerged recently in western countries and creating a new paradigm of collaborative regulation between state and non-state actors. Hu [31] established a structural model of institutional capacity of drug administration as well as an appraisal index system based on the concepts of potential capacity and realized capacity by Nielsen. Ten provincial drug administrations’ regulation capacities were then evaluated and compared based on the established model. Wu [32] proposed an evaluation index system of regulatory capability including three dimensions: constitute elements of governments’ regulatory capability, explicit form and influence factors, which provides scientific standard for governments’ judgement.

In summary, there are many researches on governments’ regulatory capability, as well as its evaluation. In this field, great achievements have been made and abundant experience has been accumulated both in theoretical research and practice. However, imperfections still exist. Studies on evaluation indicators and methods hold out a situation of hundreds of flowers in blossom, which is low in consensus about these research findings, and relatively stable evaluation mode hasn’t yet been developed. For one thing, most researches in evaluation of regulatory capability try to find out key factors influencing the regulatory capability through one-time evaluation, against which measures are taken to improve the capability, while evaluations considering dynamic condition are ignored. Therefore, it is difficult to establish a dynamic improving mode due to lack of continuous improving idea. For another thing, theoretical research on regulatory capability evaluation tends to be disconnected from practice, and many evaluation methods in theoretical research is hard to attain good results from practice, which is low in promotional value.

2.2 Regulation in government procurement of public service (GPPS)

As to the regulation in GPPS, there have been plenty of relative studies. Lodi et al. [33], Johansson et al. [34] both focused on the contract design and control to better regulate the process of GPPS. Wu et al. [32] tried to establish a relatively complete regulatory system of GPPS, and took a close look at the role transition of government in GPPS, thus underlining government’s supervision and regulation role. Cunningham and James [35] analyzed GPPS from the value of a regulatory perspective. They revealed that a ‘soft’ regulatory framework that offered little support to partnership relations between voluntary organizations and local authorities. Ainuddin et al. [36] indicated that the principle of transparency in procurement of goods and government services was important to be accommodated for the purpose of better regulation. Maciejewski [37] discussed some applications of big data methods in public administration, which also drew attention of big data application in regulation in GPPS. Ida and Talit [38] looked into structural reforms in the regulation of public bus services in Israel. They studied and examined the reasons and effectiveness of different measures taken to regulate outsourced the public service.

Academic research in the field of regulation and management in GPPS has mainly dealt with regulation mechanisms, risks, systems and the implementation of governments’ regulation responsibilities, etc. However, little research has been done in respect to evaluation of the regulatory capability in GPPS, as well as the capability maturity. At present, China is still in primary stage in GPPS, the overall level of which is rather low. In present practice, restricted by many factors such as ideological understanding, human resource, technological equipment, legal basis, etc., regulation in GPPS is still a weak link which hasn’t received adequate attention.

3 The evaluation criteria development for quality regulatory capability in GPPS based on CMM

3.1 CMM and the feasibility analysis of its application into quality regulatory capability evaluation criteria development

Proposed by Carnegie Mellon University, CMM was initially applied to deal with software development and management process. It is a description on each stage for defining, implementing, measuring, controlling and improving the software’s process. The initiator, Institute of Software Engineering of Carnegie Mellon University, divided the capability maturity of software development into 5 levels, 18 key process areas, 52 objectives and 316 key practices. CMM made it clearer and more convenient to identify the capability of present process, as well as the important problems of software quality and process improvement, thus providing guidelines to make decisions on selecting process improvement strategies. As software development itself is a project management process, it is undoubtedly logical to apply CMM into the field of project management. After that, CMM was successively applied into areas such as knowledge management [39], Risk management [40], service management [41, 42], public management and logistics management [43]. CMM has now become a relatively mature tool to define the stage of development, characteristics of stages and the direction of development. The five-level maturity model for project management proposed by Kerzner includes general terms, general processes, single method, baseline comparison and continual improvement. Each level has specific evaluation method and criterion, so that the maturity degree of this level could be obtained by aggregation, based on which deficiencies are then analyzed and improving measures are thus made to get into the next stage. Krishnan et al. [44] used CMM to assess the process maturity of technology projects management in the US federal government. Pongsuwan [45] proposed a measurement model called “Procurement Competitive Capability Maturity” (PCCM) for a company to assess current practices of procurement function and perceive the level of its capabilities. Rendon [46] presented an assessment of contract management process maturity in the US Navy based on CMM, which is used to benchmark an organization’s contract management process maturity.

Quality supervision and regulation of GPPS is a system engineering, which develops from disorder to order, from passive to active supervision, from fragmented to systematic. Therefore, it is a process which is gradually getting maturity and the comprehensive capability of management is gradually improving. Meanwhile, the core idea of CMM is just to find out and work on the disadvantages through evaluating the process of an organization and its capability maturity level, thus forming a continuous improving mode. Applying CMM into criteria development of quality regulatory capability evaluation in GPPS is feasible and reasonable. For one thing, CMM is particularly suitable for evaluating process or management capability, and here what we want to assess is just the regulatory capability in GPPS. The weak links in GPPS can be found out through maturity evaluation, which provides direction and effective guidance for departments concerned to make out appropriate improving measures and to perfect the quality supervision system. For another thing, it can provide references for senior governments and the public to evaluate local governments’ performance in their procurement of public service, as well as their supervision performance, thus urging local governments continuously improving their quality regulatory capability in the process of promoting the practice of GPPS. Therefore, it is not only feasible, but also very necessary to introduce CMM theory into evaluation and enhancement of quality regulatory capability of GPPS. Through determining the maturity level of local governments’ quality regulatory capability in its procurement of public service, and defining the weak links facing process areas, aiming at which improvements are made and capability is developed stage by stage. Governments’ regulatory capability in their procurement of public service is consequently enhanced step-by-step, and effective improving mode is thus developed.

3.2 Evaluation criteria development of regulatory capability maturity in GPPS

3.2.1 Levels of regulatory capability maturity

Using Software capability maturity levels and project management maturity levels’ classification for reference and combined with the characteristics of the quality supervision of GPPS itself, we divide the quality regulatory capability maturity of GPPS into 5 levels. They are defined as follows according to actual situation of quality regulation: initial stage (L1), repeatable stage (L2), already-defined stage (L3), quantitative management stage (L4) and continuous improvement stage (L5). In order to better describe the characteristics of each level in quality regulation of GPPS, key links of quality regulation including the general characteristics (C₁) of each level, regulation process management (C₂), multi-party participation (C₃), policy making and implementation (C₄) and effectiveness (C₅) are selected as the evaluation dimensions to compose the criteria system. Typical characteristics of each level in view of the evaluation criteria are extracted in Table 1.

Table 1
Different levels’ characteristics for quality regulatory capability maturity of GPPS

Dimensions levels C ₁ C ₂ C ₃ C ₄ C ₅

L1 Quality supervision is absent or in disorder Lack of standard procedure, the supervision is ruleless The supervision is conducted just by governments, responsibilities are not well defined Lack of specific policies for supervision, policies concerned are implemented in disorder. Disorderly supervision, GPPS is inefficiency, quality problems occur frequently

L2 Basic procedures are built, while lack of completeness and standardization There is rules to follow, standard management, which provides experiences for other practices in GPPS Government is the main party to regulate. There are rules for apportioning tasks and management There are fundamental policies for quality supervision, and the implementation is in order and in control. Standardized supervision, high resource utilization, service quality has been improved

L3 Standardized process management, quality supervision system has been developed. Regulation process is managed and controlled in standardization. Multi agents’ participation with sound coordination, including government, the third party, media and the public. A complete and orderly regulation policy system is formed. Implementation is standardized. The supervision is highly goal-directed, effective. The process is in control.

L4 The processes of quality regulation are quantitatively analyzed and controlled. There are specific standards for measuring the process. Quantitative analysis can be conducted. Mature and stable management model Sound quality supervision system for GPPS. Good coordination. Controllable performance Perfect regulation policy system with high cooperativity The implementation could be quantitatively measured. Effective regulation of GPPS, which could be quantitatively measured and evaluated.

L5 Defects in supervision could be found out and strategies for improvement could be made to develop a continuous improvement process. New concepts and technologies in the process of supervision could be quantitatively analyzed and effectively applied. The supervision process is improved continuously. Cooperative supervision, continuous improving regulation system, and the regulation performance is maximized. Relative policy system could be revised and perfected continuously and dynamically. The implementation process is also optimized and improved. Supervision effectiveness is enhanced, which could continuously improve the quality of GPPS.

Dimensions levels	C ₁	C ₂	C ₃	C ₄	C ₅
L1	Quality supervision is absent or in disorder	Lack of standard procedure, the supervision is ruleless	The supervision is conducted just by governments, responsibilities are not well defined	Lack of specific policies for supervision, policies concerned are implemented in disorder.	Disorderly supervision, GPPS is inefficiency, quality problems occur frequently
L2	Basic procedures are built, while lack of completeness and standardization	There is rules to follow, standard management, which provides experiences for other practices in GPPS	Government is the main party to regulate. There are rules for apportioning tasks and management	There are fundamental policies for quality supervision, and the implementation is in order and in control.	Standardized supervision, high resource utilization, service quality has been improved
L3	Standardized process management, quality supervision system has been developed.	Regulation process is managed and controlled in standardization.	Multi agents’ participation with sound coordination, including government, the third party, media and the public.	A complete and orderly regulation policy system is formed. Implementation is standardized.	The supervision is highly goal-directed, effective. The process is in control.
L4	The processes of quality regulation are quantitatively analyzed and controlled.	There are specific standards for measuring the process. Quantitative analysis can be conducted. Mature and stable management model	Sound quality supervision system for GPPS. Good coordination. Controllable performance	Perfect regulation policy system with high cooperativity The implementation could be quantitatively measured.	Effective regulation of GPPS, which could be quantitatively measured and evaluated.
L5	Defects in supervision could be found out and strategies for improvement could be made to develop a continuous improvement process.	New concepts and technologies in the process of supervision could be quantitatively analyzed and effectively applied. The supervision process is improved continuously.	Cooperative supervision, continuous improving regulation system, and the regulation performance is maximized.	Relative policy system could be revised and perfected continuously and dynamically. The implementation process is also optimized and improved.	Supervision effectiveness is enhanced, which could continuously improve the quality of GPPS.

3.2.2 Framework of quality regulatory capability maturity evaluation in GPPS

The proposed framework of quality regulatory capability maturity evaluation in GPPS is described as follows (Fig. 1):

Developing evaluation criteria, which means determining the critical indexes to evaluate the quality regulatory capability maturity on basis of the key links in quality supervision in GPPS.

Identifying maturity levels, which means dividing the capability governments should have to regulate the quality of their procurement of public service into different levels, as well as the characteristics of these levels.

Implementing the evaluation, which means that various experts (selected as assessors) make a judgement based on the developed criteria and characteristics of different levels. The judgement is about which level the evaluated object currently belongs to corresponding to each evaluation index in the criteria.

Aggregation of different experts’ judgements. An expertise aggregation method is designed to fully reflect the experts’ preferences and evaluation information.

Determining the order for improvement, which means that in view of the advantages and disadvantages in the process of quality supervision of GPPS, and according to the evaluation results, specific direction for next work for improvement is determined, and the capability enhancement is implemented with emphasis.

Fig.1

Flow chart of quality regulatory capability maturity evaluation in GPPS.

4 Establishment of evaluation model for quality regulatory capability maturity in GPPS based on TODIM method for PLTSs

According to Section 3.2, we can easily find that the characteristics for quality regulatory capability maturity of GPPS are described by linguistic terms with 5 levels. Therefore, the theory of PLTSs is applied to evaluate the quality regulatory capability maturity in GPPS in this paper.

4.1 Preliminaries

Firstly, some basic definitions and operations for PLTSs are reviewed in this section.

Definition 1. (Pang et al., 2016) Let S = {s₀, s₁, ⋯ , s_τ} be a LTS, a PLTS is defined as

$\begin{matrix} L (p) = {L^{(k)} (p^{(k)}) | L^{(k)} \in S, p^{(k)} \geq 0, k = 1, 2, \\ \dots, # L (p), \sum_{k = 1}^{# L (p)} p^{(k)} \leq 1} \end{matrix}$ (1)

Where # L (p) is the number of all different linguistic terms in L (p).

From the Def. 1, we can easily observe that the sum of probabilistic distribution of all possible linguistic terms is not more than 1. If $\sum_{k = 1}^{# L (p)} p^{(k)} < 1$ , then some information is not embodied owing to lack of knowledge or hesitance for DMs. To overcome this issue, Pang et al. (2016) proposed a normalization method for PLTS.

Definition 2. Let L (p) = {L^(k) (p^(k)) |L^(k) ∈ S, p^(k) $\geq 0, k = 1, 2, \dots, # L (p), \sum_{k = 1}^{# L (p)} p^{(k)} < 1}$ be a PLTS, the normalized PLTS can be defined as

$\begin{matrix} \overset{\cdot}{L} (p) = {L^{(k)} (\dot{p^{(k)}}) | L^{(k)} \in S, \dot{p^{(k)}} \geq 0, k = 1, 2, \\ \dots, # L (p), \sum_{k = 1}^{# L (p)} \dot{p^{(k)}} = 1} \end{matrix}$ (2) where $\dot{p^{(k)}} = p^{(k)} / \sum_{k = 1}^{# L (p)} p^{(k)}$ for k = {1, 2, ⋯ , # L (p)}.

In order to compare different PLTSs, the score function and deviation function are defined by Pang et al. (2016) as follows.

Definition 3. Let L (p) = {L^(k) (p^(k)) |k = 1, 2, ⋯ , # L (p)} be a PLTS, then the score function E and Δ for PLTs can be defined as $E (L (p)) = s_{α}$ (3) $Δ (L (p) = (\sum_{k = 1}^{# L (p)} (p^{(k)} (r^{(k)} - α)^{2})^{1 / 2}) / \sum_{k = 1}^{# L (p)} p^{(k)}$ (4)

Where $α = \sum_{k = 1}^{# L (p)} (p^{(k)} r^{(k)}) / \sum_{k = 1}^{# L (p)} p^{(k)}$ , and r^(k) is the subscript of linguistic term L^(k)(k = 1, 2, ⋯ , # L (p)).

Given arbitrary two PLTSs L₁ (p) and L₂ (p), then the following comparative conclusions hold:

if E (L₁ (p)) < E (L₂ (p)), then L₁ (p) ≺ L₂ (p);

if E (L₁ (p)) > E (L₂ (p)), then L₁ (p) ≻ L₂ (p);

if E (L₁ (p)) = E (L₂ (p)),then

if Δ (L₁ (p)) < Δ (L₂ (p)), then L₁ (p) ≻ L₂ (p);

if Δ (L₁ (p)) > Δ (L₂ (p)), then L₁ (p) ≺ L₂ (p);

if Δ (L₁ (p)) = Δ (L₂ (p)), then L₁ (p) = L₂ (p).

Distance measure is very important and necessary in solving MCDM problems. The Euclidean distance for PLTS proposed by Pang et al. (2016) can be described as follows:

Let $L_{1} (p) = {L_{1}^{(k)} (p_{1}^{(k)}) | k = 1, 2, \dots, # L_{1} (p)}$ and $L_{2} (p) = {L_{2}^{(k)} (p_{2}^{(k)}) | k = 1, 2, \dots, # L_{2} (p)}$ be two arbitrary PLTSs and # L₁ (p) = # L₂ (p), then the Euclidean distance between L₁ (p) and L₂ (p) can be calculated by $d (L_{1} (p), L_{2} (p)) = \sqrt{\sum_{k = 1}^{# L_{1} (p)} (p_{1}^{(k)} r_{1}^{(k)} - p_{2}^{(k)} r_{2}^{(k)})^{2} / # L_{1} (p)}$ (5) where $r_{1}^{(k)}$ and $r_{2}^{(k)}$ are the subscripts for $L_{1}^{(k)}$ and $L_{2}^{(k)}$ , respectively.

Remark 1. If # L₁ (p) < # L₂ (p), then add corresponding elements for # L₁ (p) until # L₁ (p) = # L₂ (p).

4.2 TODIM method for PLTSs to evaluate quality regulatory capability maturity in GPPS

Given an evaluation problem for quality regulatory capability maturity in GPPS, we assume that there are m criteria C₁, C₂, ⋯ , C_m, n alternatives A₁, A₂, ⋯ , A_n to be evaluated, and experts provide evaluated value by linguistic terms for every alternative in terms of all criteria. Based on processing the data, a decision-making matrix B = (b_ij) _m×n was obtained, where b_ij is a PLTS indicating the value for alternative A_i with respect to criterion C_j. The criteria weighting vector w = (w₁, w₂, ⋯ , w_n) is completely unknown satisfying $\sum_{j = 1}^{n} w_{j} = 1$ , w_j ≥ 0.

4.2.1 Obtaining the criteria weights by maximizing deviation method

As the criteria weights are completely unknown, we need a way to compute the criteria weights. Maximizing deviation method, used by a mathematical programming, is an effective way to obtain the criteria weights.

On basis of the idea of maximizing deviation method [16], the deviation value for criterion C_j can be obtained as $d_{j} = \sum_{i = 1}^{m} \sum_{q = 1, q \neq i}^{m} d (L_{ij} (p), L_{qj} (p))$ (6)

The criteria weights can be computed by the following optimization model $Maxd = \sum_{j = 1}^{n} \sum_{i = 1}^{m} \sum_{q = 1, q \neq i}^{m} w_{j} d (L_{ij} (p), L_{qj} (p))$ $s . t . \sum_{j = 1}^{n} w_{j}^{2} = 1, w_{j} \geq 0, j = 1, 2, \dots, n$

According to construct Lagrange function, we can easily obtain $w_{j} = \frac{\sum_{i = 1}^{m} \sum_{q = 1, q \neq i}^{m} d (L_{ij} (p), L_{qj} (p))}{\sum_{j = 1}^{n} \sum_{i = 1}^{m} \sum_{q = 1, q \neq i}^{m} w_{j} d (L_{ij} (p), L_{qj} (p))}$ (7)

4.2.2 TODIM method for PLTS

When decision makers face with uncertain environment, they are usually bounded rational. Prospect theory is a famous way to cope with this issue. TODIM, firstly proposed by Gomes et al. [47], and based on prospect theory, is another effective method for solving MCDM problems. Owing to the capacity of curving decision makers’ bounded rationality, it has attracted many researchers and many studies have been emerged. Hu et al. [31] proposed a new TODIM method for three-way decision model using a novel possibility degree. Ji et al. [48] proposed a project-based TODIM method for neutrosophic information. Llamazares [49] generalized traditional TODIM method by using a series of functions and proved some properties. The key idea lies in that the dominance value of one alternative over others. There are two main types of methods: distance measure and outranking value. In this paper, to compute simply, we use the former method. The main steps are shown as follows.

Firstly, calculate the relative weights of criterion C_j according to the criteria weights obtained by Equation (7) as follows $w_{jr} = w_{j} / w_{r} (j = 1, 2, \dots, n)$ (8) where w_r = max {w₁, w₂, ⋯ , w_n}

Then calculate the dominance degree for alternative A_i over A_k in terms of criterion C_j $\begin{matrix} Φ_{j} (A_{i}, A_{k}) = \\ {\begin{matrix} \sqrt{d (b_{ij}, b_{kj}) w_{jr} / (\sum_{j = 1}^{n} w_{jr})}, if b_{ij} ≻ b_{kj} \\ 0, if b_{ij} = b_{kj} \\ - \frac{1}{θ} \sqrt{d (b_{ij}, b_{kj}) (\sum_{j = 1}^{n} w_{jr}) / w_{jr}}, if b_{ij} ≺ b_{kj} \end{matrix} \end{matrix}$ (9)

Then, calculate the dominance degree for A_i over A_k in all criteria $Φ (A_{i}, A_{k}) = \sum_{j = 1}^{n} Φ_{j} (A_{i}, A_{k})$ (10)

Finally, compute the overall dominance degree for A_i as follows $Z (A_{k}) = \frac{\sum_{k = 1}^{m} Φ (A_{i}, A_{k}) - min_{i} {\sum_{k = 1}^{m} Φ (A_{i}, A_{k})}}{max_{i} {\sum_{k = 1}^{m} Φ (A_{i}, A_{k})} - min_{i} {\sum_{k = 1}^{m} Φ (A_{i}, A_{k})}}$ (11)

Rank the alternatives according the overall dominance degree.

4.2.3 Evaluation procedure for the TODIM method for PLTSs

Step 1. Calculate the criteria weights w = (w₁, w₂, ⋯ , w_n) according to Equation (7)

Step 2. Compute the relative weights w_r = (w_1r, w_2r, ⋯ , w_nr) based on Equation (8)

Step 3. Calculate the dominance degree for A_i over A_k in all criteria Φ (A_i, A_k) according to Equations (9-10)

Step 4. Compute the overall dominance degree Z (A_k) based on Equation (11)

Step 5. Rank the alternatives based on the overall dominance degree Z (A_k).

5 Case study

5.1 Description

The quality regulatory capability evaluation for GPPS in Jiangsu Province of China is taken as an example here to illustrate the specific evaluation procedure. Six typical cities in Jiangsu are selected to be evaluated. They are Nanjing (A₁), Wuxi (A₂), Suzhou (A₃), Nantong (A₄), Lianyungang (A₅) and Xuzhou (A₆), among which two (Suzhou and Wuxi) are from South of Jiangsu, two (Nanjing and Nantong) Middle of Jiangsu, and two (Xuzhou and Lianyungang) the Northern part. Therefore, these 6 cities are representative of the current condition of quality regulation in Jiangsu Province.

5.2 Evaluations

(1) Building an evaluation group of experts

To ensure the reliability and accuracy of the evaluation, our evaluation group is composed of 10 experts in the field of public management from different universities such as Nanjing University, Nanjing University of Aeronautics and Astronautics, Yangzhou University, Jiangsu University. Officials from governments concerned who are in charge of the work of procurement of public service and personnel from service suppliers are also included in our expert group. The whole group constitutes 10 experts.

(2) Collecting materials for evaluation

Materials for references involved in evaluating quality supervisory capability maturity in government procurement of public can be classified into three categories. The first category is materials about construction condition of government concerned, such as the establishment of governments’ regulation and coordination agency and special regulating organization, as well as the allocation and training of staffs, documents of policies and relative institutions, and so on. The second category is materials collected through searching on the internet such as policy information about GPPS in the 6 evaluated cities in Jiangsu, the bidding information, information from platforms of governments’ work on internet, etc. The third category is typical examples and cases about quality regulation in GPPS in these 6 cities provided by local governments or through search from the internet. All of the above information considered, initial questionnaire is designed according to different key process areas and their goals, which are delivered to all members in our evaluation group through internet, as well as all the materials for references.

(3) The expert group making a judgement (evaluation)

Members of the evaluation group go over all relative material received carefully, and they can communicate with each other anytime on line to gain further insight or discuss with each other when they have different opinions. Finally, evaluation information is collected from experts. All members in our group should make a judgment in view of each cities’ current maturity level out of the five levels (L1-L5) in CMM corresponding to the five criteria (C₁, C₂, C₃, C₄, C₅).

When judgments from each expert are all collected (Table 2), the evaluation results are sorted out and analyzed. Here, A₁, A₂, A₃, A₄, A₅, A₆ represent the six cities respectively: Nanjing, Wuxi, Suzhou, Nantong, Lianyungang and Xuzhou.

Table 2
Experts’ judgements about the 6 cities’ current level corresponding to different criteria

C ₁ C ₂ C ₃ C ₄ C ₅

A ₁ L1 : 1 L1 : 0 L1 : 1 L1 : 0 L1 : 0

L2 : 6 L2 : 6 L2 : 8 L2 : 3 L2 : 5

L3 : 3 L3 : 3 L3 : 1 L3 : 4 L3 : 5

L4 : 0 L4 : 1 L4 : 0 L4 : 3 L4 : 0

L5 : 0 L5 : 0 L5 : 0 L5 : 0 L5 : 0

A ₂ L1 : 1 L1 : 0 L1 : 2 L1 : 1 L1 : 0

L2 : 3 L2 : 5 L2 : 6 L2 : 4 L2 : 3

L3 : 5 L3 : 4 L3 : 2 L3 : 4 L3 : 5

L4 : 1 L4 : 1 L4 : 0 L4 : 1 L4 : 1

L5 : 0 L5 : 0 L5 : 0 L5 : 0 L5 : 1

A ₃ L1 : 0 L1 : 0 L1 : 0 L1 : 0 L1 : 0

L2 : 3 L2 : 6 L2 : 7 L2 : 5 L2 : 2

L3 : 5 L3 : 2 L3 : 3 L3 : 3 L3 : 5

L4 : 2 L4 : 2 L4 : 0 L4 : 2 L4 : 2

L5 : 0 L5 : 0 L5 : 0 L5 : 0 L5 : 1

A ₄ L1 : 2 L1 : 1 L1 : 2 L1 : 0 L1 : 0

L2 : 6 L2 : 6 L2 : 6 L2 : 6 L2 : 4

L3 : 2 L3 : 3 L3 : 2 L3 : 3 L3 : 6

L4 : 0 L4 : 0 L4 : 0 L4 : 1 L4 : 0

L5 : 0 L5 : 0 L5 : 0 L5 : 0 L5 : 0

A ₅ L1 : 3 L1 : 1 L1 : 2 L1 : 2 L1 : 1

L2 : 6 L2 : 7 L2 : 6 L2 : 5 L2 : 4

L3 : 1 L3 : 2 L3 : 2 L3 : 3 L3 : 5

L4 : 0 L4 : 0 L4 : 0 L4 : 0 L4 : 0

L5 : 0 L5 : 0 L5 : 0 L5 : 0 L5 : 0

A ₆ L1 : 2 L1 : 1 L1 : 3 L1 : 2 L1 : 1

L2 : 4 L2 : 6 L2 : 7 L2 : 3 L2 : 3

L3 : 4 L3 : 3 L3 : 0 L3 : 5 L3 : 6

L4 : 0 L4 : 0 L4 : 0 L4 : 0 L4 : 0

L5 : 0 L5 : 0 L5 : 0 L5 : 0 L5 : 0

	C ₁	C ₂	C ₃	C ₄	C ₅
A ₁	L1 : 1	L1 : 0	L1 : 1	L1 : 0	L1 : 0
	L2 : 6	L2 : 6	L2 : 8	L2 : 3	L2 : 5
	L3 : 3	L3 : 3	L3 : 1	L3 : 4	L3 : 5
	L4 : 0	L4 : 1	L4 : 0	L4 : 3	L4 : 0
	L5 : 0	L5 : 0	L5 : 0	L5 : 0	L5 : 0
A ₂	L1 : 1	L1 : 0	L1 : 2	L1 : 1	L1 : 0
	L2 : 3	L2 : 5	L2 : 6	L2 : 4	L2 : 3
	L3 : 5	L3 : 4	L3 : 2	L3 : 4	L3 : 5
	L4 : 1	L4 : 1	L4 : 0	L4 : 1	L4 : 1
	L5 : 0	L5 : 0	L5 : 0	L5 : 0	L5 : 1
A ₃	L1 : 0	L1 : 0	L1 : 0	L1 : 0	L1 : 0
	L2 : 3	L2 : 6	L2 : 7	L2 : 5	L2 : 2
	L3 : 5	L3 : 2	L3 : 3	L3 : 3	L3 : 5
	L4 : 2	L4 : 2	L4 : 0	L4 : 2	L4 : 2
	L5 : 0	L5 : 0	L5 : 0	L5 : 0	L5 : 1
A ₄	L1 : 2	L1 : 1	L1 : 2	L1 : 0	L1 : 0
	L2 : 6	L2 : 6	L2 : 6	L2 : 6	L2 : 4
	L3 : 2	L3 : 3	L3 : 2	L3 : 3	L3 : 6
	L4 : 0	L4 : 0	L4 : 0	L4 : 1	L4 : 0
	L5 : 0	L5 : 0	L5 : 0	L5 : 0	L5 : 0
A ₅	L1 : 3	L1 : 1	L1 : 2	L1 : 2	L1 : 1
	L2 : 6	L2 : 7	L2 : 6	L2 : 5	L2 : 4
	L3 : 1	L3 : 2	L3 : 2	L3 : 3	L3 : 5
	L4 : 0	L4 : 0	L4 : 0	L4 : 0	L4 : 0
	L5 : 0	L5 : 0	L5 : 0	L5 : 0	L5 : 0
A ₆	L1 : 2	L1 : 1	L1 : 3	L1 : 2	L1 : 1
	L2 : 4	L2 : 6	L2 : 7	L2 : 3	L2 : 3
	L3 : 4	L3 : 3	L3 : 0	L3 : 5	L3 : 6
	L4 : 0	L4 : 0	L4 : 0	L4 : 0	L4 : 0
	L5 : 0	L5 : 0	L5 : 0	L5 : 0	L5 : 0

(4) Aggregation of experts’ evaluation

According to the definition of PLTS, Table 2 can be translated into the following decision matrix B with PLTSs. Here, we assume that the five levels (L1, L2, L3, L4, L5) are the corresponding linguistic fuzzy terms s₀, s₁, s₂, s₃, s₄. The probability for the linguistic fuzzy term is calculated by ratio of the members of experts choosing this level out of the total members of experts. $B = [\begin{matrix} {(s_{0}, 0.1), (s_{1}, 0.6), (s_{2}, 0.3)} & {(s_{1}, 0.6), (s_{2}, 0.3), (s_{3}, 0.1)} \\ {(s_{0}, 0.1), (s_{1}, 0.3), (s_{2}, 0.5), (s_{3}, 0.1)} & {(s_{1}, 0.5), (s_{2}, 0.4), (s_{3}, 0.1)} \\ {(s_{1}, 0.3), (s_{2}, 0.5), (s_{3}, 0.2)} & {(s_{1}, 0.6), (s_{2}, 0.2), (s_{3}, 0.2)} \\ {(s_{0}, 0.2), (s_{1}, 0.6), (s_{2}, 0.2)} & {(s_{0}, 0.1), (s_{1}, 0.6), (s_{2}, 0.3)} \\ {(s_{0}, 0.3), (s_{1}, 0.6), (s_{2}, 0.1)} & {(s_{0}, 0.1), (s_{1}, 0.7), (s_{2}, 0.2)} \\ {(s_{0}, 0.2), (s_{1}, 0.4), (s_{2}, 0.4)} & {(s_{0}, 0.1), (s_{1}, 0.6), (s_{2}, 0.3)} \end{matrix} \to$ $\begin{matrix} {(s_{0}, 0.1), (s_{1}, 0.8), (s_{2}, 0.1)} & {(s_{1}, 0.3), (s_{2}, 0.4), (s_{3}, 0.3)} & {(s_{1}, 0.5), (s_{2}, 0.5)} \\ {(s_{0}, 0.2), (s_{1}, 0.6), (s_{2}, 0.2)} & {(s_{0}, 0.1), (s_{1}, 0.4), (s_{2}, 0.4), (s_{3}, 0.1)} & {(s_{0}, 0.3), (s_{1}, 0.5), (s_{2}, 0.1), (s_{3}, 0.1)} \\ {(s_{1}, 0.7), (s_{2}, 0.3)} & {(s_{1}, 0.5), (s_{2}, 0.3), (s_{3}, 0.2)} & {(s_{1}, 0.2), (s_{2}, 0.5), (s_{3}, 0.2), (s_{4}, 0.1)} \\ {(s_{0}, 0.2), (s_{1}, 0.6), (s_{2}, 0.2)} & {(s_{1}, 0.6), (s_{2}, 0.3), (s_{3}, 0.1)} & {(s_{1}, 0.4), (s_{2}, 0.6)} \\ {(s_{0}, 0.2), (s_{1}, 0.6), (s_{2}, 0.2)} & {(s_{0}, 0.2), (s_{1}, 0.5), (s_{2}, 0.3)} & {(s_{0}, 0.1), (s_{1}, 0.4), (s_{2}, 0.5)} \\ {(s_{0}, 0.3), (s_{1}, 0.7)} & {(s_{0}, 0.2), (s_{1}, 0.3), (s_{2}, 0.5)} & {(s_{0}, 0.1), (s_{1}, 0.3), (s_{2}, 0.6)} \end{matrix}]$

Next, quality regulatory capability maturity in GPPS of the six cities will be evaluated and ranked based on the TODIM method for PLTSs.

Step 1. Calculate the criteria weights w = (0.18, 0.2, 0.12, 0.21, 0.28) according to Equation (7)

Step 2. Compute the relative weights w_r = (0.63, 0.69, 0.44, 0.76, 1) based on Equation (8).

Step 3. Calculate the dominance degree for A_i over A_k in all criteria Φ (A_i, A_k) according to Equations (9-10) (shown in Table 3).

Table 3

Dominance degrees for 6 cities

	A ₁	A ₂	A ₃	A ₄	A ₅	A ₆
A ₁	0	–2.99	–4.9	0.11	0.99	1.19
A ₂	–1.56	0	–3.37	2.18	2.17	2.6
A ₃	0.99	0.15	0	2.35	2.37	2.61
A ₄	–4.51	–4.84	–6.14	0	1.25	1.23
A ₅	–5.26	–5.05	–6.51	–3.7	0	–3.79
A ₆	–6.46	–7.64	–7.77	–3.61	–0.92	0

Step 4. Compute the overall dominance degree $\begin{matrix} Z (A_{1}) = 0.6, Z (A_{2}) = 0.82, Z (A_{3}) = 1, \\ Z (A_{4}) = 0.38, Z (A_{5}) = 0.06, Z (A_{6}) = 0 \end{matrix}$

Therefore, the ranking result is A₃ ≻ A₂ ≻ A₁ ≻ A₄ ≻ A₅ ≻ A₆.

5.3 Comparison with TOPSIS method proposed by Pang et al. [16]

To illustrate the advantage and feasibility of our method, we carry out a comparative analysis with TOPSIS method proposed by Pang et al. [16], in which the main decision-making procedure is shown as follows:

Compute the criteria weights w = (w₁, w₂, ⋯ , w_n);

Determine the positive ideal solution (PIS) L (p) ⁺ and the negative ideal solution (NIS) L (p) ^-;

Compute the deviation degree $d_{i}^{+}$ between each alternative A_i and L (p) ⁺ according to Equation (5);

Compute the deviation degree $d_{i}^{-}$ between each alternative A_i and L (p) ^- according to Equation (5);

Compute the closeness coefficient for alternative A_i as $CI (A_{i}) = \frac{d_{i}^{-}}{max_{i} {d_{i}^{-}}} - \frac{d_{i}^{+}}{min_{i} {d_{i}^{+}}}$ ;

Rank the alternatives according to the closeness coefficient CI (A_i).

We apply the above procedure to solve our decision problem as follows:

The criteria weights are w = (0.18, 0.2, 0.12, 0.21, 0.28);

The PIS and NIS are computed as $\begin{matrix} L (p)^{+} = ({s_{1}, s_{0.6}, s_{0.3}, s_{0}}, {s_{0.8}, s_{0.6}, s_{0.4}}, \\ {s_{0.8}, s_{0.6}, s_{0}}, {s_{1}, s_{0.8}, s_{0.5}, s_{0}}, \\ {s_{1.2}, s_{0.6}, s_{0.4}, s_{0.2}}) \end{matrix}$ $\begin{matrix} L (p)^{-} = ({s_{0.6}, s_{0.2}, s_{0}, s_{0}}, {s_{0.6}, s_{0.4}, s_{0}}, \\ {s_{0.6}, s_{0}, s_{0}}, {s_{0.6}, s_{0.4}, s_{0}, s_{0}}, {s_{0.5}, s_{0.3}, s_{0}, s_{0}}) \end{matrix}$

The deviation degrees between each alternative A_i and L (p) ⁺ are $\begin{matrix} d_{1}^{+} = 0.19, d_{2}^{+} = 0.23, d_{3}^{+} = 0.51, \\ d_{4}^{+} = 0.46, d_{5}^{+} = 0.28, d_{6}^{+} = 0.28 . \end{matrix}$

The deviation degrees between each alternative A_iand L (p) ^- are $\begin{matrix} d_{1}^{-} = 0.23, d_{2}^{-} = 0.18, d_{3}^{-} = 0.29, \\ d_{4}^{-} = 0.21, d_{5}^{-} = 0.12, d_{6}^{-} = 0.2 . \end{matrix}$

The closeness coefficients for alternative A_i are $\begin{matrix} CI (A_{1}) = - 0.2, CI (A_{2}) = - 0.56, CI (A_{3}) = - 1.67, \\ CI (A_{4}) = - 1.69, CI (A_{5}) = - 1.04, CI (A_{6}) = - 0.79 . \end{matrix}$

The ranking result is A₁ ≻ A₂ ≻ A₆ ≻ A₅ ≻ A₃ ≻ A₄.

5.4 Comparison with VIKOR method proposed by Wang et al. (2018)

The main decision steps of VIKOR method proposed by Wang et al. (2018) can be described as follows.

Calculate the criteria weights w = (w₁, w₂, ⋯ , w_n) ;

Determine the PIS $R^{+} = (r_{1}^{+}, r_{2}^{+}, \dots, r_{n}^{+})$ and the NIS $R^{-} = (r_{1}^{-}, r_{2}^{-}, \dots, r_{n}^{-})$ ,

where $r_{j}^{+} = max_{i} {b_{ij}}$ , $r_{j}^{-} = min_{i} {b_{ij}}$ (j = 1, 2, ⋯ , n).

Compute the group utility $U_{i} = \sum_{j = 1}^{n} w_{j} \frac{d (b_{ij}, r_{j}^{+})}{d (r_{j}^{-}, r_{j}^{+})};$

Computer the individual regret value $R_{i} = max_{j} {\frac{d (b_{ij}, r_{j}^{+})}{d (r_{j}^{-}, r_{j}^{+})}};$

Compute the value $Q_{i} = θ \frac{U_{i} - min_{i} {U_{i}}}{\underset{i}{max_{i} {U_{i}} - min} {U_{i}}} + (1 - θ) \frac{R_{i} - min_{i} {R_{i}}}{max_{i} {R_{i}} - min_{i} {R_{i}}},$

where θ is parameter and usually equal to 0.5;

Rank the alternatives based on Q_i and choose the compromise solution(s) according to VIKOR rules (See Wang et al. (2018)).

We use the VIKOR method to solve our decision problem as follows.

To make the comparison reasonable we choose the weights w = (0.18, 0.2, 0.12, 0.21, 0.28) ;

The PIS and NIS are computed as $\begin{matrix} R^{+} = ({s_{1}, s_{0.6}, s_{0.3}, s_{0}}, {s_{0.8}, s_{0.6}, s_{0.4}}, {s_{0.8}, \\ s_{0.6}, s_{0}}, {s_{1}, s_{0.8}, s_{0.5}, s_{0}}, {s_{1.2}, s_{0.6}, s_{0.4}, s_{0.2}}) \end{matrix}$ $\begin{matrix} R^{-} = ({s_{0.6}, s_{0.2}, s_{0}, s_{0}}, {s_{0.6}, s_{0.4}, s_{0}}, {s_{0.6}, \\ s_{0}, s_{0}}, {s_{0.6}, s_{0.4}, s_{0}, s_{0}}, {s_{0.5}, s_{0.3}, s_{0}, s_{0}}); \end{matrix}$

The group utility can be obtained as $\begin{matrix} U_{1} = 0.524, U_{2} = 0.579, U_{3} = 0.279, \\ U_{4} = 0.67, U_{5} = 0.771, U_{6} = 0.768 . \end{matrix}$

The individual regret value can be obtained as $\begin{matrix} R_{1} = 0.158, R_{2} = 0.257, R_{3} = 0.115, \\ R_{4} = 0.184, R_{5} = 0.189, R_{6} = 0.184 . \end{matrix}$

We can obtain Q₁ = 0.402, Q₂ = 0.805, Q₃ = 0, Q₄ = 0.642, Q₅ = 0.761, Q₆ = 0.741 ..

As Q₃ < Q₁ < Q₄ < Q₆ < Q₅ < Q₂, we can easily obtain the ranking result A₃ ≻ A₁ ≻ A₄ ≻ A₆ ≻ A₅ ≻ A₂. Furthermore, as $Q_{1} - Q_{3} = 0.402 > \frac{1}{6 - 1}$ , U₃ and R₃ are the smallest values respectively, we can choose the compromise solution A₃.

It can be easily found that the results are different between our proposed method and the two existing methods, as shown in Table 4. The main reason lies in the fact that our proposed method uses TODIM considering the bounded rationality of decision makers. In fact, in most cases, decision makers may be bounded rational and focus more on changes between the reference point and the actual evaluation. Therefore, our method may be more reasonable than the above existing methods.

Table 4
Ranking results of different methods

Methods Ranking results

Our proposed method A₃ ≻ A₂ ≻ A₁ ≻ A₄ ≻ A₅ ≻ A₆

TOPSIS method proposed by Pang et al. (2016) A₁ ≻ A₂ ≻ A₆ ≻ A₅ ≻ A₃ ≻ A₄

VIKOR method proposed by Wang et al. (2018) A₃ ≻ A₁ ≻ A₄ ≻ A₆ ≻ A₅ ≻ A₂

Methods	Ranking results
Our proposed method	A₃ ≻ A₂ ≻ A₁ ≻ A₄ ≻ A₅ ≻ A₆
TOPSIS method proposed by Pang et al. (2016)	A₁ ≻ A₂ ≻ A₆ ≻ A₅ ≻ A₃ ≻ A₄
VIKOR method proposed by Wang et al. (2018)	A₃ ≻ A₁ ≻ A₄ ≻ A₆ ≻ A₅ ≻ A₂

5.5 Results and discussion

From the results in Table 3, we can see that Suzhou ranks first among these 6 cities, while Xuzhou ranks the 6th. In fact, as a developed city not only in Jiangsu, but also in China, Suzhou also has done very well in the implementation of the policy of GPPS. Suzhou has published different kinds of guidelines and measures to implement and promote the policy of GPPS. “Guidelines for implementation of GPPS”, “Methods for cost regulation in GPPS”, “Rules for the implementation of GPPS”, et al. have been issued in succession recent years, which contribute a lot to the successful promotion and effective management of GPPS in Suzhou. Meanwhile, there’re many innovations and good practices of GPPS in Suzhou, and plenty of experiences related to the quality supervision and regulation have also been gained. Suzhou excels not only in policy making, but also in process management, multi-part participation, as well as in the effectiveness. So, it is quite reasonable and understandable that Suzhou ranks the first. Then, we can see from Table 12 that Nanjing ranks the 3rd among these 6 cities. Nanjing is the provincial capital of Jiangsu. It should have done well in GPPS in most peoples’ opinions. As a matter of fact, it indeed has done well in certain aspects, especially in policy making and implementation, as well as in multi-party participation. As shown in Table 3, in policy making and implementation, Nanjing overmatches the other 5 cities, ranking the first. In multi-participation, Nanjing ranks 2nd, only slightly weaker than Suzhou. In order to enhance the quality regulation capability in GPPS, Nanjing should do much more in process management, and focus on the improvement of effectiveness. We also take a close look at Lianyungang and Xuzhou, which rank the 5th and 6th among the 6 cities. Although Lianyungang is better than Xuzhou in this ranking list, the advantage is rather minor. The two are almost the similar in quality regulation in GPPS. Much remains to do for them to enhance their capability. Effective policies needed to be made and issued to guide the practice, more attention should be paid to multi-party participation of the quality regulation, and they should also learn from others to do more efficiently in process management, so as to improve the effectiveness at last.

6 Conclusions

Existing research on regulatory capability evaluation focuses on evaluation of static capability, which guides less in the practice of building and improving the regulatory capability. The quality supervision capability maturity evaluation model for GPPS proposed in this paper is a dynamic evaluation method facing processes, which can better reflect the comprehensive effect in quality regulation for GPPS. Meanwhile, the evaluation model based on TODIM method for PLTSs fully reflects experts’ preferences and evaluation information. The established maturity evaluation model for quality supervision capability can not only evaluate and determine the maturity level, but also can help local governments discover their current weaknesses, thus coming up with individualized solutions for improvement, which will surely make the quality supervision capability promoted level by level, and help the formulation of the continuously improving mode for quality supervision capability in GPPS. Our research is of positive significance to perfect the regulation system and enhance the supervision capability in the practice of GPPS. Comparable evaluation results could be got through the evaluation of supervision process, giving consideration to both static and dynamic effectiveness, which will help local governments establish the continuously improving mode for supervision capability in the practice of GPPS, thus efficiently enhancing the quality supervision effectiveness. Meanwhile, combined with the practical requirement of GPPS, we have explored the new application field of CMM, as well as the improvement to this model, which will help develop the CMM theory, and enrich its theoretical system. The problem of supervision capability evaluation in GPPS is addressed in this paper. However, how to improve the quality supervision capability maturity is not addressed. In the future, we will study the mechanism of quality control for GPPS, as well as the establishment of quality management system.

Footnotes

Acknowledgments

The authors would like to thank the National Natural Science Foundation of China (71403109, 71401064), the Humanities and Social Sciences Foundation of Jiangsu Province (16JYC002), Ministry of Education Foundation of Humanities and Social Sciences (Nos. 19YJA630039, 19YJA880068).

References

Grudinschi

, Sintonen

and Hallikas

, Relationship risk perception and determinants of the collaboration fluency of buyer–supplier relationships in public service procurement, Journal of Purchasing and Supply Management 20(2) (2014), 82–91.

, Zhou

and Liu

, The US experience of contracting for public services and lessons for china: A case study of public service, Journal of Public Administration 4 (2016), 4–22.

Wang

, Reformation of government’s purchasing public service from social forces: Analysis and its implications, Journal of Jilin University: Social Sciences Edition (4) (2015), 78–89.

Yang

, Research on the government purchase of public cultural services: A case study of Jiangsu local government, Nanjing University (2018).

Dong

and Ju

, Research on the quality guarantee mechanism of government purchasing public service, Chinese Public Administration 5 (2016), 43–37.

Liu

and Liu

Z.P.

, Measurement and Evaluation of Social Regulatory Agency’s Capacity: A Comparative Study among Three Regulatory Departments, Wuhan University Journal (Philosophy & Social Sciences) 69(4) (2016), 57–74.

Wang

, Zhao

and Zeng

, Research on the quality management mechanism of Chinese Government procurement of public services, Canadian Social Science 11(8) (2015), 27–31.

Rodriguez

R.M.

, Martinez

and Herrera

, Hesitant fuzzy linguistic term sets for decision making, IEEE Transactions on Fuzzy Systems 20(1) (2012), 109–119.

Zhang

G.Q.

, Dong

Y.C.

and Xu

Y.F.

, Consistency and consensus measures for linguistic preference relation based on distribution assessment, Information Fusion 17 (2014), 46–55.

10.

Dong

Y.C.

, Wu

Y.Z.

, Zhang

H.J.

and Zhang

G.Q.

, Multi-granular unbalanced linguistic distribution assessments with interval symbolic proportions, Knowledge-based Systems 82 (2015), 139–151.

11.

Dong

Y.C.

, Xu

Y.F.

and Yu

, Computing the Numerical Scale of the Linguistic Term Set for the 2-Tuple Fuzzy Linguistic Representation Model, IEEE Transactions on Fuzzy Systems 17(6) (2009), 1366–1378.

12.

Dong

Y.C.

, Zhang

G.Q.

and Hong

W.C.

, Linguistic Computational Model Based on 2-Tuples and Intervals, IEEE Transactions on Fuzzy Systems 21(6) (2013), 1006–1018.

13.

C.C.

, Dong

Y.C.

, Herrera

, Herrera-Viedma

and Martínez

, Personalized individual semantics in computing with words for supporting linguistic group decision making. An application on consensus reaching, Information Fusion 33 (2017), 29–40.

14.

C.C.

, Rodríguez

R.M.

, Martínez

, Dong

Y.C.

and Herrera

, Personalized individual semantics based on consistency in hesitant linguistic group decision making with comparative linguistic expressions, Knowledge-Based Systems 145 (2018), 156–165.

15.

C.C.

, Dong

Y.C.

and Herrera

, A consensus model for large-scale group decision making with a feedback recommendation based on clustered personalized individual semantics and opposing consensus groups, IEEE Transactions on Fuzzy Systems 27 (2019), 221–233.

16.

Pang

, Wang

and Xu

, Probabilistic linguistic term sets in multi-attribute group decision making, Information Sciences 369 (2016), 128–143.

17.

Zhang

, Xu

, Wang

and Liao

, Consistency-based risk assessment with probabilistic linguistic preference relation, Applied Soft Computing 49(C) (2016), 817–833.

18.

S.M.

, Wang

J.Q.

and Li

, A multi-criteria decision-making model for hotel selection with linguistic distribution assessments, Applied Soft Computing (2017). https://dx-doi-org.web.bisu.edu.cn/10.1016/j.asoc.2017.08.009.

19.

and Liao

, An approach to quality function deployment based on probabilistic linguistic term sets and ORESTE method for multi-expert multi-criteria decision making, Information Fusion 43 (2018), 13–26.

20.

Peng

H.G.

, Zhang

H.Y.

and Wang

J.Q.

, Cloud decision support model for selecting hotels on tripadvisor.com with probabilistic linguistic information, International Journal of Hospitality Management 68 (2018), 124–138.

21.

Bai

, Zhang

, Qian

and Wu

, Comparisons of probabilistic linguistic term sets for multi-criteria decision making, Knowledge-Based Systems 119(C) (2016), 284–291.

22.

Gou

and Xu

, Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets, Information Sciences 372 (2016), 407–427.

23.

Long

, Building internal supervision capability in organizations, The OCM Coach and Mentor Journal 3 (2012), 2–5.

24.

Kjeldsen

A.M.

, Dynamics of public service motivation: Attraction— selection and socialization in the production and regulation of social services, Public Administration Review 74(1) (2014), 101–112.

25.

Yadav

, Building regulatory capabilities for pharmaceutical firms’ internationalization, International Journal of Pharmaceutical & Healthcare Marketing 7(1) (2013), 58–74.

26.

Mcallister

L.K.

, Dimensions of enforcement style: Factoring in regulatory autonomy and capacity, Law & Policy 32(1) (2010), 61–78.

27.

Rooij

B.V.

, Implementation of Chinese environmental law: Regular enforcement and political campaigns, Development and Change 37(1) (2006), 57–74.

28.

Liu

, Li

and Cheng

, Cooperation management, relationship quality, outsourcing effect in sanitation service outsourcing——on the example of Shenzhen, Management Review 28(2) (2016), 197–209.

29.

, The performance evaluation system of American urban public utilities regulation, Chinese Public Administration(6) (2014), 114–119.

30.

Yang

, A study on the theoretical paradigm and roadmap of enhancing china’s regulatory governance system–implications of responsive regulatory theory, Chinese Public Administration (6) (2014), 47–54.

31.

J.H.

, Yang

and Chen

X.H.

, A novel TODIM method based three-way decision model for medical treatment selection, International Journal of Fuzzy Systems 20(4) (2018), 1240–1255.

32.

, Pan

and Zhang

, The role transition researches of the government in public service outsourcing, Open Journal of Business & Management 3(4) (2015), 465–470.

33.

Lodi

, Malaguti

, Stiermoses

N.E.

and Bonino

, Design and control of public-service contracts and an application to public transportation systems, Management Science 62(1) (2016), 1165–1187.

34.

Johansson

, Siverbo

and Camén

, Managing cooperation, coordination, and legitimacy, Accounting Auditing & Accountability Journal 29(6) (2016), 1012–1037.

35.

Cunningham

and James

, Analysing public service outsourcing: The value of a regulatory perspective, Environment & Planning C 35(6) (2016).

36.

Ainuddin , Abdullah

, Djumardin and Nurjaya

, The essence of transparency principle in the procurement of goods and government services through the exchange (Ruilslag): Towards good governance in public services, American and Chinese Law Review (8) (2016), 597–614.

37.

Maciejewski

, To do more, better, faster and more cheaply: Using big data in public administration, International Review of Administrative Sciences (online first) (1) (2016).

38.

Ida

and Talit

, Regulation of public bus services: The Israeli experience, Transport Policy 42 (2015), 156–165.

39.

Lin

S.F.

, Understanding the effectiveness of capability maturity model integration by examining the knowledge management of software development processes, Total Quality Management & Business Excellence 20(5) (2009), 509–521.

40.

Cafaggi

and Pistor

, Regulatory capabilities: A normative framework for assessing the distributional effects of regulation, Regulation & Governance 9(2) (2015), 95–107.

41.

Wang

K.J.

, Widagdo

, Lin

Y.S.

, Yang

H.L.

and Hsiao

S.L.

, A service innovation framework for start-up firms by integrating service experience engineering approach and capability maturity model, Service Business 10(4) (2016), 1–50.

42.

Carroll

and Helfert

, Service capabilities within open innovation - revisiting the applicability of capability maturity models, Journal of Enterprise Information Management 28(2) (2015), 275–303.

43.

Benmoussa

, Abdelkabir

, Abd

and Hassou

, Capability/maturity-based model for logistics processes assessment, International Journal of Productivity & Performance Management 64(1) (2017), 28–51.

44.

Krishnan

, Thompson

S.H.

and Lymm

, Determinants of electronic participation and electronic government maturity: Insights from cross-country data, International Journal of Information Management 37(4) (2017), 297–312.

45.

Pongsuwan

, How does procurement capability maturity affect e-procurement adoption and leverage purchasing in supply chain? International Journal of Business and Economic Development 4(3) (2016), 45–54.

46.

Rendon

R.G.

, Benchmarking contract management process maturity: A case study of the US navy, Benchmarking: An International Journal 22(7) (2015), 1481–1508.

47.

Gomes

L.F.A.M.

and Lima

M.M.P.P.

, TODIM: Basics and application to multicriteria ranking of projects with environmental impacts, Foundations of Computing and Decision Sciences 16 (1991), 113–127.

48.

, Zhang

H.Y.

and Wang

J.Q.

, A projection-based TODIM method under multi-valued neuromorphic environments and its application in personnel selection, Neural Computing & Applications 29 (2018), 221–234.

49.

Llamazares

, An analysis of the generalized TODIM method, European Journal of Operational Research 269 (2018), 1041–1049.

Evaluation for quality regulatory capability maturity in government procurement of public service based on probabilistic linguistic term sets

Abstract

Keywords

1 Introduction

2 Literature review

2.1 Evaluation of regulatory capability

2.2 Regulation in government procurement of public service (GPPS)

3 The evaluation criteria development for quality regulatory capability in GPPS based on CMM

3.1 CMM and the feasibility analysis of its application into quality regulatory capability evaluation criteria development

3.2 Evaluation criteria development of regulatory capability maturity in GPPS

3.2.1 Levels of regulatory capability maturity

4.1 Preliminaries

4.2.1 Obtaining the criteria weights by maximizing deviation method

5 Case study

5.1 Description

5.2 Evaluations

5.4 Comparison with VIKOR method proposed by Wang et al. (2018)

Table 4 Ranking results of different methods Methods Ranking results Our proposed method A3 ≻ A2 ≻ A1 ≻ A4 ≻ A5 ≻ A6 TOPSIS method proposed by Pang et al. (2016) A1 ≻ A2 ≻ A6 ≻ A5 ≻ A3 ≻ A4 VIKOR method proposed by Wang et al. (2018) A3 ≻ A1 ≻ A4 ≻ A6 ≻ A5 ≻ A2

6 Conclusions

Footnotes

Acknowledgments

References