Evaluation of Energy Saving and Emission Reduction Effects for Electricity Retailers in China Based on Fuzzy Combination Weighting Method

Featured Application

The application of this research aims to provide an effective indicator system and evaluation method of energy saving and emission reduction effects for current electricity retailers in China, and give the specific directions for the electric power industry to adopt energy saving and emission reduction actions.

Abstract

China’s electricity market is in the environment for a round of new electric power reform, energy planning and transformation and the carbon market construction. The current market players are in urgent need of implementing their own energy saving and emission reduction actions. Relatively extensive and systematic researches on the assessment of the energy saving and emission reduction effects for the power plants, power grid companies, and technical equipment have been carried out at home and abroad. However, there are still vacancies in the researches on those for electricity retailers emerged on the sales side. Based on the carding and analysis of related policies and guidance, in this paper, relevant indicators are considered to build the evaluation indicator system of the energy saving and emission reduction effects for electricity retailers. The combination weights are gained by means of analytic hierarchy process and entropy weight method. Then, after the combined empowerment of indicators, the multi-level fuzzy comprehensive evaluation of energy saving and emission reduction effects for electricity retailers is conducted. Finally, choosing 10 electricity retailers (numbered from A to J) as evaluation objects, this model is used for obtaining the evaluation results and ranking of energy saving and emission reduction effects of electricity retailers, which provides reasonable ideas for the construction of evaluation indicator system and effective comprehensive evaluation methods of energy saving and emission reduction effects for market players in the electricity sales side. The results of example analysis show that, from a single dimension, the best electricity retailers in market transactions, technical means, integrated energy services, management system, and social responsibilities are followed by B, J, D, G, C, or I. However, from a global perspective, the sorted evaluation results are D, J, I, A, H, G, E, B, F, and C, which reflects the overall energy saving and emission reduction effects of electricity retailers through the two-level fuzzy comprehensive evaluation.

1. Introduction

1.1. Research Background and Significance

The transformation and upgrading of China’s energy structure requires all walks of life to take an active part in energy saving and emission reduction, in order to cope with climate changes and work together to fulfill the national commitment to energy saving and emission reduction. As one of the most important component in the energy industry, the electric power industry is also bound to be involved in the energy saving and emission reduction actions, which aims at developing the way of low-carbon electricity vigorously to have the environmental pollution cut down and improve the energy efficiency utilization. At present, with the further development of the new round of electric power reform, the electricity sale side forms a market structure with the electricity retailers as the main competitive players. To push for the energy saving and emission reduction process in the electricity sales side, it is necessary to combine the multi-party policy documents. Namely, to analyze important documents in three aspects of the electric power reform, energy planning transformation, and carbon market construction issued by government departments. The attention to these policy documents should be placed on the following two points. Firstly, the current reform reflects the necessity of setting up electricity retailers in China’s electricity sales market. Secondly, all three have released the signal of new energy development in the market. To achieve green power as the long-term goal of China’s electric power industry, market players should actively participate in energy saving and emission reduction at this stage. Therefore, in the research on the energy saving and emission reduction effects for current electricity retailers in China, it is possible to make a reasonable assessment by combining the policy documents closely and understanding the market development orientation, which helps to provide guidance for electricity retailers to improve the effects to enhance the competitiveness and achieve long-term development by taking timely actions.

1.2. Research Status

At this stage, domestic and foreign scholars have conducted numerous researches on the energy saving and emission reduction of the electric power industry in China. On the one hand, some researches laid particular emphasis on the power production technologies and power equipments [1,2,3,4], qualitative assessment and quantitative analysis were carried out to evaluate the impact on energy saving and emission reduction by improving and applying those technologies and equipments.

Liu [1] analyzed the effects of energy saving and emission reduction for electric systems while using high-voltage frequency conversion technology, which proved that the appliance of this technology can help power plants to achieve a high-level energy saving. Jiang et al. [2] conducted the assessment of the effects of central heating supplied by large coal-fired power unit and then put forward relative measures to improve the energy efficiency. Lu et al. [3] researched on the effects after the application of advanced equipments in the fields of power transmission and transformation. The use of switching equipment to achieve energy saving and emission reduction was put forward. Luo and Ya [4] proposed to realize the saving and emission reduction in the electric power industry through resource optimization configuration technology and implemented corresponding actions at the strategic level.

On the other hand, most researches focused on the use of different comprehensive evaluation methods to assess the energy saving and emission reduction effects for the power plants [5,6,7,8,9,10,11,12,13,14] and power grid companies [15,16,17,18].

Xu and Zeng [5] established an evaluation indicator system of energy saving and emission reduction technologies form the resource and energy consumption, pollutant discharge, economic benefits, and technical performance. Next, the interval-value comprehensive method was selected to assess the effects. Chen [6] selected evaluation indicators according to the subsystems of energy saving and consumption reduction, pollutant discharge reduction, energy saving, and emission reduction relations of thermal power companies, then conducted the assessment. Cao et al. [7] built an indicator system mainly reflected the actual production status of thermal power plants and evaluated the energy saving and emission reduction effects through grey correlation analysis method. Wang and Xie [8] chose the technical indicators of biomass power generation to finish the assessment. Li et al. [9] designed an evaluation indicator system for thermal power companies from two perspectives of energy saving and pollutant reduction. The effects were assessed based on entropy-weighted extentic method. Jia et al. [10] adopted the way that combined factor analysis and DEA (data envelopment analysis) to analyze the energy saving and emission reduction effects of power generation enterprises. During the process of evaluating energy saving and emission reduction performance of power generation companies, Zhang [11] established the indicator system from six dimensions, including energy resource utilization, pollutant discharge, and efficiency improvement, etc. It also put forward the evaluation model based on network-level analysis method and improved gray clustering decision-making. The evaluation indicator system that is proposed by Bo et al. [12] includes aspects, such as coal saving, electricity saving, water saving, and pollutant discharge, which could evaluate the status of emissions reduction of coal-fired power plant more comprehensively. Cao et al. [13] utilized the indicators of consumption and emissions to have an integrated evaluation for power plants, which was carried out by means of entropy weight based on fuzzy matter element model. Ding et al. [14] studied on the benefits of energy saving and emission reduction sides for domestic small hydropower ecological protection projects through econometric models. Zhou [15] put forward projection pursuit based on AHP (analytic hierarchy process) to construct an assessment model. Coal-fired electricity replacement, grid losses, and pollutant emissions were considered for regional power grids. Zeng et al. [16] analyzed the effects of power grid enterprises from three angles, followed by the generation side, supply side, and demand side, which reflects the dedication of energy saving and emission reduction under different perspectives. Liu [17] researched on the contribution to energy saving and emission reduction not only form power grid enterprises, but upstream companies and downstream users. To evaluate the potential of energy saving and emission reduction for the regional power grid, Wu et al. constructed three types of indicators, including power flow, power supply structure, and technology economy [18].

From the above research status, we can know that the quantitative indicators of energy consumption, wastewater discharge, and exhaust pollutant emissions are often determined to establish the indicator system of the energy saving and emission reduction effects in most previous studies. However, the indicator system established only based on these aspects is the lack of timely interpretation of new policies. The selection of evaluation indicators needs to be further combined with qualitative indicators that are closely related to policies. The evaluation indicator system of the energy saving and emission reduction effects still needs to be improved. These qualitative indicators refer to the difficulty of obtaining accurate data, or need to be considered form several aspects together as a whole, which still reflect the energy saving and emission reduction effects of companies in many ways. For example, the responsiveness to energy planning and market reform, the execution of participation in carbon market construction and the extent to which relevant knowledge is imparted to employees. Simultaneously, research objects of the energy saving and emission reduction effects are concentrated on power technologies or equipments, power plants, and power grid companies. In addition to the above studies, references [19,20,21] also explored the energy saving and emission reduction benefits brought by the improvement of coal-fired power plant boilers and steam turbines. Reference [22] analyzed the impact of the application of distributed generation and micro grid technology on the effects of power plants. Reference [23,24] studied the implementation path of energy saving and emission reduction for power generation companies and the management measures of power grid companies, respectively. While there are few studies on the evaluation in the electricity sales side. Therefore, the scope of evaluation of the energy saving and emission reduction effects needs to be further expanded.

The fuzzy comprehensive evaluation method is widely used to assess objects with ambiguity. Reference [25] constructed a model combining fuzzy evaluation with AHP. In [26], the fuzzy evaluation based on ISM-AHP (interpretative structural modelling method and analytic hierarchy process) was applied to build a multi-level hierarchical interpretation structure model for quantitative analysis. Reference [27] combined the fuzzy min-max method with the defuzzified centroid method to establish a logic system. In [28], the improved interval number was used for ANP (analytic network process). On this basis, the fuzzy comprehensive evaluation model was proposed to effectively solve the problem of information loss and data fluctuation. It can be seen that in order to improve the objectivity of this method, a certain number of researches have corrected the weights of indicators by combining different methods.

1.3. Main Research Contents

The research contents of this paper are mainly divided into six parts. In the first part, the influence of policy opinions on the energy saving and emission reduction actions on the sales side is arranged, the status of energy saving and emission reduction is analyzed, and the future development trend is prejudged from the view of China’s new electric power reform, energy planning and transition, and carbon market construction, which provides guidance for the selection of evaluation indicator system of the energy saving and emission reduction effects for electricity retailers in China. In the second part, the energy saving and emission reduction effects of electricity retailers are set as the total evaluation target. Qualitative and quantitative indicators are chosen from five dimensions of market transactions, technical means, integrated energy services, management system, and social responsibilities. Then, the three-level evaluation indicator system of the energy saving and emission reduction effects for electricity retailers is constructed. In the third part, the indicator hierarchy is firstly classified and subjective weights of indicators are determined by AHP. Next, objective weights are determined based on the entropy weight method, in which the method is used for modifying the subjectivity of AHP. At last, combination weights of the evaluation indicator system are gained. In the fourth part, a fuzzy evaluation model on the basis of the combination weighting method is proposed to evaluate the energy saving and emission reduction effects for electricity retailers. In the fifth part, the example analysis proves that both the evaluation indicator system and the evaluation model based on fuzzy combination weighting method put forward in this paper can make a reasonable and scientific evaluation of the energy saving and emission reduction effects for electricity retailers in China. In the sixth part, conclusions are summarized to reflect the main innovation and the value of research in this paper.

2. Present Situation and Development Prospect Analysis of Energy Saving and Emission Reduction in China’s Electric Power Industry

2.1. Overview of Relevant Policy Guidance in the Electric Power Industry

In recent years, China has been committed to accelerating the economic restructuring and development mode transformation, advocating efforts to develop green and low-carbon industries to support the economic development while achieving energy conservation and emission reduction. During this period, the government issued relevant policy documents to guide the work orientation for various industries to accelerate the pace for several times.

Since 2008, China has entered the energy transformation. In recent years, the increasingly severe energy environment situation has also made a strong call to the whole society to actively take part in energy saving and emission reduction, which helps to accelerate the process of energy transition. Due to a series of problems, such as large energy consumption, low energy conversion efficiency, and serious environmental pollution, the electric power industry has always been the focus of energy upgrading, conservation and emission reduction [29].

In 2015, China launched a new round of electric power reform. A diversified market players represented by electricity retailers was formed in the sales side market. In 2016, China issued a number of special plans on energy to accelerate the national transformation and upgrading of energy resources, including the electric power industry. In September of the same year, China officially became the 23rd performing party of the Paris Agreement. It measured whether it has implemented its commitment to address climate change through five major indicators, including carbon intensity, energy structure, forest reserves, carbon market pilot reform and support strength for developing countries. Obviously, the green and low carbon development is set as an important part of its ecological civilization construction. At the end of 2017, the construction of carbon emissions trading system on a national scale was officially launched. The development of a green and low-carbon economy was promoted through a reasonable market mechanism to control and reduce greenhouse gas emissions. Then, the Chinese Certified Emission Reduction projects (CCER) would be added to help companies to achieve the transition from high carbon emissions to low carbon development. The carding of multi-party documents that relevant to electric power reform and energy planning during the 13th Five-Year Plan in China is shown in Figure 1. The full interpretation of these documents will help market players in the electric power industry make a respond to the latest policies in time, take concrete measures to implement energy saving and emission reduction actions and take every effort to achieve their own environmental targets.

2.2. Analysis on the Development Direction of Energy Saving and Emission Reduction

First of all, the new electric power reform has opened the sales side. On the one hand, the potential huge interests in the electricity sales market attracts diversified capital to form a sales company to participate in the fierce competition. By the end of 2017, the number of electricity retailers in China that have been publicized has reached more than 3200, and, as a result, a multi-competition pattern dominated by electricity retailers has been formed in the sales market. On the other hand, the release of dividends in the new energy field has also been driven by this reform. In order to satisfy the ever-increasing electricity demand in the market, electricity retailers need to carry out the value-added services other than the purchase and sale business, and build an integrated service platform to transform into integrated energy service providers. Secondly, with the gradual advancement of energy transition during the 13th Five-Year Plan period in China, it is set to control the total energy consumption to within 5 billion tons of standard coal by 2020 and promise to achieve a 65% reduction in emissions by 2030. The goal requires that the electricity development must conform to the concept of low-carbon economy. Therefore, as a member of the main body in the sales market, electricity retailers should actively respond to the optimization and transition of energy structure, establish a low carbon energy system, implement its own energy saving and emission reduction actions and strive to build companies with leading and first-class integrated energy services. Thirdly, the beginning of the national carbon market construction has also brought new opportunities for electricity retailers. Electricity retailers can enter the carbon market to act as agents for carbon trading with huge data resources and rich market trading experience, which will support the comprehensive construction of the carbon market and effectively stimulate the energy saving and emission reduction potential for other enterprises.

With the background of the new electric power reform, energy planning and development, and the carbon market construction, it is an inevitable trend for China’s electric power industry to insist the low-carbon opinions and promote energy saving and emission reduction. As an indispensable group on the road of energy saving and emission reduction, electricity retailers should take measures on market-oriented transactions in the sales side, related technology development, integrated value-added services, internal management, and social responsibilities, which improves core competitiveness and accelerates the transformation into the integrated energy service providers to help the realization of energy saving and emission reduction goal in China.

3. Selection of Evaluation Indicators of Energy Saving and Emission Reduction Effects for Electricity Retailers in China

To begin with, we consider the background of the electric power system reform, energy structure transition and optimization, and the current carbon market construction status in this paper. After that, the evaluation indicator system is proposed according to the principles of scientificalness, comprehensiveness, systematicness, feasibility, and comparability [30], in which the energy saving and emission reduction effects of electricity retailers are regarded as the overall evaluation goal. Meanwhile, five evaluation criteria are selected based on those policy documents, including market transactions, technical means, integrated energy services, management system, and social responsibilities. To further refine the five criteria, we have determined more detailed three-level indicators. Not only consider the relevant businesses that have operated by some electricity retailers, but the availability of data. Finally, the three-level evaluation indicator system is built, as displayed in the following Figure 2. The meaning of some indicators is shown in Appendix A. The selection of evaluation indicators meets the combination of qualitative and quantitative indicators. Among them, the selection of qualitative indicators is supported by the latest policy orientation, which has a strong practical significance for electricity retailers in China.

If only one complete system is used, the evaluation can only be studied from a global perspective. Therefore, the classification of the indicator system into three levels is to conduct a multi-level evaluation of the energy saving and emission reduction effects for electricity retailers. As a result, the weight structure distribution of different levels can be obtained one by one and the importance ranking results of the next level indicators to the upper are obtained, simultaneously. On the basis of the distribution results, electricity retailers can take measures to improve the energy saving and emission reduction effect from the individual indicators and avoid useless costs.

4. Determination of Indicator Weights Based on Combination Weighting Method

4.1. Preprocessing of the Evaluation Indicators

We chose the Delphi method to quantify qualitative indicators. Several experts complete the scoring process according to the uniform criteria. Suppose that $M$ is the number of experts and $S_k^i$ is the score of the qualitative indicator $k$ assessed by expert $i$. After the scores of all the experts are finished, the quantified score $S_k$ of indicator $k$ is given, as follows:

$$S_k=\frac{1}{M}{\displaystyle \sum }_{i=1}^M{S}_k^i$$

(1)

In order to eliminate the influence of units, types, and economic implications of different indicators on the evaluation results, the raw data of evaluation indicators needs to be preprocessed firstly. Suppose that $x_{ij}^0$ is the indicator original value. Then, the normalization of benefit type and cost type indicators is given, as follows:

$$x_{ij}=x_{ij}{}^0/max{x}_{ij}{}^0$$

(2)

$$x_{ij}=min{x}_{ij}{}^0/x_{ij}{}^0$$

(3)

where $x_{ij}$ is the normalized value. We have the normalization matrix $X^{*}$, as follows:

$$X^{*}=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \cdots & x_{1m}\\ x_{21}& x_{21}& \cdots & x_{2m}\\ ⋮& ⋮& \ddots & ⋮\\ x_{n1}& x_{n1}& \cdots & x_{nm}\end{array}\right]$$

where $n$ is the number of evaluation indicators and $m$ is that of evaluation schemes. $i=1,2,\cdots ,n$, $j=1,2,\dots ,m$.

4.2. Analytic Hierarchy Process

Analytic hierarchy process (AHP) is often used to obtain the subjective weights of indicators. It is an evaluation method that combines quantitative and qualitative analysis with the advantage of simple calculation. In general, the overall hierarchy is divided into the target hierarchy, program hierarchy, and criterion hierarchy to make problems more rational when using AHP to make decisions [31,32]. The process of determining subjective weights through AHP is shown, as follows:

1. Divide the hierarchy of indicators

In this paper, the specific hierarchy division of the indicator system is shown in

Table 1. Hierarchy division of the evaluation indicator system of energy saving and emission reduction effects for electricity retailers in China.

Target Hierarchy	Program Hierarchy	Criterion Hierarchy	Type of Indicators
			Quantitative	Qualitative
Energy saving and emission reduction effects for electricity retailers $U$	Market transactions $U_1$	A proportion of new energy investment $U_{11}$	√
		Ability to obtain allowances for the carbon market trading spreads as an agent $U_{12}$		√
		CCER trading volume $U_{13}$	√
		Customer electricity cost reduction rate $U_{14}$	√
		A reasonable degree of electricity price setting $U_{15}$		√
	Technical means $U_2$	Investment in research of energy saving and emission reduction technologies $U_{21}$	√
		Construction scale of charging facilities for electric vehicles $U_{22}$	√
		Construction level of monitoring platform for energy saving services $U_{23}$		√
		Ability to collect and analyze the data of smart electricity utilization $U_{24}$		√
	Integrated energy services $U_3$	Output value of energy management contract projects $U_{31}$	√
		Electricity saving growth rate at the user side $U_{32}$	√
		Quality of energy saving and management design $U_{33}$		√
		Level of carbon asset management services $U_{34}$		√
	Management system $U_4$	Energy saving and emission reduction policies of electricity retailers $U_{41}$		√
		Implementation of energy saving and emission reduction rules of employees $U_{42}$		√
	Social responsibilities $U_5$	Propaganda of low-carbon economic awareness $U_{51}$		√
		Completion rate of the annual energy-saving emission reduction target $U_{52}$	√

.

2. Construct the pairwise judgment matrix between hierarchies

The nine-level scale method is applied to compare the elements in pairs. The meaning of the scale $a_{ij}$ of 1 to 9 is given in

Table 2. The 1–9 degree scale implications of analytic hierarchy process (AHP).

Scale Values	Implications of ${\mathit{a}}_{\mathit{i}\mathit{j}}$
1	Indicator $i$ is as important as indicator $j$
3	Indicator $i$ is slightly more important than indicator $j$
5	Indicator $i$ is more important than indicator $j$
7	Indicator $i$ is strongly more important than indicator $j$
9	Indicator $i$ is extremely more important than indicator $j$
2,4,6,8	The middle value of the above two adjacent scale judgment
Reciprocal	Ratio of the importance of indicator $j$ to indicator $i$

, as follows.

The judgment matrix $A$ is defined, as follows:

$$A=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1m}\\ a_{21}& a_{21}& \cdots & a_{2m}\\ ⋮& ⋮& \ddots & ⋮\\ a_{n1}& a_{n1}& \cdots & a_{nm}\end{array}\right]$$

3. Hierarchical single arrangement and consistency check

Hierarchical single arrangement refers to calculating the maximum eigenvalue ${\lambda }_{\max }$ of the single-layer judgment matrix and the corresponding eigenvector $\xi$. The normalized $\xi$ is used to get the ranking weights of each indicator at the same level when compared with the importance of a certain indicator at the previous level. The formula for determining ${\lambda }_{\max }$ and $\xi$ is given in Equation (4).

$$A\xi ={\lambda }_{\max }\xi$$

(4)

The procedure of consistency check for the constructed judgement matrix is shown, as follows:

(1)

Calculate the consistency indicators $CI$

$$CI=\left({\lambda }_{\max }-r\right)/\left(r-1\right)$$

(5)

where $r$ is the order of the judgment matrix.

(2)

Determine the average random consistency indicator $RI$

After 1000 times repeated calculations through the order from 1st to 15th, the value of $RI$ is measured in

Table 3. The assignment table for $RI$.

$\mathit{r}$	Values of $\mathit{R}\mathit{I}$	$\mathit{r}$	Values of $\mathit{R}\mathit{I}$
1	0	9	1.46
2	0	10	1.49
3	0.52	11	1.52
4	0.89	12	1.54
5	1.12	13	1.56
6	1.24	14	1.58
7	1.36	15	1.59
8	1.41	—	—

[33].

(3)

Calculate the consistency ratio $CR$

$$CR=CI/RI$$

(6)

A consistency check is the way to determine whether the consistency of judgement matrix is within a reasonable range by checking the values of $CR$. When $CR<0.1$, the judgment matrix is considered to have passed the consistency check, otherwise it needs to be properly corrected.

4.3. Entropy Weight Method

Entropy weight method is a common method for calculating the objective weights of indicators. It reflects the ability of evaluation objects to provide effective information by determining the relative proximity [34,35]. Weights that are given by the subjective weighting method can be adjusted and corrected by means of entropy weight method, which improves to get the scientific and accurate evaluation results. The determination of the objective weights of indicators based on entropy weight method is shown, as follows:

• Construct the standardized judgment matrix
  The standardized judgment matrix constituted by the pre-processed indicator data is $X^{*}$.
• Measure the information entropy

The total number of evaluation objects is $m$ and that of indicators is $n$. Then the information entropy $H_i$ of indicator $i$ is calculated, as follows:

$$H_i=-k{\displaystyle \sum }_{i=1}^m{f}_{ij}ln{f}_{ij},i=1,2,\cdots ,m$$

(7)

$$f_{ij}=x_{ij}/{\displaystyle \sum }_{i=1}^m{x}_{ij}$$

(8)

$$k=\frac{1}{\ln m}$$

(9)

where $x_{ij}$ is the normalized value. When $f_{ij}=0$, there is $f_{ij}ln{f}_{ij}=0$.

The objective weights of indicators are given by Equation (10).

$$w_i=\frac{1-H_i}{{\displaystyle \sum _{i=1}^m\left(1-H_i\right)}}$$

(10)

where $0\le w_i\le 1,{\displaystyle {\displaystyle \sum }_{i=1}^m}{w}_i=1$.

4.4. Determination of the Combination Weight

In the practical application of AHP, it is difficult to completely reflect the actual situation of the evaluation objects only based on subjective experience, which may lead to the final evaluation results deviating from reality and have certain limitations. In reference [26], the ISM-AHP combination weighting method is applicable to systems with many variables and unclear structures, but the structural relationship formed is too complicated. In the evaluation with a small number of variables, the difficulty is increased. In reference [36], multiplication is applied to connect the subjective and objective weights, which can improve the ability to reflect information of data to a certain extent. In reference [37], integration weights of indicators are defined according to AHP and entropy weight method, as displayed in Equation (11).

$$w_i^{\prime }=a{w}_i^1+\left(1-a\right)w_i^2$$

(11)

where $w_i^1$ and $w_i^2$ are the indicator weights that are based on AHP and the entropy weight method, respectively. The integration weights still have partial subjectivity through this method, because the assignment $a$ is determined by expert scoring method. While in this paper, after determining the subjective weights by AHP, the information entropy $H_i$ is introduced to eliminate the subjectivity in the evaluation process so that the information of original data can be fully utilized, and the reliability of evaluation results can be effectively improved. The combination weights of evaluation indicators are given, as shown in Equation (12).

$$w_i^{\prime }=w_i^1{H}_i+w_i^2\left(1-H_i\right)$$

(12)

where ${\displaystyle {\displaystyle \sum }_{i=1}^m}{w}_i^{\prime }=1$, $w_i^1$, and $w_i^2$ are the indicator weights that are calculated by AHP and the entropy weight method, respectively.

5. Construction of Fuzzy Comprehensive Evaluation Model

5.1. Basic Theory of Fuzzy Comprehensive Evaluation

On the basis of fuzzy mathematics, the fuzzy comprehensive evaluation assesses objects through fuzzy transformation and the principle of maximum membership degree, is widely used in management science, economic, and environmental evaluation. Fuzzy evaluation can be used to quantify qualitative indicators, which has strong systematicness and it greatly reduces the subjectivity in the evaluation process, and is suitable for the evaluation of non-deterministic problems [38,39,40,41].

5.2. Construction of Fuzzy Comprehensive Evaluation Model Based on Combination Weighting Method

1. Decide the factor set and evaluation set

Assume that $N$ is the number of single factors belonging to the same level, $u_i\left(i=1,2,\cdots ,N\right)$ is the evaluation factor, $U=\left\{u_1,u_2,\cdots ,u_N\right\}$ is the factor set, $n$ is the rating level, $v_j\left(j=1,2,\cdots ,n\right)$ is the evaluation rating standard, and $V=\left\{v_1,v_2,\cdots ,v_n\right\}$ is the determined evaluation set. Five levels for the evaluation of energy saving and emission reduction effects for electricity retailers are confirmed in this paper, namely, $V$ = {Excellent, Good, Moderate, Poor, Extremely poor}. $H=\left\{5,4,3,2,1\right\}$ is the corresponding scale.

2. Construct the fuzzy relation matrix

The fuzzy relation matrix is also called the membership degree matrix, in which $r_{ij}$ represents the relationship of the membership degree between the evaluation factor $u_i$ and the corresponding evaluation level $v_j$. In this paper, the membership degree is determined by the Delphi method. When considering the construction of the indicator system and the impact of specific indicators on the energy saving and emission reduction effects of electricity retailers, experts judge these indicators to determine the membership degree. The fuzzy vector $R_i$ formed by the evaluation factor $u_i$ is defined in Equation (12).

$$R_i=\left(r_{i1},r_{i2},\cdots ,r_{ij},\cdots r_{Nn}\right),i=1,2,\cdots ,N,j=1,2,\cdots ,n$$

(13)

where $0<r_{ij}<1$. The fuzzy relation matrix $R$ composed of $n$ elements is shown in Equation (13).

$$R=\left[\begin{array}{cccc}{r}_{11}& r_{12}& \cdots & r_{1n}\\ r_{21}& r_{21}& \cdots & r_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ r_{N1}& r_{N1}& \cdots & r_{Nn}\end{array}\right]$$

(14)

3. Determine the result set of fuzzy evaluation

In order to make the best of all the information of the matrix, the $M\left(·,\oplus \right)$ operator is selected to determine the fuzzy judgment result set $B$. The calculation of fuzzy judgment is given by Equation (14).

$$B=w\circ R$$

(15)

where $w$ is the combination weights of the evaluation indicators given through AHP and the entropy weight method.

4. Determine fuzzy comprehensive evaluation results

In accordance with the principle of maximum membership degree, the energy saving and emission reduction effects of electricity retailers are classified into the corresponding evaluation levels based on the fuzzy evaluation results.

In order to conduct a further assessment of the overall energy saving and emission reduction effects of electricity retailers, multi-level fuzzy evaluation should be carried out after obtaining the single-level fuzzy comprehensive evaluation results. In the light of the principle of maximum membership degree, the level of the maximum membership degree is the final evaluation level of the energy saving and emission reduction effects of the evaluated electricity retailers.

The evaluation process of energy saving and emission reduction effects for electricity retailers based on fuzzy combination weighting method constructed in this paper is as shown in Figure 3.

6. Example Analysis

In this paper, ten electricity retailers that numbered from A to J are selected as the evaluation objects. The energy saving and emission reduction effects of these five electricity retailers are evaluated based on the fuzzy combination weighting method. Firstly, qualitative indicators are qualified by experts according to Equation (1) with interval scores of [1,2,3,4,5,6,7,8,9,10] points. These experts come from some of the electricity retailers that have been carrying out relevant business activities in accordance with the policy orientation, who obviously have many years of experience in the electric power industry. They also have a deep understanding of the electric power reform, energy transformation, and carbon market construction process and they hold reasonable opinions.

Since the selected evaluation indicators are all benefit types, the raw data of all the indicators are first normalized according to Equation (2). The processed data is displayed in

Table 4. Normalized data of energy saving and emission reduction effects evaluation indicators of electricity retailers.

Three-Level Indicators	Electricity Retailers
	A	B	C	D	E	F	G	H	I	J
$U_{11}$	0.8689	0.8060	0.7355	0.9398	0.9995	0.7626	0.8507	0.8829	0.8960	1.0000
$U_{12}$	0.8975	0.8604	0.8157	0.9520	0.9760	0.8124	1.0000	0.9324	0.9520	0.9237
$U_{13}$	0.1489	0.3925	0.2684	0.6444	1.0000	0.3327	0.5553	0.7106	0.2977	0.3340
$U_{14}$	0.6190	0.7619	0.5524	0.9048	0.7143	0.6476	0.7810	0.7143	1.0000	0.8571
$U_{15}$	0.8481	0.9335	0.8404	0.9279	1.0000	0.9346	0.8038	0.9479	0.9157	0.9579
$U_{21}$	0.7125	0.5375	0.3656	0.8031	0.4219	0.3250	0.6906	0.8625	1.0000	0.8906
$U_{22}$	0.6000	0.4889	0.2889	1.0000	0.7111	0.4444	0.5333	0.4444	0.3333	0.5556
$U_{23}$	0.7713	0.5923	0.6477	0.8054	0.8707	0.5526	0.9134	0.8366	0.8125	1.0000
$U_{24}$	0.9407	0.9021	0.7352	0.8455	1.0000	0.6717	0.9545	0.7669	0.7228	0.9076
$U_{31}$	0.8521	0.6549	0.2993	0.9085	1.0000	0.5880	0.4366	0.7852	0.6127	0.8627
$U_{32}$	0.3064	0.4641	0.2368	0.6855	1.0000	0.5685	0.3371	0.3832	0.6552	0.8382
$U_{33}$	0.9595	0.8639	0.8155	0.9269	0.7402	0.6862	0.8493	0.7750	0.9291	1.0000
$U_{34}$	0.8904	0.8800	0.7774	1.0000	0.9814	0.8403	0.9709	0.8834	0.9592	0.9825
$U_{41}$	0.9016	0.9147	0.9357	0.9921	0.9501	0.8635	1.0000	0.8898	0.9777	0.9606
$U_{42}$	0.9265	0.9027	0.9870	0.8519	0.9146	0.8249	1.0000	0.8303	0.8908	0.9243
$U_{51}$	0.7123	0.8630	0.7511	0.9372	1.0000	0.6644	0.7477	0.8196	0.7123	0.8345
$U_{52}$	0.9615	0.9707	0.9791	1.0000	0.9791	0.8678	0.9637	0.9749	0.9791	0.9791

.

6.1. Single-Level Fuzzy Comprehensive Evaluation

(1) Determine the subjective weights

Firstly, the subjective weights of different levels of indicators are determined based on AHP. By consulting experts’ opinions, the pairwise comparison judgment matrix is constructed. Then, the maximum eigenvalues and corresponding eigenvectors are solved according to Equation (4). The weights of the evaluation indicators are obtained by normalizing the maximum eigenvectors, as displayed in

Table 5. Subjective weights of energy saving and emission reduction evaluation indicators of electricity retailers.

Program Hierarchy	Weights of Indicators	Criterion Hierarchy	Weights of Indicators	Consistency Check
$U_1$	0.0939	$U_{11}$	0.1443	${\lambda }_{\max }$ = 5.2461 $CI$ = 0.0615 $CR$ = 0.0549
		$U_{12}$	0.4309
		$U_{13}$	0.3155
		$U_{14}$	0.0665
		$U_{15}$	0.0429
$U_2$	0.2188	$U_{21}$	0.5280	${\lambda }_{\max }$ = 4.2496 $CI$ = 0.0832 $CR$ = 0.0936
		$U_{22}$	0.3221
		$U_{23}$	0.0604
		$U_{24}$	0.0895
$U_3$	0.5800	$U_{31}$	0.3326	${\lambda }_{\max }$ = 4.1179 $CI$ = 0.0393 $CR$ = 0.0442
		$U_{32}$	0.1136
		$U_{33}$	0.2572
		$U_{34}$	0.2975
$U_4$	0.0412	$U_{41}$	0.2500	${\lambda }_{\max }$ = 2 Complete consistency
		$U_{42}$	0.7500
$U_5$	0.0661	$U_{51}$	0.1429	${\lambda }_{\max }$ = 2 Complete consistency
		$U_{52}$	0.8571

.

It can be seen from Table 5 that weights of the criterion hierarchy indicators that are determined by AHP have passed the consistency check. In the same way, the consistency check of weights of the program hierarchy indicators are conducted. There are ${\lambda }_{\max }$ = 5.3839, $CI$ = 0.096, $CR$ = 0.0857 < 1, as a result, the consistency check is also passed.

(2) Determine the objective weights

The normalized judgment matrices are constructed from the normalized data, and the standardized judgment matrices are processed according to the Equations (7)–(10) by the entropy weight method. The objective weights of evaluation indicators are shown in

Table 6. Objective weights of energy saving and emission reduction evaluation indicators of electricity retailers.

Single-Level Indicators	Two-Level Indicators	Three-Level Indicators	The Weights of Indicators
$U$	$U_1$	$U_{11}$	0.0105
		$U_{12}$	0.0050
		$U_{13}$	0.2814
		$U_{14}$	0.0320
		$U_{15}$	0.0044
	$U_2$	$U_{21}$	0.1329
		$U_{22}$	0.1300
		$U_{23}$	0.0339
		$U_{24}$	0.0179
	$U_3$	$U_{31}$	0.1072
		$U_{32}$	0.1993
		$U_{33}$	0.0140
		$U_{34}$	0.0064
	$U_4$	$U_{41}$	0.0023
		$U_{42}$	0.0042
	$U_5$	$U_{51}$	0.0171
		$U_{52}$	0.0014

.

(3) Calculate the combination weights

AHP and entropy weight method are used synthetically to determine the subjective weights and objective weights of the indicators, respectively. The combination weights of indicators are given by Equation (12) with the results, as shown in

Table 7. Combination weights of energy saving and emission reduction effects evaluation indicators of electricity retailers.

Single-Level Indicators	Two-Level Indicators	Three-Level Indicators	Weights of Energy Saving and Emission Reduction Effects Indicators of Electricity Retailers
			AHP	Entropy Weight Method	Combination Weights
$U$	$U_1$	$U_{11}$	0.1443	0.0105	0.1440
		$U_{12}$	0.4309	0.0050	0.4305
		$U_{13}$	0.3155	0.2814	0.3136
		$U_{14}$	0.0665	0.0320	0.0663
		$U_{15}$	0.0429	0.0044	0.0429
	$U_2$	$U_{21}$	0.5280	0.1329	0.5176
		$U_{22}$	0.3221	0.1300	0.3171
		$U_{23}$	0.0604	0.0339	0.0602
		$U_{24}$	0.0895	0.0179	0.0892
	$U_3$	$U_{31}$	0.3326	0.1072	0.3278
		$U_{32}$	0.1136	0.1993	0.1170
		$U_{33}$	0.2572	0.0140	0.2565
		$U_{34}$	0.2975	0.0064	0.2971
	$U_4$	$U_{41}$	0.2500	0.0023	0.2499
		$U_{42}$	0.7500	0.0042	0.7494
	$U_5$	$U_{51}$	0.1429	0.0171	0.1425
		$U_{52}$	0.8571	0.0014	0.8569

.

According to the distribution results of weights, we see that the importance ranking results of the two-level indicators to the energy saving and emission reduction effects of electricity retailers are followed by integrated energy services, technical means, market transactions, social responsibilities, and management system. It can be seen from the above that the level of integrated energy services has the greatest impact on the energy saving and emission reduction effects for electricity retailers among the two-level indicators, while the management system has the worst. To explore the impact of the three-level indicators on the two-level, the analysis results are as follows.

From the perspective of market transactions, the most important indicator is the ability to obtain allowances for the carbon market trading spreads as an agent, while the least important is the reasonable degree of electricity price setting. From the perspective of technical means, the most important indicator is the investment in research of energy saving and emission reduction technologies, while the least important is the construction level of monitoring platform for energy saving services. On the integrated energy services side, the most important indicator is the output value of energy management contract projects, while the least important is the construction scale of charging facilities for electric vehicles. However, the importance of the four three-level indicators included is not much different. From the view of the management system, the indicator of implementation of energy saving and emission reduction rules of employees is obviously more important than the energy saving and emission reduction policies of electricity retailers. From the perspective of social responsibilities, the indicator of completion rate of the annual energy-saving emission reduction target is obviously more important than the propaganda of low-carbon economic awareness.

The importance ranking of indicators is beneficial to the electricity retailers to take measures from a single aspect in the future, in order to achieve an effective improvement of their energy saving and emission reduction effects with relatively small investment.

(4) Obtain the results of single-level fuzzy comprehensive evaluation

The three-level indicators are scored by experts based on the evaluation set $V$ = {Excellent, Good, Moderate, Poor, Extremely poor} and the scale $H=\left\{5,4,3,2,1\right\}$. Next, the fuzzy relation matrix $B_i\left(i=1,2,3,4,5\right)$ corresponding to $U_1$, $U_2$, $U_3$, $U_4$, $U_5$ is built, respectively. The fuzzy evaluation values of single-level fuzzy comprehensive evaluation indicators are calculated by Equation (15), as shown in

Table 8. Single-level fuzzy comprehensive evaluation results.

Electricity Retailers	Fuzzy Evaluation Value
	${\mathit{B}}_1$	${\mathit{B}}_2$	${\mathit{B}}_3$	${\mathit{B}}_4$	${\mathit{B}}_5$
A	0.0288	0	0	0	0.1714
	0.2298	0.2839	0.162	0.4496	0.1999
	0.2555	0.5726	0.6117	0.4997	0.5996
	0.2817	0.1276	0.2013	0.05	0.0285
	0.2014	0	0.0234	0	0
B	0	0	0	0	0.1714
	0.1367	0	0.0234	0.1499	0.3998
	0.6589	0.1903	0.3851	0.4997	0.2284
	0.194	0.4793	0.5243	0.3497	0.1999
	0.0086	0.3145	0.0656	0	0
C	0	0	0	0.1499	0.6855
	0.0947	0	0	0.5496	0.1999
	0.3647	0.1109	0.1107	0.2498	0.0855
	0.3128	0.3191	0.4678	0.05	0.0285
	0.2251	0.5512	0.4198	0	0
D	0.1995	0.1268	0.1484	0	0.3713
	0.4542	0.2938	0.4588	0.1999	0.3713
	0.3436	0.3824	0.3399	0.5996	0.2569
	0	0.1633	0.0513	0.1999	0
	0	0.0178	0	0	0
E	0.335	0.1625	0.1358	0	0.3998
	0.457	0.25	0.1484	0.2998	0.5996
	0.1788	0.261	0.4495	0.5996	0
	0.0265	0.1035	0.2133	0.1	0
	0	0.207	0.0513	0	0
F	0	0	0	0	0
	0.0172	0.0634	0.0468	0.1499	0
	0.1384	0.2081	0.2546	0.5496	0.057
	0.3611	0.4337	0.5207	0.2998	0.5711
	0.4807	0.2788	0.1763	0	0.3713
G	0.1722	0	0.0594	0.05	0
	0.4425	0.2923	0.2296	0.7495	0
	0.3113	0.4615	0.2367	0.1999	0.057
	0.0713	0.2304	0.276	0	0.5711
	0	0	0.1967	0	0.3713
H	0.0288	0	0	0	0.1714
	0.4858	0.386	0	0.1499	0.714
	0.4562	0.4749	0.5497	0.5496	0.114
	0.0265	0.1232	0.4487	0.2998	0
	0	0	0	0	0
I	0.1391	0.3106	0	0	0.6855
	0.4413	0.207	0.4105	0.05	0.1999
	0.166	0.1174	0.2744	0.5996	0.0855
	0.1882	0.3491	0.248	0.3497	0.0285
	0.0627	0	0.0656	0	0
J	0.0288	0	0.0747	0	0.5141
	0.3019	0.6926	0.3429	0.1999	0.3998
	0.2669	0.2023	0.3902	0.5996	0.057
	0.1488	0.0535	0.1905	0.1999	0.0285
	0.2509	0.0357	0	0	0

. And the level distribution is shown in Figure 4.

One can observe that the single-level fuzzy comprehensive evaluation can analyze the energy saving and emission reduction effects for the five electricity retailers in the aspects of market transactions, technical means, integrated energy services, management system and social responsibilities. On the basis of the principle of maximum membership degree, the evaluation levels of energy saving and emission reduction effects for electricity retailer A to J from a single dimension are shown in

Table 9. Level of energy saving and emission reduction effects for electricity retailers from a single dimension.

Electricity Retailers	${\mathit{U}}_1$	${\mathit{U}}_2$	${\mathit{U}}_3$	${\mathit{U}}_4$	${\mathit{U}}_5$
A	Poor	Moderate	Moderate	Moderate	Moderate
B	Moderate	Poor	Poor	Moderate	Good
C	Moderate	Extremely poor	Poor	Good	Excellent
D	Good	Moderate	Good	Moderate	Excellent
E	Good	Moderate	Moderate	Moderate	Good
F	Extremely poor	Poor	Poor	Moderate	Poor
G	Good	Moderate	Poor	Good	Poor
H	Good	Moderate	Moderate	Moderate	Good
I	Good	Poor	Good	Moderate	Excellent
J	Good	Good	Moderate	Moderate	Excellent

.

6.2. Two-Level Fuzzy Comprehensive Evaluation

The fuzzy relation matrices $R$ of the two-level indicators are constructed based on $B_1$, $B_2$, $B_3$, $B_4$, $B_5$ that are determined in the single-level evaluation. Then set {100, 80, 60, 40, 0} as the evaluation scores corresponding to $V$ = {Excellent, Good, Moderate, Poor, Extremely poor}.

Table 10. Two-level fuzzy comprehensive evaluation results.

Electricity Retailers	Fuzzy Comprehensive Evaluation Vectors	Maximum Membership Degree	Fuzzy Evaluation Levels	Comprehensive Evaluation Scores	Sorted Resuls
A	(0.0140, 0.2094, 0.5643, 0.1751, 0.0325)	0.5643	Moderate	59.014	4
B	(0.0113, 0.0590, 0.3626, 0.4548, 0.1077)	0.4548	Poor	45.798	8
C	(0.0515, 0.0447, 0.1387, 0.3745, 0.3852)	0.3852	Extremely poor	32.028	10
D	(0.1571, 0.4058, 0.3548, 0.0737, 0.0039)	0.4058	Good	72.41	1
E	(0.1722, 0.2357, 0.3593, 0.1530, 0.0750)	0.3593	Moderate	46.534	7
F	(0, 0.4880, 0.2326, 0.4809, 0.2329)	0.4809	Poor	37.096	9
G	(0.0527, 0.2696, 0.2795, 0.2549, 0.1386)	0.2795	Moderate	53.804	6
H	(0.0140, 0.1834, 0.4958, 0.3020,0)	0.4958	Moderate	57.9	5
I	(0.1263, 0.3401, 0.2308, 0.2542, 0.0439)	0.3401	Good	63.854	3
J	(0.0800, 0.4134, 0.3241, 0.1463, 0.0314)	0.4134	Good	66.37	2

shows the final scores of the overall energy saving and emission reduction effects of electricity retailers, which are obtained through the quantization of evaluation levels.

It can be seen form the above, the final fuzzy evaluation levels of the ten electricity retailers’ energy saving and emission reduction effects that are determined by the principle of maximum membership degree are followed by Moderate, Poor, Extremely poor, Good, Moderate, Poor, Moderate, Moderate, Good, and Good. The comprehensive evaluation scores of the ten electricity retailers are obtained by quantifying evaluation levels. As shown in Figure 5 and Figure 6, among them, the comprehensive evaluation score of electricity retailers D is 72.41, which has the best energy saving and emission reduction effects. Combined with the results of single-level fuzzy evaluation, the company D needs to continue to strengthen actions in market transactions and integrated energy services to improve its energy saving and emission reduction effects. Electricity retailers C has the worst energy saving and emission reduction effects with the scores of 32.028. The company C has fulfilled social responsibilities better to promote the energy saving and emission reduction. However, from a holistic perspective, the main reason for the poor performance of energy saving and emission reduction effects of electricity retailer C may be that there are great problems in the two aspects of technical means and integrated energy services, and there is still room for improvement in market transactions and management system.

7. Conclusions

In this paper, firstly, we discuss the research vacancy at home and abroad on the evaluation of energy saving and emission reduction effects in China's electricity industry. On the basis, electricity retailers emerged on the sales market are treated as the research objects. Then, key indicators are screened to construct the corresponding evaluation indicator system by interpreting the multi-party policy documents that are related to the electric power reform, energy transformation, and carbon market construction. Secondly, AHP and entropy weight method are grouped together to obtain the modified weights of indicators and the model is established based on fuzzy comprehensive evaluation theory. Thirdly, the multi-level fuzzy comprehensive evaluation of energy saving and emission reduction effects for electricity retailers is conducted in accordance with the principle of maximum membership degree, a total number of five levels are reserved for the effects, including Excellent, Good, Moderate, Poor, and Extremely poor. Through the single-level fuzzy comprehensive evaluation, the energy saving, and emission reduction effects for electricity retailers in five aspects of market transactions, technical means, integrated energy services, management system, and social responsibilities are obtained. Through the two-level fuzzy comprehensive evaluation, the overall evaluation level is determined. Then, the energy saving and emission reduction effects for electricity retailers is sorted by quantifying the evaluation levels. The results of example analysis show that the method applied to the evaluation of energy saving and emission reduction effects for electricity retailers in China can fit the characteristics of the evaluation indicators with a good performance. At the same time, it can also draw a reasonable evaluation result.

The main research findings of this paper are as follows:

(1)

Choose the emerged electricity retailers as evaluation objects and take the qualitative factors of policies into consideration in the process of constructing the indicator system. Therefore, the indicator system that is proposed in this paper can better reflect the specific impact of the new electric power reform, energy planning and transformation, and the carbon market construction on China’s current energy saving and emission reduction actions in the electricity sales side. In a word, it enlarges the research scope for market players in China’s electricity sales side on the evaluation of energy saving and emission reduction effects and it improves the totality of the existing evaluation indicator system in the electric power industry.

(2)

Apply the fuzzy combination weighting method into the evaluation of energy saving and emission reduction effects for electricity retailers. The weights of indicators given by combining AHP and entropy weight method are more comprehensive, accurate, and scientific. Moreover, qualitative indicators can be reasonably quantified through the multi-level fuzzy comprehensive evaluation, which helps to provide a valid method for electricity retailers that are actively involved in the current electricity sales market in China to assess the effects. Therefore, it gives the reference point for electricity retailers in China to realize the sustainable development in the sales side effectively by means of taking timely and appropriate actions on energy saving and emission reduction, implementing the concept of low carbon electricity to improve their core competitiveness.

We will focus our future research on the following points:

(1)

With the continuous improvement of China’s electric power reform, energy planning and transformation, and the carbon market construction, timely interpretation of policy documents will be conducted so as to analyze the implications and impacts on energy saving and emission reduction actions of electricity retailers. Furthermore, the selection of indicators will be carried out around the latest market environment, and the existing evaluation indicator system will be improved and revised.

(2)

In the future research, according to the actual operation status of electricity retailers and the availability of data, we will consider converting some qualitative indicators into quantitative ones. To improve the reliability of evaluation results, the quantification process based on the expert scoring method will be replaced by actual data.

(3)

Based on the data distribution of indicators, we will study the corresponding membership function in the middle and later time of the sales market development. Then, the fuzzy evaluation value will be calculated by means of the explicit membership function and a more scientific and practical evaluation method will be realized.