Photovoltaics (PV) has been combined with many other industries, such as agriculture. But there are many problems for the sustainability of PV agriculture. Timely and accurate sustainability evaluation of modern photovoltaic agriculture is of great significance for accelerating the sustainable development of modern photovoltaic agriculture. In order to improve the timeliness and accuracy of evaluation, this paper proposes an evaluation model based on interval type-2 Fuzzy AHP-TOPSIS and least squares support vector machine optimized by fireworks algorithm. Firstly, the criteria system of modern photovoltaic agriculture sustainability is constructed from three dimensions including technology sustainability, economic sustainability and social sustainability. Then, analytic hierarchy process (AHP) and technique for order preference by similarity to an ideal solution (TOPSIS) methods are improved by using interval type-2 fuzzy theory, and the traditional evaluation model based on interval type-2 Fuzzy AHP-TOPSIS is obtained, and the improved model is used for comprehensive evaluation. After that, the optimal parameters of least squares support vector machine (LSSVM) model are obtained by Fireworks algorithm (FWA) training, and the intelligent evaluation model for the sustainability of modern photovoltaic agriculture is constructed to realize fast and intelligent calculation. Finally, an empirical analysis is conducted to demonstrate the scientificity and accuracy of the proposed model. This study is conducive to the comprehensive evaluation of the sustainability of modern photovoltaic agriculture, and can provide decision-making support for more reasonable development model in the future of modern photovoltaic agriculture.
In recent years, the application field of photovoltaic renewable energy is expanding and the application depth is deepening [
According to existing literature, it can be found that no scholars have carried out the sustainability evaluation of modern photovoltaic agriculture. The researches about modern photovoltaic agriculture mainly focus on the influencing factors of the development of photovoltaic agriculture [
Considering that no scholars have carried out evaluation research on the sustainability of photovoltaic agriculture, this paper combs other research methods of sustainability evaluation [
The above evaluation methods belong to the traditional evaluation methods, which are mature and accurate, but the calculation process is very complex. Intelligent evaluation methods can process data quickly and accurately [
The main contributions of this paper are as follows:
The criteria system of modern photovoltaic agriculture sustainability is constructed from three dimensions including technology sustainability, economic sustainability and social sustainability.
AHP and TOPSIS are improved by using interval type-2 fuzzy theory, and the traditional evaluation model based on interval type-2 Fuzzy AHP-TOPSIS is obtained.
The optimal parameters of LSSVM model are obtained by Fireworks algorithm training, and the intelligent evaluation model for the sustainability of modern photovoltaic agriculture is constructed to realize fast and intelligent calculation.
Above all, this paper constructs the sustainability evaluation index system of modern photovoltaic agriculture, and establishes sustainability evaluation models of modern photovoltaic agriculture based on interval type-2 fuzzy AHP-TOPSIS and FWA-LSSVM. The rest of this paper is arranged as follows:
In order to construct the sustainability evaluation criteria system of modern photovoltaic agriculture, we need to understand the connotation of modern photovoltaic agriculture. Modern photovoltaic agriculture is a new type of agriculture which widely applies solar power generation to many fields, such as modern agricultural research, planting, breeding, irrigation, pest control and agricultural machinery power supply [
Modern photovoltaic agriculture includes many aspects, which are high systematic and hierarchical. Following the principles of comprehensiveness, independence, measurability and guidance is conducive to the sustainable evaluation of modern photovoltaic agriculture. According to the above construction principles, combined with the actual development of modern photovoltaic agriculture, this paper constructs the sustainable evaluation criteria system of modern photovoltaic agriculture.
As the future direction of agricultural development, modern photovoltaic agriculture plays a positive role in cost saving, environmental protection, social development and technological innovation. With the increasing concern for sustainable development, modern photovoltaic agriculture has already started to seek the coordinated development of economy, society and technology instead of the simple pursuit of economic growth in the past. Therefore, the sustainability evaluation of modern photovoltaic agricultural technology is conducive to a profound and comprehensive understanding of the impact from various aspects. On the basis of the index selection criteria, the objective environment of projects and the difficulty of data acquisition are fully considered, and the criteria system of modern photovoltaic agriculture sustainability is constructed. The criteria system mainly includes technology sustainability, economic sustainability and social sustainability. And the criteria system for sustainability evaluation of modern photovoltaic agriculture consists of 15 s level indexes, as shown in
Target layer | Criterion layer | Scheme layer | Index type I | Index type II |
---|---|---|---|---|
Sustainability evaluation of modern |
Technology |
Installation and operation level of photovoltaic system | Qualitatively | Cost index |
Light radiation resource condition | Qualitatively | Cost index | ||
Intelligent level of the greenhouse | Qualitatively | Cost index | ||
The stability of greenhouse architecture | Qualitatively | Cost index | ||
The energy saving property of greenhouse building | Qualitatively | Cost index | ||
Economic |
The net present value | Quantitatively | Profit index | |
The internal rate of return | Quantitatively | Profit index | ||
The return on total assets | Quantitatively | Profit index | ||
The asset liability ratio | Quantitatively | Cost index | ||
The total assets turnover | Quantitatively | Cost index | ||
Social |
Energy saving and emission reduction | Quantitatively | Profit index | |
The improvement of energy outcomes | Qualitatively | Profit index | ||
The promotion of employment | Qualitatively | Profit index | ||
Ecological efficiency | Quantitatively | Profit index | ||
The impact on vegetation | Qualitatively | Profit index |
The sustainability evaluation of modern photovoltaic agriculture is complicated, the evaluation process is affected by a variety of complex factors, with a certain degree of uncertainty. And the method of interval type-2 fuzzy numbers is effective to deal with many uncertain factors and obtain robust results. Interval type-2 fuzzy numbers have been widely used in many fields [
AHP is a multi-criteria analysis method which can deal with qualitative problems quantitatively. AHP is one of the most commonly used multi criteria decision-making methods because of its scientific hierarchy construction and clear logical structure [
The calculation process of interval type-2 fuzzy AHP model is as follows:
Combined with interval type-2 fuzzy numbers theory, pairwise comparison matrix is established for indexes of different levels and types.
Decision makers usually use semantic form to evaluate the objects in the measurement analysis of research projects. But it is difficult for decision-makers to define interval type-2 fuzzy numbers directly. Therefore, according to the semantic expression given by the decision-maker, it needs to be transformed into interval type-2 fuzzy numbers.
Test the consistency of comparison matrix
The interval type-2 fuzzy numbers are calculated with
The consistency index (CI) of the weight matrix of the object to be measured is tested, and the calculation process is shown in
Integrate the interval type-2 fuzzy number comparison matrix by geometric average method
The interval type-2 fuzzy number comparison matrix of the object to be measured can be integrated according to
The fuzzy weight of each index of the object to be measured can be calculated by
TOPSIS is one of the traditional multi criteria decision-making models. It is a method to rank based on the distance between the evaluation objects and the ideal solutions, so as to determine the quality of the evaluation objects [
Assuming that there are m items to be evaluated, N indexes and T experts in related fields to score, the main steps of interval type-2 fuzzy ideal point method are as follows:
Transform semantic variables into interval type-2 fuzzy numbers
There are both quantitative and qualitative indicators in the index system. It is difficult to realize the horizontal comparison of semantic expression of different types of indexes, so it is necessary to standardize them and transform semantic variables into interval type-2 fuzzy numbers. Then the interval type 2 fuzzy decision matrix of expert k can be expressed by
Integrate interval type-2 fuzzy matrix
Collect the measurement score data of all objects to be measured for input, and then the integrated interval type-2 fuzzy decision matrix can be determined as
Construct weighted normalized fuzzy decision matrix
The weighted normalized fuzzy decision matrix of the object to be measured can be calculated by
Determine fuzzy positive and negative ideal solutions
The positive ideal solution and the negative ideal solution are expressed as
Calculate the distance between each alternative and the fuzzy positive and negative ideal solutions
The calculation formulas of the distance between the measurement score of each index of the object to be measured and the positive and negative ideal solutions are shown in
Calculate and sort the similarity coefficients of each alternative
The similarity coefficients of each alternative can be calculated with
Least squares support vector machine (LSSVM) is an improvement of standard support vector machine (SVM). LSSVM uses equality constraints instead of inequality constraints of SVM, and uses kernel function to transform the prediction problem into solving equations, which can greatly improve the accuracy and speed of evaluation [
It is supposed that the given sample set is
For LSSVM, the optimization problem changes into the following:
In order to solve the above problems, Lagrange function is established as below:
Take a derivation of each variable of the function and make them have a value of 0, as shown in
Eliminate
By solving the above linear equations, the following results are obtained:
Considering that the RBF kernel function has a wide range of convergence and application, this paper chooses it as the kernel of LSSVM. The expression is as follows:
By analyzing the relevant theories of LSSVM, we can see that the difficulty of establishing LSSVM model is determining kernel function parameter
FWA is a simulation of the whole process of fireworks explosion. When fireworks explode, a large number of sparks will be generated, which can continue to explode and produce new sparks, thus it will make beautiful and colorful patterns. In the FWA, each firework can be regarded as a feasible solution in the solution space of the optimization problem, so the process of fireworks explosion can be regarded as the process of searching for the optimal solution. In the specific optimization problem, FWA involves the number of sparks produced by fireworks explosion, the radius of explosion, and how to select a group of optimal fireworks and sparks to carry out the next explosion [
In the FWA, the number of sparks and explosion radius of fireworks are different. The fireworks with poor fitness have larger explosion radius, which makes them have greater exploration ability, while the fireworks with good fitness have smaller explosion radius, which makes them have greater excavation ability. In addition, the introduction of Gauss mutation sparks can further increase the diversity of the population [
Therefore, we can know that the three most important parts of FWA are explosion parameters, mutation parameters and selection strategy [
Explosion parameters
In the explosion parameters, the number of sparks and explosion radius of fireworks are calculated according to the fitness value of fireworks. For firework
Mutation parameters
The setting of mutation parameters is to increase the diversity of explosion spark population. The mutation sparks in FWA generate Gaussian mutation sparks by Gaussian mutation. Suppose that firework
In FWA, the explosion sparks and mutation sparks generated by explosion parameters and mutation parameters may exceed the boundary range of feasible region, so they must be mapped to a new location by mapping rules by
Selection strategy
In order to transmit the information of excellent individuals to the next generation, it is necessary to select a certain number of individuals as the fireworks of the next generation from the explosion sparks and variation sparks.
Suppose that there are
Based on the previous description, the specific steps of FWA are as follows [
Step 1. Randomly select
Step 2. Calculate the fitness value
Step 3. Generate
Step 4. From the fireworks, explosion sparks and Gauss mutation spark population,
Step 5. Judge the stop condition. If the stop condition is satisfied, jump out of the program and output the optimal result; if not, return to Step 2 to continue the loop.
In this section, on the basis of the evaluation model of modern photovoltaic agriculture sustainability based on interval type-2 Fuzzy AHP-TOPSIS, the intelligent evaluation model of modern photovoltaic agriculture sustainability based on FWA-LSSVM is proposed, that is, the index value of modern photovoltaic agriculture sustainability evaluation index system is taken as the input, and the LSSVM is optimized by FWA, so as to obtain the optimal value of LSSVM, finally, the sustainability evaluation results of modern photovoltaic agriculture can be obtained and analyzed. The flow chart of the proposed model is shown in
The specific steps are as follows:
Step 1. Construct a sustainable evaluation index system for modern photovoltaic agriculture.
Step 2. Score the evaluation indexes according to the classification of indexes and assign weights to semantic variables.
Step 3. Transform semantic variables into interval type-2 fuzzy numbers, integrate interval type-2 fuzzy matrix and construct weighted normalized fuzzy decision matrix.
Step 4. Determine fuzzy positive and negative ideal solutions, calculate the distance between each alternative and the fuzzy positive and negative ideal solutions, then calculate and sort the similarity coefficients of each alternative.
Step 5. Initialize the parameters of LSSVM and FWA, optimize the parameters of LSSVM model with FWA, then output and analysis the intelligent evaluation results.
In order to achieve the hierarchical measurement of different levels of indexes, it is necessary to classify different indexes on the basis of the level differences, that is, to define the index set. Here, according to the evaluation index system, we divide the indexes into different levels, including the first level indexes and the second level indexes.
Set of the first level indexes
The set of the first level indexes can be expressed as
Set of the second level indexes
The set of the first level indexes can be expressed as follows:
Technical characteristic index
Economic characteristic index
Social characteristic index
Due to the differences in various aspects of the projects to be measured, the measurement results also have the characteristics of diversity. Through the integration of semantic variables, the corresponding set of comments V is established, as shown in
All possible states of the objects to be measured should be fully included in the set of comments. The reasonable construction of the comments set will have an important impact on the accuracy and scientificity of the measurement results. Therefore, we should define the comments set on the basis of full investigation and expert advice.
Comments set of the interval type-2 fuzzy AHP model
There are five semantic variables in the comments set of the interval type-2 fuzzy AHP model. They are absolutely strong (AS), very strong (VS), fairly strong (FS), slightly strong (SS) and equal (E). The expression is shown in
The correspondence between semantic variables of interval type-2 fuzzy AHP model and interval type-2 fuzzy numbers can be shown in
Semantic variables
Interval type-2 fuzzy numbers
The reciprocal of interval type-2 fuzzy numbers
Absolutely strong (AS)
((7, 8, 9, 9;1, 1),
((0.11, 0.11, 0.12, 0.14;1, 1),
Very strong (VS)
((5, 6, 8, 9;1, 1),
((0.11, 0.12, 0.17, 0.2;1, 1),
Fairly strong (FS)
((3, 4, 6, 7;1, 1),
((0.14, 0.17, 0.25, 0.33;1, 1),
Slightly strong (SS)
((1, 2, 4, 5;1, 1),
((0.2, 0.25, 0.5, 1;1, 1),
Equal (E)
((1, 1, 1, 1;1, 1),(1, 1, 1, 1;1, 1))
((1, 1, 1, 1;1, 1),(1, 1, 1, 1;1, 1))
Comments set of the interval type-2 fuzzy TOPSIS model
There are seven semantic variables in the comments set of the interval type-2 fuzzy TOPSIS model. They are very low (VL), low (L), medium low (ML), medium (M), medium high (MH), high (H), very high (VH). The expression is shown in
The correspondence between semantic variables of interval type-2 fuzzy TOPSIS model and trapezoidal interval type-2 fuzzy numbers can be shown in
Semantic variables | Trapezoidal interval type-2 fuzzy numbers |
---|---|
Very low (VL) | ((0, 0, 0, 1;1, 1),(0, 0, 0, 0.05;0.9, 0.9)) |
Low (L) | ((0, 0.1, 0.1, 0.3;1, 1),(0.05, 0.1, 0.1, 0.2;0.9, 0.9)) |
Medium low (ML) | ((0.1, 0.3, 0.3, 0.5;1, 1),(0.2, 0.3, 0.3, 0.4;0.9, 0.9)) |
Medium (M) | ((0.3, 0.5, 0.5, 0.7;1, 1),(0.6, 0.7, 0.7, 0.8;0.9, 0.9)) |
Medium high (MH) | ((0.5, 0.7, 0.7, 9;1, 1),(0.6, 0.7, 0.7, 0.8;0.9, 0.9)) |
High (H) | ((0.7, 0.9, 0.9, 1;1, 1),(0.8, 0.9, 0.9, 0.95;0.9, 0.9)) |
Very high (VH) | ((0.9, 1, 1, 1;1, 1),(0.95, 1, 1, 1;0.9, 0.9)) |
In order to comprehensively evaluate the sustainability of modern photovoltaic agriculture, this paper selects five modern photovoltaic agricultural projects for research. The basic information of the five projects is shown below:
A1: The installed photovoltaic capacity is 75 MW, with an estimated annual average power generation capacity of 98.86 million kWh. 50 new vegetable greenhouses, 25 flower greenhouses and 20 Chinese herbal medicine greenhouses are arranged in the field with steel structure.
A2: This project is a fishery-photovoltaic complementary photovoltaic power plant project. The installed PV capacity is 200 MW, and the average annual power generation is expected to be 257.86 million kWh. The project covers an area of 3,333,300 square meters. In addition, 22 vegetable greenhouses are arranged in the field with steel structure.
A3: This project is a distributed photovoltaic power plant for cowshed. The installed PV capacity is 20 MW, with an estimated annual average power generation capacity of 27.12 million kWh. The cowshed covers an area of 666,700 square meters.
A4: The installed photovoltaic capacity is 50 MW, with an estimated annual average power generation capacity of 63.92 million kWh. 60 new vegetable greenhouses are arranged in the field with steel structure.
A5: This project is a water conservancy PV model. The installed capacity of photovoltaic is 35 MW, and the average annual power generation is expected to be 45.02 million kWh. The PV is used to supply power to farmland drainage and irrigation, water-saving irrigation and its control system. 16 flower greenhouses are arranged in the field with steel structure.
30 experts are invited from photovoltaic industry, agricultural development and energy economy to form a decision-making group to score the alternatives, so as to judge the advantages and disadvantages of the sustainability of modern photovoltaic agricultural projects.
Based on the established sustainability evaluation index system of modern photovoltaic agriculture, experts evaluated this five modern photovoltaic agricultural projects. The scoring results evaluated by experts are shown in
Scheme | Expert | u_{11} | u_{12} | u_{13} | u_{14} | u_{15} | u_{21} | u_{22} | u_{23} | u_{24} | u_{25} | u_{31} | u_{32} | u_{33} | u_{34} | u_{35} |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A1 | E_{1} | VL | L | VL | L | VH | H | H | MH | M | H | ML | H | MH | MH | M |
E_{2} | ML | L | VL | L | M | M | L | L | ML | L | H | M | H | ML | L | |
…… | ||||||||||||||||
E_{30} | ML | M | L | ML | ML | ML | M | H | L | L | M | ML | ML | L | L | |
A2 | E_{1} | L | ML | L | VL | M | ML | L | L | MH | H | H | L | M | M | ML |
E_{2} | MH | VH | L | ML | MH | H | M | ML | L | MH | L | MH | MH | H | H | |
…… | ||||||||||||||||
E_{30} | H | ML | ML | H | L | VL | L | L | VH | H | MH | M | ML | L | M | |
A3 | E_{1} | L | L | L | ML | VL | L | H | M | L | L | H | VL | H | H | M |
E_{2} | MH | VH | L | L | M | MH | L | ML | H | M | H | H | H | L | M | |
…… | ||||||||||||||||
E_{30} | M | MH | M | L | MH | M | H | M | M | ML | L | ML | L | M | MH | |
A4 | E_{1} | L | VH | MH | VL | VL | L | H | H | VL | L | ML | MH | MH | ML | L |
E_{2} | VH | MH | M | L | L | ML | H | L | MH | M | M | M | ML | MH | VL | |
…… | ||||||||||||||||
E_{30} | ML | ML | L | H | MH | MH | M | ML | ML | ML | MH | VH | H | H | M | |
A5 | E_{1} | H | ML | VL | MH | H | M | L | L | M | H | H | M | L | ML | H |
E_{2} | M | H | ML | M | ML | ML | M | M | ML | L | M | L | MH | M | L | |
…… | ||||||||||||||||
E_{30} | L | H | VL | L | L | L | ML | H | L | L | L | ML | M | ML | M |
According to the corresponding relationship between semantic variables and interval type-2 fuzzy numbers in
u_{1} | u_{2} | u_{3} | |
---|---|---|---|
u_{1} | [E, E, E] | [1/FS, FS, 1/VS] | [VS, VS, 1/SS] |
u_{2} | [FS, 1/FS, VS] | [E, E, E] | [VS, VS, FS] |
u_{3} | [1/VS, 1/VS, SS] | [1/VS, 1/VS, 1/FS] | [E, E, E] |
u_{11} | u_{12} | u_{13} | u_{14} | u_{15} | |
---|---|---|---|---|---|
u_{11} | [E, E, E] | [1/VS, 1/FS, SS] | [1/VS, FS, VS] | [1/VS, 1/FS, VS] | [1/SS, FS, VS] |
u_{12} | [VS, FS, 1/SS] | [E, E, E] | [1/FS, FS, FS] | [1/FS, FS, VS] | [FS, VS, VS] |
u_{13} | [VS, 1/FS, 1/VS] | [FS, 1/FS, 1/FS] | [E, E, E] | [FS, 1/FS, SS] | [VS, SS, SS] |
u_{14} | [VS, FS, 1/VS] | [FS, 1/FS, 1/VS] | [1/FS, FS, 1/SS] | [E, E, E] | [FS, 1/FS, 1/FS] |
u_{15} | [SS, 1/FS, 1/VS] | [1/FS, 1/VS, 1/VS] | [1/VS, 1/SS, 1/SS] | [1/FS, FS, FS] | [E, E, E] |
u_{21} | u_{22} | u_{23} | u_{14} | u_{25} | |
---|---|---|---|---|---|
u_{21} | [E, E, E] | [SS, E, 1/FS] | [VS, VS, FS] | [1/VS, 1/FS, VS] | [VS, VS, FS] |
u_{22} | [1/SS, E, FS] | [E, E, E] | [SS, FS, FS] | [1/FS, FS, VS] | [VS, VS, VS] |
u_{23} | [1/VS, 1/VS, 1/FS] | [1/SS, 1/FS, 1/FS] | [E, E, E] | [FS, 1/FS, SS] | [E, SS, SS] |
u_{14} | [VS, FS, 1/VS] | [FS, 1/FS, 1/VS] | [1/FS, FS, 1/SS] | [E, E, E] | [FS, 1/FS, 1/FS] |
u_{25} | [1/VS, 1/VS, 1/FS] | [1/VS, 1/VS, 1/VS] | [E, 1/SS, 1/SS] | [1/FS, FS, FS] | [E, E, E] |
u_{31} | u_{32} | u_{13} | u_{14} | u_{35} | |
---|---|---|---|---|---|
u_{31} | [E, E, E] | [1/SS, 1/SS, 1/SS] | [1/VS, FS, VS] | [1/VS, 1/FS, VS] | [SS, 1/FS, E] |
u_{32} | [SS, SS, SS] | [E, E, E] | [1/FS, FS, FS] | [1/FS, FS, VS] | [FS, 1/SS, 1/FS] |
u_{13} | [VS, 1/FS, 1/VS] | [FS, 1/FS, 1/FS] | [E, E, E] | [FS, 1/FS, SS] | [VS, SS, SS] |
u_{14} | [VS, FS, 1/VS] | [FS, 1/FS, 1/VS] | [1/FS,FS, 1/SS] | [E, E, E] | [FS, 1/FS, 1/FS] |
u_{35} | [1/SS, FS, E] | [1/FS, SS, FS] | [1/VS, 1/SS, 1/SS] | [1/FS, FS, FS] | [E, E, E] |
Similarly, based on the corresponding relationship between semantic variables and interval type-2 fuzzy numbers in
Index | CR_{1} | CR_{2} | CR_{3} | |
---|---|---|---|---|
Index of the first level | 0.0325 | 0.0933 | 0.0763 | |
Index of the second level | Technology sustainability | 0.0384 | 0.0940 | 0.0721 |
Economic sustainability | 0.0940 | 0.0882 | 0.0788 | |
Social sustainability | 0.0876 | 0.0933 | 0.0733 |
From the data in
The geometric average decision matrix of sustainability evaluation indexes of modern photovoltaic agriculture is obtained by
Index | The numerical value of geometric average decision matrix |
---|---|
u_{1} | ((1.23, 1.11, 2.43, 1.04;1, 1),(1.28, 2.33, 2.21, 2.18;0.9, 0.8)) |
u_{2} | ((1.28, 1.8, 3.53, 3.86;1, 1),(2.32, 2.22, 1.23, 3.89;0.8, 0.8)) |
u_{3} | ((1.23, 1.73, 2.26, 2.51;1, 1),(1.51, 1.79, 2.21, 2.46;0.8, 0.8)) |
u_{11} | ((1.32, 1.23, 2.41, 2.74;1, 1),(1.41, 1.8, 2.34, 2.67;0.8, 0.8)) |
u_{12} | ((2.08, 2.48, 3.21, 3.58;1, 1),(2.16, 2.55, 3.14, 3.5;0.8, 0.8)) |
u_{13} | ((1.31, 1.61, 2.17, 2.46;1, 1),(1.38, 1.67, 2.11, 2.4;0.8, 0.8)) |
u_{14} | ((0.3, 0.38, 0.58, 0.76;1, 1),(0.32, 0.4, 0.55, 0.71;0.8, 0.8)) |
u_{15} | ((1.91, 2.34, 3.11, 3.48;1, 1),(2, 2.42, 3.04, 3.41;0.8, 0.8)) |
u_{21} | ((0.28, 0.3, 0.39, 0.47;1, 1),(0.28, 0.31, 0.37, 0.44;0.8, 0.8)) |
u_{22} | ((0.37, 0.46, 0.67, 0.84;1, 1),(0.39, 0.48, 0.64, 0.79;0.8, 0.8)) |
u_{23} | ((0.39, 0.48, 0.65, 0.79;1, 1),(0.41, 0.5, 0.63, 0.75;0.8, 0.8)) |
u_{24} | ((0.52, 0.64, 0.96, 1.28;1, 1),(0.55, 0.66, 0.91, 1.19;0.8, 0.8)) |
u_{25} | ((1.04, 1.43, 2.08, 2.4;1, 1),(1.13, 1.5, 2.02, 2.33;0.8, 0.8)) |
u_{31} | ((1.25, 1.53, 2.04, 2.31;1, 1),(1.31, 1.59, 1.99, 2.25;0.8, 0.8)) |
u_{32} | ((2.22, 2.43, 3.47, 3.88;1, 1),(2.31, 2.74, 3.39, 3.79;0.8, 0.8)) |
u_{33} | ((1.31, 1.65, 2.28, 2.64;1, 1),(1.38, 1.71, 2.22, 2.56;0.8, 0.8)) |
u_{34} | ((1.45, 1.98, 2.39, 2.68;1, 1),(1.52, 1.84, 2.33, 2.62;0.8, 0.8)) |
u_{35} | ((2.01, 2.43, 3.21, 3.62;1, 1),(2.1, 2.51, 3.14, 3.53;0.8, 0.8)) |
According to the data in
Index | Fuzzy weight matrix |
---|---|
u_{1} | ((0.21, 0.3, 0.57, 0.82;1, 1),(0.23, 0.32, 0.53, 0.76;0.8, 0.8)) |
u_{2} | ((0.17, 0.28, 0.58, 0.86;1, 1),(0.19, 0.31, 0.54, 0.78;0.8, 0.8)) |
u_{3} | ((0.09, 0.13, 0.27, 0.46;1, 1),(0.09, 0.13, 0.24, 0.4;0.8, 0.8)) |
u_{11} | ((0.03, 0.04, 0.07, 0.10;1, 1),(0.03, 0.04, 0.06, 0.09;0.8, 0.8)) |
u_{12} | ((0.13, 0.19, 0.37, 0.52;1, 1),(0.14, 0.21, 0.35, 0.48;0.8, 0.8)) |
u_{13} | ((0.04, 0.06, 0.12, 0.18;1, 1),(0.05, 0.07, 0.11, 0.17;0.8, 0.8)) |
u_{14} | ((0.23, 0.32, 0.56, 0.76;1, 1),(0.25, 0.34, 0.53, 0.71;0.8, 0.8)) |
u_{15} | ((0.03, 0.04, 0.09, 0.14;1, 1),(0.03, 0.05, 0.08, 0.13;0.8, 0.8)) |
u_{21} | ((0.14, 0.2, 0.36, 0.51;1, 1),(0.16, 0.21, 0.34, 0.47;0.8, 0.8)) |
u_{22} | ((0.24, 0.33, 0.58, 0.79;1, 1),(0.26, 0.35, 0.55, 0.74;0.8, 0.8)) |
u_{23} | ((0.22, 0.2, 0.53, 0.73;1, 1),(0.24, 0.32, 0.5, 0.68;0.8, 0.8)) |
u_{24} | ((0.04, 0.05, 0.09, 0.13;1, 1),(0.04, 0.05, 0.08, 0.11;0.8, 0.8)) |
u_{25} | ((0.14, 0.19, 0.32, 0.42;1, 1),(0.15, 0.2, 0.3, 0.39;0.8, 0.8)) |
u_{31} | ((0.23, 0.3, 0.51, 0.66;1, 1),(0.25, 0.32, 0.48, 0.62;0.8, 0.8)) |
u_{32} | ((0.17, 0.23, 0.38, 0.51;1, 1),(0.19, 0.24, 0.36, 0.48;0.8, 0.8)) |
u_{33} | ((0.04, 0.06, 0.11, 0.15;1, 1),(0.06, 0.1, 0.14;0.8, 0.8)) |
u_{34} | ((0.14, 0.2, 0.37, 0.52;1, 1),(0.15, 0.21, 0.34, 0.48;0.8, 0.8)) |
u_{35} | ((0.15, 0.19, 0.35, 0.48;1, 1),(0.15, 0.21, 0.33, 0.45;0.8, 0.8)) |
According to the interval type-2 fuzzy TOPSIS model, the positive and negative ideal solutions of interval type-2 fuzzy numbers are calculated, as shown in
Ideal solution | Fuzzy value |
---|---|
x^{+} | (0.012, 0.0854, 0.0126, 0.015, 0.14, 0.1456, 0.0253, 0.0007, 0.0423, 0.023, 0.0561, 0.0222, 0.028, 0.0146, 0.0049) |
x^{−} | (0.002, 0.1055, 0.0551, 0.0344, 0.0016, 0.0943, 0.0324, 0.0911, 0.0376, 0.0446, 0.0455, 0.0127, 0.0121, 0.0109, 0.0837) |
Combined with the positive and negative ideal solutions, the distance between modern photovoltaic agricultural projects and the positive and negative ideal solutions can be obtained, as shown in
A1 | A2 | A3 | A4 | A5 | |
---|---|---|---|---|---|
d^{+} | 0.0856 | 0.0768 | 0.2389 | 0.1243 | 0.0945 |
d^{−} | 0.2830 | 0.1593 | 0.0032 | 0.0987 | 0.0432 |
Finally, the similarity coefficient of sustainability of each modern photovoltaic agricultural project is calculated. The calculation results are shown in
A1 | A2 | A3 | A4 | A5 | |
---|---|---|---|---|---|
C | 0.5900 | 0.7022 | 0.1029 | 0.3597 | 0.5107 |
From the sustainability evaluation results, we can see that the order of sustainability of the five modern photovoltaic agricultural projects is as follows: C(A2)>C(A1)>C(A5)>C(A4)>C(A3). It can be concluded that the sustainability evaluation result of modern photovoltaic agricultural project A2 is the best.
In this paper, the sustainability evaluation model of modern photovoltaic agriculture based on interval type-2 Fuzzy AHP-TOPSIS method is used to get the objective and accurate results of 5 samples of modern photovoltaic agriculture sustainability evaluation. However, according to the above calculation, it can be found that the calculation of the model is more complex, the efficiency is low, and the workload is large. When facing the massive data of modern photovoltaic agriculture projects, this method is bound to be difficult to quickly and effectively calculate the sustainability evaluation results of modern photovoltaic agriculture. Therefore, this paper will further use the FWA-LSSVM model constructed above for research. The other 15 samples are selected as the training set, and the existing 5 samples are used to complete the sustainability evaluation of the modern photovoltaic agriculture. After that, the intelligent evaluation results are compared with the evaluation results in the previous section to verify the effectiveness of the FWA-LSSVM model.
The parameters of FWA are set as follows: the maximum number of iterations
In order to verify the effectiveness of the intelligent evaluation model proposed in this paper, this part continues to use the above 5 photovoltaic agricultural projects for empirical analysis, taking these five photovoltaic agricultural projects as test samples, and selecting another 15 photovoltaic agricultural projects as training samples. FWA-LSSVM, PSO-LSSVM, LSSVM and SVM models are applied to the sustainability evaluation of modern photovoltaic agriculture projects for comparative experiments. The calculation results are shown in
Modern photovoltaic agriculture projects | Approximate coefficient of sustainability evaluation | FWA-LSSVM | PSO-LSSVM | LSSVM | SVM |
---|---|---|---|---|---|
A1 | 0.5900 | 0.6136 | 0.6431 | 0.6726 | 0.7098 |
A2 | 0.7022 | 0.6741 | 0.7794 | 0.8122 | 0.8146 |
A3 | 0.1029 | 0.1065 | 0.0926 | 0.1217 | 0.0836 |
A4 | 0.3597 | 0.3795 | 0.3201 | 0.3120 | 0.2913 |
A5 | 0.5107 | 0.4750 | 0.4698 | 0.4557 | 0.6021 |
Mean absolute percentage error (MAPE), root mean square error (RMSE) and average absolute error (AAE) are used to compare the evaluation errors of each intelligent evaluation model.
It can be seen from
Therefore, the results of the example analysis show that the proposed FWA-LSSVM model can evaluate the sustainability of modern photovoltaic agriculture scientifically and effectively. On the basis of interval type-2 fuzzy AHP-TOPSIS evaluation method, the intelligent algorithm is introduced, and expert knowledge is obtained by intelligence learning to generalize the expert scoring process in comprehensive evaluation. Then, the sustainable evaluation results of modern photovoltaic agriculture are obtained through FWA-LSSVM model, finally achieve the purpose of fast calculation and supporting relevant decision-making.
The healthy and sustainable development of modern photovoltaic agriculture can reduce the consumption of non-renewable energy in agriculture, improve the utilization rate of renewable energy, and significantly promote the efficiency of agricultural development. In order to realize the healthy and sustainable development of photovoltaic agriculture, this paper designs a set of modern photovoltaic agriculture sustainability evaluation system, mainly including an evaluation index system and a new hybrid evaluation method. Firstly, the evaluation index system of the sustainability of modern photovoltaic agriculture is constructed from three aspects, including technology sustainability, economic sustainability and social sustainability, and it solves the problems in which aspects the sustainability of modern photovoltaic agriculture is mainly reflected. Then, based on the interval type-2 fuzzy AHP-TOPSIS method, the comprehensive evaluation is carried out after the evaluation indexes are scientifically weighted, and the evaluation results are obtained from the perspective of traditional evaluation methods. After that, FWA is chosen to optimize the parameters of LSSVM, and finally the FWA-LSSVM model of modern photovoltaic agriculture sustainability is constructed, and the evaluation results are obtained from the perspective of modern intelligent evaluation method. Through the analysis of an example, the scientificity and accuracy of the evaluation model proposed in this paper are verified. The traditional evaluation model can get accurate results, while the intelligent evaluation model can achieve the purpose of fast calculation and supporting relevant decisions. To sum up, the research conclusions of this paper can provide decision-making support for putting forward a more reasonable development mode for modern photovoltaic agriculture. The application of the model proposed in this paper to other fields is an important direction for future research.