Grey Relational Projection Method Research Articles

An integrated design concept evaluation model based on interval valued picture fuzzy set and improved GRP method.

The objective of this research is to enhance the precision and efficiency of design concept assessments during the initial stages of new product creation. Design concept evaluation, which occurs at the end of the conceptual design phase, is a critical step in product development. The outcome of this evaluation significantly impacts the product's eventual success, as flawed design concepts are difficult to remedy in later stages. However, the evaluation of new product concepts is a procedure that encompasses elements of subjectivity and ambiguity. In order to deal with the problem, a novel decision-making method for choosing more logical new product concepts is introduced. Basically, the evaluation process is outlined in three main phases: the construction of evaluation index system for design concept alternatives, the calculation of weights for evaluation criteria and decision-makers, the selection of the best design concept alternatives. These stages are composed of a hybrid method based on kano model, multiplicative analytic hierarchy process (AHP) method, the entropy of IVPFS and improved grey relational projection (GRP) under interval-valued picture fuzzy set (IVPFS). The novel approach integrates the strength of interval-valued picture fuzzy number in handling vagueness, the advantage of multiplicative AHP and the merit of improved GRP method in modelling multi-criteria decision-making. In final, the effectiveness of the proposed model is validated through comparisons with other models. The potential applications of this study include but are not limited to product development, industrial design, and innovation management, providing decision-makers with a more accurate and comprehensive design concept evaluation tool.

Configuration Optimization of Mobile Photovoltaic-Diesel-Storage Microgrid System Based on CPS-MOEA

This paper presents a two-step approach for optimizing the configuration of a mobile photovoltaic-diesel-storage microgrid system. Initially, we developed a planning configuration model to ensure a balance between the mobility of components and a sustainable power supply. Then, we introduced a method that merges optimization and decision-making. The first phase identifies Pareto optimal solutions (POSs) with a favorable distribution by using a multi-objective evolutionary algorithm with classification-based preselection (CPS-MOEA). In the second phase, we utilize the fuzzy C-means algorithm (FCM) and the grey relational projection (GRP) method for comprehensive decision-making. This aims to select the most suitable and compromise solution from the POSs, closely aligning with the decision-maker’s preferences. Beyond addressing the optimal planning and configuration issue, the experimental results show that the method surpasses other widely used multi-objective optimization algorithms, including the Preference Inspired Co-evolution Algorithm (PICEA-g), the Multi-Objective Particle Swarm Optimization Algorithm (MOPSO), and the third stage of Generalized Differential Evolution (GDE3).

Using Autonomous Learning Mode to Improve Students’ Learning Willingness and Resilience

In China, English teaching has become a key part of the education system at all levels. However, despite the significant resources invested in the education system, many students lack the necessary motivation and perseverance to learn. The interactive autonomous learning mode is a newly emerged educational approach that aims to enhance students’ motivation and resilience in learning through interaction and self-motivation. Existing works mostly focus on qualitative analysis and case studies; however, few have comprehensively considered the multiple factors or the future trend. To address this research gap, this paper proposes three novel research methods: predicting future learning willingness using a grey prediction model, evaluating the effectiveness of a learning resilience enhancement strategy using the TOPSIS analysis method, and analyzing the relationship between learning willingness and learning resilience enhancement using an improved grey relation projection method. These methods not only provide a comprehensive and accurate analytical framework, but they also contribute to educational reform and teaching practice.

Failure mode and effects analysis using an improved pignistic probability transformation function and grey relational projection method

Failure mode and effects analysis (FMEA) is an important risk analysis tool that has been widely used in diverse areas to manage risk factors. However, how to manage the uncertainty in FMEA assessments is still an open issue. In this paper, a novel FMEA model based on the improved pignistic probability transformation function in Dempster–Shafer evidence theory (DST) and grey relational projection method (GRPM) is proposed to improve the accuracy and reliability in risk analysis with FMEA. The basic probability assignment (BPA) function in DST is used to model the assessments of experts with respect to each risk factor. Dempster’s rule of combination is adopted for fusion of assessment information from different experts. The improved pignistic probability function is proposed and used to transform the fusion result of BPA into probability function for getting more accurate decision-making result in risk analysis with FMEA. GRPM is adopted to determine the risk priority order of all the failure modes to overcome the shortcoming in traditional risk priority number in FMEA. Applications in aircraft turbine rotor blades and steel production process are presented to show the rationality and generality of the proposed method.

Picture hesitant fuzzy grey compromise relational bidirectional projection method with application in multi-attribute recommendation

In view of the technical defects of the existing grey relational projection method, a new grey compromise relational bidirectional projection method is proposed. By incorporating the information expression advantage of picture hesitant fuzzy number, the distance formula of picture hesitant fuzzy statistics is constructed based on the centralized trend measurement and discrete trend measurement in descriptive statistics. On this basis, a multi-attribute recommendation method of picture hesitant fuzzy grey compromise relational bidirectional projection is proposed by combining compromise idea and bidirectional projection technology. The validity and advantage of this method are verified by numerical analysis, which also suggested the rationality of the picture hesitant fuzzy statistical distance and the grey compromise relational bidirectional projection method.

Competitive Equilibrium Analysis of Power Generation Transaction Subjects Considering Tradable Green Certificates

The implementation of renewable portfolio standards (RPS) and tradable green certificate schemes will exert significant influences on the market equilibrium outcomes and generation firms’ strategic behaviors. To quantitatively investigate these influences, firstly, considering the difference in power generation cost and the uncertainty of renewable energy power generation, the equilibrium model for various trade subjects in the electricity market is established. Secondly, the nondominated sorting genetic algorithm II is adopted for solving the equilibrium model to find well-distributed Pareto-optimal solutions. Finally, the grey relational projection method is used to calculate the priority membership of each decision-making scheme so as to determine the optimal compromise solution. The simulation focuses on analyzing the impact of RPS on the equilibrium results and market behavior of power generators and introduces the Lerner index to quantify the market power of generators. The results show that: (1) An increase in the quota ratio can effectively increase power generation in renewable energy generators. The game between thermal power generators and renewable energy generators raises the prices of both markets at the same time. (2) Improving the forecasting accuracy is conducive to alleviating the market power behavior of various power generators, thereby ensuring the healthy operation of the power market.

Early Warning Evaluation and Warning Trend Analysis of the Resource and Environment Carrying Capacity in Altay Prefecture, Xinjiang

Ecologically fragile areas in China account for more than half of its land area. Performing early warning assessments and trend analyses of resource and environment carrying capacity in ecologically fragile areas can lay a scientific foundation for ecological conservation in the areas. Based on the connotation of resource and environment carrying capacity, an early warning index system of resource and environment carrying capacity in Altay prefecture was constructed from the three aspects natural resource carrying capacity, eco-environment carrying capacity, and economic and social support capacity. The grey relational projection method model was used to analyze the current alarm situation of the resource and environment carrying capacity in Altay prefecture from 2011 to 2020, and then the back propagation (BP) neural network and a mathematical statistics software were used to predict the evolution of the alarm situation of the resource and environment carrying capacity in Altay prefecture from 2021 to 2025. The results demonstrated that (1) the natural resource carrying capacity subsystem was the main system of the development of the resource and environment carrying capacity in Altay prefecture, and its impact on the resource and environment carrying capacity in Altay prefecture was greater than the eco-environment carrying capacity and economic and social support capacity; (2) the resource and environmental carrying capacity of Altay prefecture showed a slight upward trend from 2011 to 2020, although the range was constrained and the level of warning remained “moderate warning”. A spatial pattern of “weak in the middle, strong in the two poles” was exhibited by the warning scenario about the carrying capacity of each county and city. Except for the warning of Habahe County and Qinghe County, where the warning was slightly worse than that in 2020, the warning of resource and environment carrying capacity in Altay prefecture and other counties and cities would show a trend of fluctuation and decline from 2021 to 2025. However, the degree of alarm did not change substantially and remained at the level of “moderate warning”; (3) the main factors restricting the mitigation of the warning of resource and environment carrying capacity in Altay prefecture included a low soil fertility index, a small total reservoir capacity, low per capita mineral resource reserves, a low water resource development and utilization rate, a low comprehensive utilization rate of industrial solid waste, and a low land output rate.

Optimisation for sandy pebble deep foundation pit support based on multi-objective fuzzy grey relation projection method

ABSTRACT Many influencing factors should be considered in the selection of deep foundation pit supporting scheme. And the impact of different factors on supporting scheme is difficult to measure. There is a grey correlation between many influencing factors and the selection of supporting schemes. In this paper, the multi-objective fuzzy grey relation projection method can be obtained by weighting method and used to select the support of foundation pit. Therefore, a set of corresponding evaluation indexes of deep foundation pit support is put forward and the weight of each evaluation index is given. Then the weight is brought into the multi-objective fuzzy grey relation projection method to select the supporting mode of foundation pit. This method is applied to the selection of the supporting mode of the foundation pit of sand-pebble station, and the optimal supporting mode is obtained. The results is as follows : (1) It is effective to select the supporting scheme of foundation pit by fuzzy grey relational projection method. (2) The evaluation index of deep foundation pit supporting is reasonable. (3) It is of certain reference value to adopt bored pile + steel support method for sandy pebble foundation pit.

Comprehensive evaluation of power quality of coal mine power grid based on equilibrium empowerment and improved grey relational projection method

Aiming at the problem that the current comprehensive evaluation system of power quality is not fully applicable to coal mine power grid, and the load characteristics of coal mine electrical equipment are less considered, a comprehensive evaluation method of power quality of coal mine power grid based on equilibrium empowerment and improved grey relational projection is proposed. According to the actual situation and load characteristics of coal mine power grid, the power quality index system of coal mine power grid is established, and the grade is divided according to the national standard. The G-1 method is used to determine the subjective weight of the index, the improved CRITIC method is used to determine the objective weight of the index, and the subjective and objective weights are combined with the equilibrium idea of game theory to determine the equilibrium weight, so as to overcome the limitation of single weight. The TOPSIS method is combined with the GRA method, and the positive and negative ideal sequence is introduced to make up for the deficiency of the traditional GRA method. The vector projection method is used to construct the grey relational projection model, and the projection value is used to comprehensively evaluate the power quality of coal mine power grid. The example analysis shows that the proposed method is effective and feasible, can correctly evaluate the power quality of each test point, and can reasonably divide the power quality grade of each test point, which provides a basis for power quality management.

Comprehensive benefit evaluation of solar PV projects based on multi-criteria decision grey relation projection method: Evidence from 5 counties in China

The photovoltaic poverty alleviation program is an innovation of sustainable development strategy by the Chinese government, which aims to promote the development of renewable energy while reducing rural poverty through the systematic deployment of solar photovoltaic (PV). Nevertheless, the actual benefits of photovoltaic poverty alleviation projects (PV-PAPs) need to be verified. Yet, little research currently explored the regional differences of large-scale PV deployment. This study intends to construct a comprehensive benefit evaluation system in 4 dimensions of finance, energy, environment and society including 15 secondary indicators. The multi-criteria decision making (MCDM) grey relation projection (GRP) method and first-hand field survey data of 5 counties in China were used to evaluate the comprehensive benefit of PV-PAPs. The results show that PV-PAPs have good benefits potential with a solid demonstration effect and robust replicability. However, obvious differences were found between actual performance and theoretical design, benefits vary enormously among regions, modes, and solar resource areas. Management styles, operational and maintenance mechanisms are the main sources of regional differences. Besides, sensitive analysis show that financial benefit of PV-PAPs is relatively vulnerable to risk factors. Finally, corresponding policy recommendations are proposed to facilitate the sustainable development of PV-PAPs.

A multi-criteria decision-making framework for site selection of distributed PV power stations along high-speed railway

The construction of distributed photovoltaic power stations (DPVPS) along high-speed railway can supply power for the traction power supply system (TPSS) of high-speed railway. The DPVPS site selection is a natural call from the practice with the consideration of full use of solar PV. This paper addresses a multi-criteria decision-making (MCDM) framework for DPVPS site selection along high-speed railway for the first time. In this framework, an evaluation criteria system is established. Considering the particularity of DPVPS site selection problem along high-speed railway, two new criteria namely power consumption capacity of high-speed railway TPSS and impact on high-speed railway TPSS are presented innovatively. In view of the strong grey correlations among criteria, the fuzzy grey relational projection (FGRP) method is applied to select the optimal site which is greatly suitable to deal with the grey correlations. A case in Hebei Province with sensitivity analysis also illustrates the robustness and effectiveness of the framework. The calculation results of the case indicate that the sub-criteria of impact on high-speed railway TPSS (C26) has the largest comprehensive weight, which is 0.129. Among the four candidate sites, G1 gets the highest final score of 0.653. This paper puts forward an effective tool for railway companies to choose the most suitable site to build DPVPS along high-speed railway, which has the certain practical significance.

China's overcapacity industry evaluation based on TOPSIS grey relational projection method with mixed attributes

PurposeThis paper takes the seven overcapacity industries such as the textile industry, electricity and heat, steel, coal, automobile manufacturing, nonferrous metals and petrochemical industry as research objects and proposes a TOPSIS grey relational projection group decision method with mixed multiattributes, which is used for the ranking of the seven industries with overcapacity and provided relevant departments with a basis for decision-making.Design/methodology/approachFirst, an evaluation index system from four aspects is established. Secondly, the attributes of linguistic information are converted into two-dimensional interval numbers and triangular fuzzy numbers, and an evaluation matrix is constructed and normalized. This paper uses the AHP method to determine the subjective weights and uses the coefficient of variation method to determine the objective weights. Moreover, this paper sets up the optimization model with the largest comprehensive evaluation value to determine the combined weights. Finally, the TOPSIS grey relational projection method is proposed to calculate the closeness of grey relational projections and to rank them.FindingsThis paper analyzes the problem of overcapacity in seven industries with the TOPSIS grey relational projection method. The results show that the four industries of automobile manufacturing, textile, coal and petrochemical are all in serious overcapacity levels, while the three industries of steel, nonferrous metals and electric power are relatively in weak overcapacity level in the three years of 2016–2018. TOPSIS grey relational projection method ranks the overcapacity degree of the seven major overcapacity industries, making the relative overcapacity degree of each industry more clear and providing a reference for the government to formulate targeted policies and measures for each industry.Practical implicationsBy using TOPSIS grey relational projection method to evaluate the overcapacity of the seven major overcapacity industries, on the one hand, it makes the relative overcapacity degree of each industry more clear, on the other hand, it can provides the basis for the government and decision-making departments. This helps them promote better the healthy and orderly economic development of the seven major industries and avoid resource waste caused by overcapacity.Originality/valueThis article solves the single evaluation method caused by the limited indicators in the past, combines TOPSIS and the grey relational projection method and applies it to the overcapacity evaluation of the industry, not only applies it to the evaluation of overcapacity for the first time but also involves novel problems and methods, which expands the scope of application of the model.

Multi-attribute decision making using grey relational projection method based on interval type-2 trapezoidal fuzzy numbers

Multi-attribute decision making using grey relational projection method based on interval type-2 trapezoidal fuzzy numbers

A grey relational projection method for multi attribute decision making based on three trapezoidal fuzzy numbers

A grey relational projection method for multi attribute decision making based on three trapezoidal fuzzy numbers

Grey relational bidirectional projection method based on trapezoidal type-2 intuitionistic fuzzy numbers

Grey relational bidirectional projection method based on trapezoidal type-2 intuitionistic fuzzy numbers

Multi-Objective Optimal Reactive Power Dispatch of Power Systems by Combining Classification-Based Multi-Objective Evolutionary Algorithm and Integrated Decision Making

For the purpose of addressing the multi-objective optimal reactive power dispatch (MORPD) problem, a two-step approach is proposed in this paper. First of all, to ensure the economy and security of the power system, the MORPD model aiming to minimize active power loss and voltage deviation is formulated. And then the two-step approach integrating decision-making into optimization is proposed to solve the model. Specifically speaking, the first step aims to seek the Pareto optimal solutions (POSs) with good distribution by using a multi-objective optimization (MOO) algorithm named classification and Pareto domination based multi-objective evolutionary algorithm (CPSMOEA). Furthermore, the reference Pareto-optimal front is generated to validate the Pareto front obtained using CPSMOEA; in the second step, integrated decision-making by combining fuzzy c-means algorithm (FCM) with grey relation projection method (GRP) aims to extract the best compromise solutions which reflect the preferences of decision-makers from the POSs. Based on the test results on the IEEE 30-bus and IEEE 118-bus test systems, it is demonstrated that the proposed approach not only manages to address the MORPD issue but also outperforms other commonly-used MOO algorithms including multi-objective particle swarm optimization (MOPSO), preference-inspired coevolutionary algorithm (PICEAg) and the third evolution step of generalized differential evolution (GDE3).

A novel multiple attribute decision making method based on grey relational projection and its application for e-commerce risk assessment

With respect to multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant fuzzy elements, the traditional grey relational projection (GRP) method is extended to solve multiple attribute decision making problems under hesitant fuzzy environment. Since the weights of attributes are incompletely known, a nonlinear optimisation model is established, i.e., a reasonable weight vector of attributes should make all alternatives have the largest grey relational projections on positive ideal solution and the smallest grey relational projections on negative ideal solution. Then, based on the hesitant fuzzy decision matrix provided by decision makers, all feasible alternatives are ranked according to the descending order of relative grey relational projections and the most desirable alternative(s) should have the largest grey relational projection on positive ideal solution and the smallest grey relational projection on negative ideal solution. Finally, a numerical example of e-commerce risk assessment is given to illustrate the application of the proposed method.

A Social Beetle Swarm Algorithm Based on Grey Target Decision-Making for a Multiobjective Distribution Network Reconfiguration Considering Partition of Time Intervals

With the increased distributed generation (DG) and the combination of residential, commercial, and industrial loads connected to the distribution networks, it is more difficult to ensure the safe and economic operation of the distribution networks because of the great volatility and randomness of DG and complex loads. In this paper, with the aim of minimizing network loss, load balance, and maximum voltage deviation, a multiobjective reconfiguration model of the distribution network is established under the condition of satisfying network constraints. Moreover, a new social beetle swarm optimization algorithm (SBSO) considering two social behaviors is adopted to solve the complex problem according to the characteristics of the distribution network reconfiguration (DNRC). Based on the SBSO algorithm, grey target decision-making (GTDM) strategy is used to choose the best beetle in the process of solving the multiobjective problem. Additionally, The grey relation projection (GRP) method is used to divide the time period of DNRC according to the change of DG and loads in a day, in order to reduce the number of switching operations. Finally, the effectiveness of the proposed multiobjective model and algorithm are verified on the standard IEEE-33 system and IEEE-69 system.

Model for selection of hospital constructions with probabilistic linguistic GRP method

Probabilistic linguistic term sets are used to express uncertain decision information in multiple attribute group decision making problems. For probabilistic linguistic multiple attribute group decision making (MAGDM) with weight determined by CRITIC (Criteria Importance Through Intercriteria Correlation) method, the probabilistic linguistic grey relational projection method is proposed in this paper. Firstly, the correlation coefficient among attributes and standard deviation of each attribute are utilized to compute the attributes weights. Then the most ideal alternative is decided by means of counting the grey relational projection (GRP) from probabilistic linguistic positive ideal solution and probabilistic linguistic negative ideal solution. In the end, a numerical example for site selection of hospital constructions is applied to further account for the extended method. The result demonstrates the availability of the proposed method and it can be used in other fields which refers to problems of selection.

Two-Step Many-Objective Optimal Power Flow Based on Knee Point-Driven Evolutionary Algorithm

To coordinate the economy, security and environment protection in the power system operation, a two-step many-objective optimal power flow (MaOPF) solution method is proposed. In step 1, it is the first time that knee point-driven evolutionary algorithm (KnEA) is introduced to address the MaOPF problem, and thereby the Pareto-optimal solutions can be obtained. In step 2, an integrated decision analysis technique is utilized to provide decision makers with decision supports by combining fuzzy c-means (FCM) clustering and grey relational projection (GRP) method together. In this way, the best compromise solutions (BCSs) that represent decision makers’ different, even conflicting, preferences can be automatically determined from the set of Pareto-optimal solutions. The primary contribution of the proposal is the innovative application of many-objective optimization together with decision analysis for addressing MaOPF problems. Through examining the two-step method via the IEEE 118-bus system and the real-world Hebei provincial power system, it is verified that our approach is suitable for addressing the MaOPF problem of power systems.