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Abrasive water jet (AWJ) machining does not impact material quality and modern machining processes. The trials follow the Taguchi L25 orthogonal array and the workpiece material is Ti grade 5 alloy. The optimal process parameters are determined using response surface methodology and these parameters include transverse speed (TS), pressure (P), abrasive flow rate (AFR) and stand-off distance (SoD). The aim of this research is to identify, evaluate, and improve the impression of AWJ machining parameters on response variables (machining time [MT], surface roughness [SR], and hardness). Achieving this objective involves utilizing grey relational analysis in conjunction with principal component analysis. TS has the least influence on performance while AFR has the greatest. The best configuration for the lowest MT, SR, and Highest Hardness Rockwell C scale (HRC) is (AFR = 600 g/min, SoD = 4 mm, P = 20 kpsi, and quality = 5 approximately, speed 75 mm/min). Here, quality = 5 corresponds to a TS of approximately 75 mm/min and the factor AFR has the greatest impact on material machining performance, according to the analysis of variance, followed by factors P, standoff distance, and TS. The chronological sequence of influence is as follows: AFR > P > SoD > TS with contributions of 85.45%, 8.06%, 2.90%, and 2.09%, respectively. Experiments showed that the proposed methodology enhanced AWJ machining performance by 0.3665 which is represented as multi-response performance index.

How to identify key nodes is a challenging and significant research issue in complex networks. Some existing evaluation indicators of node importance have the disadvantages of limited application scope and one-sided evaluation results. This paper takes advantage of multiple centrality measures comprehensively, by regarding the identification of key nodes as a multi-attribute decision making (MADM) problem. Firstly, a new local centrality (NLC) measure is put forward through considering multi-layer neighbor nodes and clustering coefficients. Secondly, combining the grey relational analysis (GRA) method and the susceptible-infectious-recovered (SIR) model, a modified dynamic weighted technique for order preference by similarity to ideal solution (TOPSIS) method is proposed. Finally, the effectiveness of the NLC is illustrated by applications to nine actual networks. Furthermore, the experimental results on four actual networks demonstrate that the proposed method can identify key nodes more accurately than the existing weighted TOPSIS method.

Identifying the influential nodes in complex networks is a challenging and significant research topic. Though various centrality measures of complex networks have been developed for addressing the problem, they all have some disadvantages and limitations. To make use of the advantages of different centrality measures, one can regard influential node identification as a multi-attribute decision-making problem. In this paper, a dynamic weighted Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is developed. The key idea is to assign the appropriate weight to each attribute dynamically, based on the grey relational analysis method and the Susceptible–Infected–Recovered (SIR) model. The effectiveness of the proposed method is demonstrated by applications to three actual networks, which indicates that our method has better performance than single indicator methods and the original weighted TOPSIS method.

This paper proposed an innovative method based on the semantic differential of Kansei Engineering and the correlation analysis of machine learning in the case of small-size samples, which could achieve the evaluation of users’ subjective feelings to form factors of modeling language and color schemes in the process of product design. It used grey relational analysis and the entropy method to analyze and study the design of modeling and color of guide signs in a public space, and converted the subjective assessment process of designer and user in art design into numeric operation that quantifies and treats data. This research faced two problems: one was to analyze the form correlation between the modeling and color of designed guide signs and the architecture and environment of a public space where the signs are placed, and the other was to convert the subjective assessment of designed guide signs into objective quantified data. The paper took vertical guide boards in a guide sign system as a research object, analyzed and resolved it according to the primitive type of form factors of modeling language, and converted them into numbered sequences of the form factor type. Then, guide boards using different color schemes were utilized to conduct group tests on users; the uniformity of guide boards and architectural style was evaluated through a semantic differential method of Kansei engineering; the test data was analyzed and treated using the grey relational degree, Pearson correlation coefficient and the entropy method; the user’s qualitative assessment on the correlation degree of the modeling form and architectural style of guide boards using different color schemes was converted into quantitative numerical parameters; and finally, we obtained the assessment results of the correlation degree and significance of integrated color and modeling language form factors.

Specific to the users’ assessment discrepancies on the style design of guide signs using different colors, this paper proposed a color scheme evaluation approach with uniform color space based on the grey correlation degree, used Pearson correlation coefficient to make a numerical analysis on users’ subjective assessment, presented a modified entropy method based on standardization, and made a comprehensive assessment on the uniformity of style design in different colors and architectural style. Thus, the numerical analysis results of the uniformity between the guide signs in different color schemes and modeling forms and the architectural style of public spaces were obtained. This research method can provide a new research means and numerical computation method to the study of color and form correlation in product design and style design. Meanwhile, it also provides a theoretical foundation and application method for artistic design by virtue of high-performance computing platforms.

This study is based on Taguchi’s design of experiments along with grey relational analysis (GRA) to optimize the milling parameters to minimize surface roughness, tool wear, and vibration during machining of Inconel-625 while using coconut oil as cutting fluid (CF). The experiments were conducted based on Taguchi’s L₉ orthogonal array (OA). Taguchi’s S/N was used for identifying the optimal cutting parameter for individual response. Analysis of variance (ANOVA) was employed to analyze the outcome of individual parameters on responses. The surface roughness was mostly influenced by feed. Flank wear was influenced by speed and the vibration was mostly influenced by the depth of cut as well as speed. The multi-response optimization was done through GRA. From GRA, the optimal parameters were identified. Further, nanoboric acid of 0.5 and 0.9wt.% was mixed with coconut oil to enhance lubricant properties. Coconut oil with 0.5wt.% of nanoboric acid minimizes the surface roughness and flank wear by 3.92% and 6.28% and reduces the vibration in the $z$-axis by 4.85%. The coconut oil with 0.5wt.% of nanoboric acid performs better than coconut oil with 0.9wt.% of nano boric acid and base oil.

In this study, an attempt has been taken to find out the appropriate optimal parameter setting that will provide the best quality product depending on experimental data during Electro Discharge Machining (EDM) of Titanium grade 6 alloy with the help of brass electrode and to compare the optimized results achieved from two optimization techniques. For this study, Face Centered Central Composite Design- (FCCCD) based Response Surface Methodology (RSM) coupled with Technique for order of preference by similarity to ideal solution (TOPSIS) and Grey Relational Analysis (GRA) has been applied to optimize the process parameters i.e. gap voltage ($V_g)$, peak current ($I_P)$, pulse on time ($T_{\mathrm{\text{on}}})$, and duty cycle ($\mathrm{\Gamma }$). Radial overcut (ROC), surface roughness ($R_a)$, material removal rate (MRR) and tool wear rate (TWR) are selected as output performance characteristics. To find out the significant process parameters, Analysis of variance (ANOVA) test has been performed at 95% confidence level. For validation of the study, confirmation experiments have been performed at optimal parameters setting which show the enhancement of Relative Closeness Coefficient ($S_{iw})$ up to 0.144082 using TOPSIS and Grey Relational Grade (GRG) up to 0.198014 using GRA, respectively.

Fiber metal laminates (FML) are used in outer covering of the fuselage skin structure. The thrust force and the torque generated during drilling process affect the quality of the holes on the structure. The magnitude of cutting forces is controlled by optimizing the drilling process parameters. In this study, the influence of drilling parameters such as spindle speed, feed rate and the weight percentage of layered double hydroxides (LDH) in the binder epoxy on the thrust force and torque during drilling operation was studied. The experiments were designed based on Taguchi’s L₉ orthogonal array. The Gray Relational Analysis was used as multi-objective optimization tool for finding the optimal combination of process parameters. The spindle speed was identified as the most influencing process parameter to affect the drill quality in the FMLs. SEM images taken on the drilled specimens for the best and worst input parameter settings were compared and discussed. The regression models were generated to predict the output response values within the range of actual experiments.

Erosion–corrosion is a common mechanism in the degradation of systems in the mining, chemical, and petrochemical industries. Surface modification can help to reduce the detrimental effects of erosion–corrosion. This study uses the plasma spray process for coating nichrome on duplex stainless steel (DSS2205) to improve the surface characteristics. Erosion tests were performed to analyze the effect of parameters such as impact velocity (150, 175 and 200m/s), impact angle (30^∘, 60^∘ and 90^∘), and erodent particle discharge rate (2.5, 3.75 and 5g/min). According to the findings, the maximum erosion rate ($1.89\times 10^{-6}$g/g) was found at a flow velocity of 200m/s and 30^∘ impact angle with a discharge rate of 2.5g/min. While the minimal erosion rate was observed at a low velocity of 150m/s, 90^∘ impact angle, and 5g/min discharge rate. Electrochemical polarization studies were carried out on the eroded specimens using a corrosive solution containing 3.5% NaCl. Corrosion potentials and current densities were estimated from polarization graphs using the Tafel extrapolation method. The erosion–corrosion properties of the samples were subjected to metallurgical characterization to evaluate the influence of nichrome plasma coatings to assess the potential causes of failure. The grey relational analysis (GRA) was further used for improving the erosion–corrosion process parameters and found the optimum solution as flow velocity of 150m/s, 30^∘ impact angle with a discharge rate of 5g/min. The validation test confirmed an increase of 20–30% in grade when using the optimum process parameters.

In the process of vehicle interior sound quality research, the subjective assessment usually requires a lot of manpower, time and material resources. It is necessary to choose appropriate objective indexes to predict the subjective results. In this paper, a sound quality evaluation index analysis and selection scheme based on grey relational analysis (GRA) is designed. In order to make a reasonable prediction of the subjective indexes with the limited data, GRA of the objective indexes and subjective indexes is conducted. Because three subjective indexes are considered in our study, an indicator that can represent the three chosen subjective indexes is established for the subsequent analysis. Furthermore, the comprehensive ranking and the hierarchical cluster analysis (HCA) of the objective indexes are involved to make the selection of objective indexes easy and meaningful. Finally, the objective indexes are divided into five groups by HCA. According to the clustering results, four objective indexes including “fluctuation”, “sharpness”, “articulation index” and “roughness” are suitable for predicting and representing the subjective indexes to some degree. The scheme proposed in this paper lays the foundation for further optimization and control of vehicle interior sound quality. The method can also be applied to solve other similar multi-factor analysis and selection problems.

Classification algorithm selection is an important issue in many disciplines. Since it normally involves more than one criterion, the task of algorithm selection can be modeled as multiple criteria decision making (MCDM) problems. Different MCDM methods evaluate classifiers from different aspects and thus they may produce divergent rankings of classifiers. The goal of this paper is to propose an approach to resolve disagreements among MCDM methods based on Spearman's rank correlation coefficient. Five MCDM methods are examined using 17 classification algorithms and 10 performance criteria over 11 public-domain binary classification datasets in the experimental study. The rankings of classifiers are quite different at first. After applying the proposed approach, the differences among MCDM rankings are largely reduced. The experimental results prove that the proposed approach can resolve conflicting MCDM rankings and reach an agreement among different MCDM methods.

Flow-based methods based on the outranking relation theory are extensively used in multiple criteria classification problems. Flow-based methods usually employed an overall preference index representing the flow to measure the intensity of preference for one pattern over another pattern. A traditional flow obtained by the pairwise comparison may not be complete since it does not globally consider the differences on each criterion between all the other patterns and the latter. That is, a traditional flow merely locally considers the difference on each criterion between two patterns. In contrast with traditional flows, the relationship-based flow is newly proposed by employing the grey relational analysis to assess the flow from one pattern to another pattern by considering the differences on each criterion between all the other patterns and the latter. A genetic algorithm-based learning algorithm is designed to determine the relative weights of respective criteria to derive the overall relationship index of a pattern. Our method is tested on several real-world data sets. Its performance is comparable to that of other well-known classifiers and flow-based methods.

Performance evaluation is one of the most important problems for retail chains and may have effect on tactical and strategic decisions. This paper proposes a grey-based multi-criteria performance evaluation model for retail sector. This model integrates Decision-Making Trial and Evaluation Laboratory (DEMATEL) and modified Grey Relational Analysis (GRA) methods. First, the grey-based DEMATEL method is used for determining the importance of performance indicators to be used in GRA based on the experts’ assessments. Then, the proposed modified GRA method is used for the performance evaluation and ranking of retail stores with respect to the predetermined performance indicators. Finally, the effectiveness and the applicability of the developed approach are illustrated with a case study with the actual data taken from a retail chain in Turkey.

Decision making remains a prominent issue in all the problem domains. To make better decisions, multiple factors of the given problem need to be considered and evaluated. Multi-criteria decision-making methods have been used popularly for solving decision-making problems characterized by multiple factors. When multiple factors are considered, it is recommended to categorize the factors into the main criteria and sub-criteria. In this paper, GRAP-an integrated ranking algorithm has been developed by combining Grey Relational Analysis, Rank Sum, and Preference Ranking Organization Method Enrichment Evaluation methods (PROMETHEE) to solve decision-making problems. The weights of the sub-criteria are calculated using the Rank Sum method. Grey Relational Analysis method is used to convert the sub-criteria values into main criteria values in the form of evaluation scores of alternatives. The final ranking scores of the alternatives are obtained using the PROMETHEE method. A decision model is developed using the proposed GRAP algorithm and applied to the Job Profile selection case study. The developed decision model showed much better results compared to other MCDM approaches namely the Simple Additive Weight method, TOPSIS, VIKOR, and Complex Proportional Assessment (COPRAS). Further, a sanity check has been carried out by comparing the results of the decision model with experts’ opinions.

Electrical discharge machining is an alternative process for machining complex and intricate shapes. In this paper, an inter-relationship of various electrical discharge machining parameters, namely discharge current, pulse on and off time and dielectric flow rate on material removal rate (MRR), tool wear rate (TWR), surface finish (SR_a) and dimensional tolerance using a Taguchi–Grey relational analysis. The response surface methodology is used to develop a second order model for MRR, TWR and SR_a in terms of process parameters. Finally, a multi-objective optimization problem is formulated by using MRR, TWR and SR_a. The multi-objective problem is then optimized through a modified particle swarm optimization (PSO) algorithm to find the optimum level of parameters. In this research, the results of the proposed method are validated through confirmation experiment. The work piece material used for experimentation is stainless steel of S304 grade.

Multiobjective optimization (MOO) helps to achieve simultaneous improvement of more than one output characteristic in machining processes where complex interaction between the input parameter exists. This study focuses on the comparative analysis of design of experiment (DoE)-based grey relational analysis (GRA) combined with principal component analysis (PCA) and analytic hierarchy process (AHP). Experiments were conducted with millisecond (ms) duration pulsed Nd: YAG laser using the Box–Behnken design (BBD) approach of the response surface methodology (RSM) at three different levels of input parameters. The output parameters, i.e., hole circularity at top (HCT), hole circularity at bottom (HCB), and hole taper (HT), were determined for various input parameters like pulse current (I), pulse width ($P_w$), gas pressure ($G_p$), workpiece thickness ($T_i$), and incidence angle ($\theta$) during laser percussion inclined hole drilling (LPIHD) in the carbon fiber reinforced polymer (CFRP) of three different thickness, i.e., 1mm, 3mm, and 5mm at incidence angles of 0, 10, and 20 degrees. Multiobjective function based on RSM has been developed for GRA-PCA and GRA-AHP and further optimizations were performed using the desirability approach of RSM. The analysis revealed that the angle of incidence is the most significant factor for controlling the output parameters. Interaction of pulse current and thickness ($I\times T_i$) has a major impact on output responses. The GRA-PCA approach gives the average improvement of 2%, 9%, and 37%, respectively, for HCT, HCB, and HT, whereas in the case of GRA-AHP, the corresponding improvements are only 1%, 6%, and 11%. Therefore, the GRA-PCA approach is a more effective tool for the MOO of LPIHD in CFRP.

Magnetic field-assisted electrochemical spark drilling (MA-ECSD) is a cost-effective triplex hybrid machining technique that has been developed to enhance the machining depth and surface roughness of insulated and hard-to-scribe materials. The study presented adopts a reformed approach for creation of dynamic magnetic field during drilling of Sodalime glass where a 34 AWG copper wire coiled electromagnet has been installed in the in-house designed and fabricated setup of MA-ECSD. The experimental plan is based on Box–Behnken design (BBD) of Response Surface Methodology (RSM) and significance of parameters is determined using ANOVA. Multi-objective optimization (MOO) is performed by applying Grey Relational Analysis (GRA). A noncontact optical profilometer measures the machining depths and surface roughness of drilled holes. The installed electromagnet generated dynamic magnetic field intensity (MFI) ranging between 0.00 and 0.18 Tesla. Preliminary experiments were conducted to select and set the range of input parameters. Significant effect of voltage, NaOH concentration and MFI on machining depth and surface roughness is found and optimal parameter settings obtained are 24V, 30wt% and 0.09 Tesla. Machining depth increased by about 13.03% with rise in voltage-NaOH concentration and surface roughness improved by 25.3% with elevation in voltage-MFI. Dynamic MFI generated from electromagnet helped in smooth motion of electrolyte in the fine space amidst cathode and glass slide due to magnetohydrodynamic effect (MHD) which resulted in enhanced machining depth and surface roughness. The experimental and predicted results obtained after confirmatory test are appreciable which is evident from SEM images and images obtained from Optical profilometer.

This study delves into enhancing the mechanical properties of glass fiber-reinforced polymers (GFRPs) by integrating multi-walled carbon nanotubes (MWCNTs) using the hand layup method. Integrated response surface methodology (RSM) combined with grey relational analysis (GRA) and mother optimization algorithm (MOA) was employed to predict multiple responses simultaneously. Fabrication parameters: MWCNT loading, sonication time, oven curing temperature and output responses, ultimate tensile strength (UTS), and shear beam strength in longitudinal and traverse directions are considered. The experiments are planned as per the Box-Behnken design of RSM, and responses have been noted. GRA applications are used to convert multi-responses into a single response, i.e. GRG. RSM is applied to postulate the mathematical equation to create a relationship between the fabrication parameters and GRG. The MOA is then used to maximize GRG value, which indicates enhanced multi-responses. Research shows that adding MWCNTs considerably strengthens GFRPs’ mechanical aspects. The predicted fabricating setting is validated with confirmatory tests, showing considerable improvements in mechanical properties.

As real world data, larceny-theft rates are most likely to have both linear and nonlinear components. A single model such as the linear or nonlinear model may not be sufficient to model the larceny-theft rate. Thus, a hybridization of the linear and nonlinear models is proposed for modeling the larceny-theft rate. The proposed model combines Support Vector Regression (SVR) and Autoregressive Integrated Moving Average (ARIMA) models. Particle swarm optimization is used to optimize the parameters of SVR and ARIMA models. The proposed model is equipped with features selection that combines grey relational analysis and SVR to choose the significant economic indicators for the larceny-theft rate. The experimental results show that the proposed model has better accuracy than the linear, nonlinear, and existing hybrid models in modeling the larceny-theft rate of United States.

An evaluation index system is based on combining the operability of indicators and the trends of distribution network; also taking reactive power compensation device into consideration. In order to avoid being too subjective or objective, Analytic Hierarchy Process and Entropy Weight Coefficient method are combined together to give a new and comprehensive weighting method. Finally, Grey Relational Analysis is used to calculate the level which the case is related to the ideal sample. Three methods are integrated to turn into a new comprehensive evaluation method, in terms of the new index system, making a difference to distribution network.