PROGRESS OF GREY SYSTEM MODELS

The progress of grey system models is reviewed, and the general grey numbers, the grey sequence op- erators and several most commonly used grey system models are introduced, such as the absolute degree of grey incidence model, the grey cluster model based on endpoint triangular whitenization functions, the grey cluster model based on center-point triangular whitenization functions, the grey prediction model of the model GM （ 1,1）, and the weighted multi-attribute grey target decision model.

NOVEL GENERALIZED GREY INCIDENCE MODEL BASED ON INTERVAL GREY NUMBERS

To extend the traditional generalized grey incidence model, a novel grey incidence model based on inter- val grey numbers is constructed. Considering the numerical information of indexes cannot be accurately obtained and can be defined as interval grey numbers, the interval grey numbers are defined as standard interval grey num- bers which are split in white part and grey part. The absolute degree of incidence and relative degree of incidence based on the interval grey numbers are constructed and their arithmetic are given. Finally, an example about commercial aircraft index selection illuminates the effectiveness of the model. The results show that the model can sort indexes better and can extend the grey incidence models significantly.

Prediction model of interval grey number based on DGM(1,1)

In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.By mining the geometric features of interval grey number sequences on a two-dimensional surface,all the interval grey numbers are converted into real numbers by means of certain algorithm,and then the prediction model is established based on those real number sequences.The entire process avoids the algebraic operations of grey number,and the prediction problem of interval grey number is usefully solved.Ultimately,through an example＇s program simulation,the validity and practicability of this novel model are verified.

ENTROPY MEASUREMENT OF INTERVAL GREY SEQUENCE AND ITS APPLICATION

The uncertainty measurement method for grey information theory and the metric formula are established, and its application in decision-making is researched. The entropy measurement of grey sequence based on the limited interval grey number sequence is different from the Shannon probability entropy. The measurement formula of grey number and its properties are studied, such as the invariance, the applicable conditions, and the grey entropy of union and intersection of two grey numbers, and so on. Finally, the algorithm for interval grey sequence and an example are given to show the effectiveness of the method.

Fundamental definitions and calculation rules of grey mathematics: a review work

Grey mathematics is the mathematical foundation of the grey system theory. Recently, some important results have been achieved. In order to accelerate the development of grey mathematics, the results are summarized and redefined. This paper includes the fundamental definitions and calculation rules of the grey hazy set, grey number, grey matrix and grey function. Grey mathematics includes four types of operation, i.e. the grey operation, the whitened operation, the covered operation and the only potential true operation. According to its intrinsic quality, the covered operation, which differs from the interval one, is called as the whole-proximate calculation that means the proximate calculation spreads through the whole range of the covered set of every grey number, and we confirm that it may be a new branch of computational or applied mathematics. The overview should develop the grey system theory and grey mathematics.

Significant genomic introgression from grey junglefowl(Gallus sonneratii)to domestic chickens(Gallus gallus domesticus)

Background Chicken is one of the most numerous and widely distributed species around the world,and many studies support the multiple ancestral origins of domestic chickens.The research regarding the yellow skin phenotype in domestic chickens(regulated by BCO2)likely originating from the grey junglefowl serves as crucial evidence for demonstrating the multiple origins of chickens.However,beyond the BCO2 gene region,much remains unknown about the introgression from the grey junglefowl into domestic chickens.Therefore,in this study,based on wholegenome data of 149 samples including 4 species of wild junglefowls and 13 local domestic chicken breeds,we explored the introgression events from the grey junglefowl to domestic chickens.Results We successfully detected introgression regions besides BCO2,including two associated with growth trait(IGFBP2 and TKT),one associated with angiogenesis(TIMP3)and two members of the heat shock protein family(HSPB2 and CRYAB).Our findings suggest that the introgression from the grey junglefowl may impact the growth performance of chickens.Furthermore,we revealed introgression events from grey junglefowl at the BCO2 region in multiple domestic chicken breeds,indicating a phenomenon where the yellow skin phenotype likely underwent strong selection and was retained.Additionally,our haplotype analysis shed light on BCO2 introgression event from different sources of grey junglefowl into domestic chickens,possibly suggesting multiple genetic flows between the grey junglefowl and domestic chickens.Conclusions In summary,our findings provide evidences of the grey junglefowl contributing to the genetic diversity of domestic chickens,laying the foundation for a deeper understanding of the genetic composition within domestic chickens,and offering new perspectives on the impact of introgression on domestic chickens.

Case Retrieval Strategy of Turning Process Based on Grey Relational Analysis

To solve the problem of long response time when users obtain suitable cutting parameters through the Internet based platform,a case-based reasoning framework is proposed.Specifically,a Hamming distance and Euclidean distance combined method is designed to measure the similarity of case features which have both numeric and category properties.In addition,AHP(Analytic Hierarchy Process)and entropy weight method are integrated to provide features weight,where both user preferences and comprehensive impact of the index have been concerned.Grey relation analysis is used to obtain the similarity of a new problem and alternative cases.Finally,a platform is also developed on Visual Studio 2015,and a case study is demonstrated to verify the practicality and efficiency of the proposed method.This method can obtain cutting parameters which is suitable without iterative calculation.Compared with the traditional PSO(Particle swarm optimization algorithm)and GA(Genetic algorithm),it can obtain faster response speed.This method can provide ideas for selecting processing parameters in industrial production.While guaranteeing the characteristic information is similar,this approach can select processing parameters which is the most appropriate for the production process and a lot of time can be saved.

A Hybrid Optimization Approach of Single Point Incremental Sheet Forming of AISI 316L Stainless Steel Using Grey Relation Analysis Coupled with Principal Component Analysiss

We investigated the parametric optimization on incremental sheet forming of stainless steel using Grey Relational Analysis(GRA) coupled with Principal Component Analysis(PCA). AISI 316L stainless steel sheets were used to develop double wall angle pyramid with aid of tungsten carbide tool. GRA coupled with PCA was used to plan the experiment conditions. Control factors such as Tool Diameter(TD), Step Depth(SD), Bottom Wall Angle(BWA), Feed Rate(FR) and Spindle Speed(SS) on Top Wall Angle(TWA) and Top Wall Angle Surface Roughness(TWASR) have been studied. Wall angle increases with increasing tool diameter due to large contact area between tool and workpiece. As the step depth, feed rate and spindle speed increase,TWASR decreases with increasing tool diameter. As the step depth increasing, the hydrostatic stress is raised causing severe cracks in the deformed surface. Hence it was concluded that the proposed hybrid method was suitable for optimizing the factors and response.

Energy-Saving Distributed Flexible Job Shop Scheduling Optimization with Dual Resource Constraints Based on Integrated Q-Learning Multi-Objective Grey Wolf Optimizer

The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worker constraints.As one critical factor of production,effective utilization of worker resources can increase productivity.Meanwhile,energy consumption is a growing concern due to the increasingly serious environmental issues.Therefore,the distributed flexible job shop scheduling problem with dual resource constraints(DFJSP-DRC)for minimizing makespan and total energy consumption is studied in this paper.To solve the problem,we present a multi-objective mathematical model for DFJSP-DRC and propose a Q-learning-based multi-objective grey wolf optimizer(Q-MOGWO).In Q-MOGWO,high-quality initial solutions are generated by a hybrid initialization strategy,and an improved active decoding strategy is designed to obtain the scheduling schemes.To further enhance the local search capability and expand the solution space,two wolf predation strategies and three critical factory neighborhood structures based on Q-learning are proposed.These strategies and structures enable Q-MOGWO to explore the solution space more efficiently and thus find better Pareto solutions.The effectiveness of Q-MOGWO in addressing DFJSP-DRC is verified through comparison with four algorithms using 45 instances.The results reveal that Q-MOGWO outperforms comparison algorithms in terms of solution quality.

Enhancing Hyper-Spectral Image Classification with Reinforcement Learning and Advanced Multi-Objective Binary Grey Wolf Optimization

Hyperspectral(HS)image classification plays a crucial role in numerous areas including remote sensing(RS),agriculture,and the monitoring of the environment.Optimal band selection in HS images is crucial for improving the efficiency and accuracy of image classification.This process involves selecting the most informative spectral bands,which leads to a reduction in data volume.Focusing on these key bands also enhances the accuracy of classification algorithms,as redundant or irrelevant bands,which can introduce noise and lower model performance,are excluded.In this paper,we propose an approach for HS image classification using deep Q learning(DQL)and a novel multi-objective binary grey wolf optimizer(MOBGWO).We investigate the MOBGWO for optimal band selection to further enhance the accuracy of HS image classification.In the suggested MOBGWO,a new sigmoid function is introduced as a transfer function to modify the wolves’position.The primary objective of this classification is to reduce the number of bands while maximizing classification accuracy.To evaluate the effectiveness of our approach,we conducted experiments on publicly available HS image datasets,including Pavia University,Washington Mall,and Indian Pines datasets.We compared the performance of our proposed method with several state-of-the-art deep learning(DL)and machine learning(ML)algorithms,including long short-term memory(LSTM),deep neural network(DNN),recurrent neural network(RNN),support vector machine(SVM),and random forest(RF).Our experimental results demonstrate that the Hybrid MOBGWO-DQL significantly improves classification accuracy compared to traditional optimization and DL techniques.MOBGWO-DQL shows greater accuracy in classifying most categories in both datasets used.For the Indian Pine dataset,the MOBGWO-DQL architecture achieved a kappa coefficient(KC)of 97.68%and an overall accuracy(OA)of 94.32%.This was accompanied by the lowest root mean square error(RMSE)of 0.94,indicating very precise predictions with minimal error.In the case of the Pavia University dataset,the MOBGWO-DQL model demonstrated outstanding performance with the highest KC of 98.72%and an impressive OA of 96.01%.It also recorded the lowest RMSE at 0.63,reinforcing its accuracy in predictions.The results clearly demonstrate that the proposed MOBGWO-DQL architecture not only reaches a highly accurate model more quickly but also maintains superior performance throughout the training process.

Management of Strawberry Grey Mold Disease Using Biocontrol Agents and Plant Extracts

Strawberry (Fragaria × ananassa Duch.) is a significant global soft fruit crop, prized for its nutrient content and pleasant flavor. However, diseases, particularly grey mold caused by Botrytis cinerea Pers. Fr. poses major constraints to strawberry production and productivity. Grey mold severely impacts fruit quality and quantity, diminishing market value. This study evaluated five B. cinerea isolates from various locations in the Ri-Bhoi district of Meghalaya. All isolates were pathogenic, with isolate SGM 2 identified as highly virulent. Host range studies showed the pathogen-producing symptoms in the fava bean pods, marigold, gerbera, and chrysanthemum flowers and in the fava bean, gerbera, and lettuce leaves. In vitro tests revealed that neem extract (15% w/v) achieved the highest mycelial growth inhibition at 76.66%, while black turmeric extract (5% w/v) had the lowest inhibition at 9.62%. Dual culture methods with bio-control agents indicated that Bacillus subtilis recorded the highest mean inhibition at 77.03%, while Pseudomonas fluorescens had the lowest at 20.36% against the two virulent isolates. Pot evaluations demonstrated that B. subtilis resulted in the lowest percent disease index at 20.59%, followed by neem extract at 23.31%, with the highest disease index in the control group at 42.51%. Additionally, B. subtilis significantly improved plant growth, yielding an average of 0.32 kg compared to 0.14 kg in the control. The promising results of B. subtilis and neem leaf extract from this study suggest their potential for eco-friendly managing grey mold in strawberries under field conditions.

Optimization of Agricultural Industrial Structure in Changping District of Beijing Based on Grey Relational Analysis

In the economic development of Beijing,although the share of the total amount of agricultural industry in the overall economy is relatively low,it has an important impact on the daily life of residents,social stability and the development of other industries.Changping District,as an important agricultural production base of Beijing,its agricultural development has an indispensable strategic significance for the stability and growth of the entire regional economy.Therefore,it is very important to study the structure of agricultural industry in Changping District.Based on the detailed analysis of the agricultural industrial structure of Changping District,this paper uses the grey relation theory to analyze the different industries in the agricultural industrial structure of Changping District,including planting,forestry,animal husbandry,fishery and agricultural,forestry,service industries,in order to reveal the impact of these industries on the agricultural industrial structure of Changping District.Through this study,it comes up with specific and feasible suggestions for the optimization of agricultural industrial structure in Changping District,and provides valuable reference for the agricultural development of other areas in Beijing.

NOVEL GREY DECISION MAKING MODEL AND ITS NUMERICAL SIMULATION

A grey multi-stage decision making method is proposed for a type of grey multi-index decision problems with weighted values completely unknown and attributes as interval grey numbers. Firstly, a method for compar- ing two grey numbers based on probability is developed to calculate weighted values of the attributes. Secondly, the experts＇ evaluation scores for attribute values are presented in terms of internal grey numbers. Finally, a weight solving method for multiple-stages evaluation is proposed. An example analysis verifies the availability of the proposed method. The method provides a new way of thinking for solving grey decision problem.

Optimizing Grey Wolf Optimization: A Novel Agents’ Positions Updating Technique for Enhanced Efficiency and Performance

Grey Wolf Optimization (GWO) is a nature-inspired metaheuristic algorithm that has gained popularity for solving optimization problems. In GWO, the success of the algorithm heavily relies on the efficient updating of the agents’ positions relative to the leader wolves. In this paper, we provide a brief overview of the Grey Wolf Optimization technique and its significance in solving complex optimization problems. Building upon the foundation of GWO, we introduce a novel technique for updating agents’ positions, which aims to enhance the algorithm’s effectiveness and efficiency. To evaluate the performance of our proposed approach, we conduct comprehensive experiments and compare the results with the original Grey Wolf Optimization technique. Our comparative analysis demonstrates that the proposed technique achieves superior optimization outcomes. These findings underscore the potential of our approach in addressing optimization challenges effectively and efficiently, making it a valuable contribution to the field of optimization algorithms.

Study on the Yield Prediction Model of Processing Tomato Based on the Grey System Theory

[Objective] The research aimed to study the yield prediction model of processing tomato based on the grey system theory.[Method] The variation trend of processing tomato yield was studied by using the grey system theory,and GM（1,1）grey model of processing tomato yield prediction was established.The processing tomato yield in Xinjiang during 2001-2009 was as the example to carry out the instance analysis.[Result] The model had the high forecast accuracy and strong generalization ability,and was reliable for the prediction of recent processing tomato yield.[Conclusion] The research provided the reference for the macro-control of tomato industry,the processing and storage of tomato in Xinjiang.

Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.

MULTIVARIATE ABSOLUTE DEGREE OF GREY INCIDENCE BASED ON DISTRIBUTION CHARACTERISTICS OF POINTS

The analysis result of absolute degree of grey incidence for multivariate time series is often inconsistent with the qualitative analysis. To overcome this shortage, a multivariate absolute degree of grey incidence based on distribution characteristics of points is proposed. Based on the geometric description of multivariate time se- ries, the neighborhood extrema are extracted in the different regions, and a characteristic point set is constructed. Then according to the distribution of the characteristic point set, a characteristic point sequence reflecting the ge- ometric features of multivariate time series is obtained. The incidence analysis between multivariate time series is transformed into the relational analysis between characteristic point sequences, and a grey incidence model is established. The model possesses the properties of translational invariance, transpose and rank transform invari- ance, and satisfies the grey incidence analysis axioms. Finally, two cases are studied and the results prove the ef- fectiveness of the model.

Ranking grey numbers based on dominance grey degrees

With respect to the decision making problems where a lot of fuzzy and grey information always exists in the real-life decision making information system methods as fuzzy mathematics, it is difficult for such uncertainty probability, and interval numbers to deal with. To this end, based on the thought and method of grey numbers, grey degrees and interval numbers, the concept of dominance grey degree is defined. And then a method of ranking interval grey numbers based on the dominance grey degree is proposed. After discussing the relevant properties, the paper finally uses an example to demonstrate the effectiveness and applicability of the model. The result shows that the proposed model can more accurately describe uncertainty decision making problems, and realize the total ordering process for multiple-attribute decision-making problems.

Grey集上的逻辑和运算算子

通过定义单位区间I的全体灰信息域上的偏序关系,给出grey集和grey关系在一个格上的定义。由单位区间上的模糊逻辑和运算算子,依据经典扩张原理构造了定义在格Θ(I)上相应的grey算子。由格运算的性质导出grey关系合成运算的表示,依照模糊化算子和判决化算子的定义得出对应的grey算子。讨论有关算子的基本性质并举例说明其应用。通过对grey语义的语言值上一组运算的数学描述,旨在提高信息系统对灰信息的处理能力,将处理范围由模糊语言值拓展到基于gray语义的语言值。

Grey 子集的分解及 Grey 子群的代数结构

讨论了如下两个问题：（１）在文献［１］的基础上对Ｇｒｅｙ子集的分解定理进一步完善，并给出了更一般形式的Ｇｒｅｙ子集的分解定理；（２）证明了：群的所有正规Ｇｒｅｙ子群构成幂等的半单Ａｂｌｅ半群。