Grey System Theory

Warehouses constitute a key component of supply chain networks. An improvement to the operational efficiency and the productivity of warehouses is crucial for supply chain practitioners and industrial managers. Overall warehouse efficiency largely depends on synergic performance. The managers preemptively estimate the overall warehouse performance (OWP), which requires an accurate prediction of a warehouse's key performance indicators (KPIs). This research aims to predict the KPIs of a ready-made garment (RMG) warehouse in Bangladesh with a low forecasting error in order to precisely measure OWP. Incorporating advice from experts, conducting a literature review, and accepting the limitations of data availability, this study identifies 13 KPIs. The traditional grey method (GM)-the GM (1, 1) model-is established to estimate the grey data with limited historical information but not absolute. To reduce the limitations of GM (1, 1), this paper introduces a novel particle swarm optimization (PSO)-based grey model-PSOGM (1, 1)-to predict the warehouse's KPIs with less forecasting error. This study also uses the genetic algorithm (GA)-based grey model-GAGM (1, 1)-the discrete grey model-DGM (1, 1)-to assess the performance of the proposed model in terms of the mean absolute percentage error and other assessment metrics. The proposed model outperforms the existing grey models in projecting OWP through the forecasting of KPIs over a 5-month period. To find out the optimal parameters of the PSO and GA algorithms before combining them with the grey model, this study adopts the Taguchi design method. Finally, this study aims to help warehouse professionals make quick OWP estimations in advance to take control measures regarding warehouse productivity and efficiency.

Yüksek volatilite dönemlerinde hisse senedi yatırımı yapmak, volatilitenin nispeten düşük olduğu dönemlere göre yatırımcılar açısından daha zor olmaktadır. Bu dönemlerde, piyasaların etkinlik seviyeleri azalış göstermekte ve yatırımcıların asimetrik bilgilere maruz kalmaları daha fazla söz konusu olmaktadır. Bu nedenle, gerek hisse senedi seçimi yapılırken gerekse seçilen hisse senetleri ile portföy oluştururken birtakım modem yaklaşımlara sahip modellere oldukça ihtiyaç duyulmaktadır.

Bu çalışmada, yüksek volatilitenin hakim olduğu 2008 Küresel Finansal Krizi döneminde, Gri Sistem Teorisi Destekli Markowitz Portföy Optimizasyonu yapılmıştır. Böylece belirsizliklerin hakim olduğu bu dönemde yatırımcıların karar verme süreçlerinde kullanabilecekleri bir modelin geliştirilmesi amaçlanmıştır. Ayrıca geliştirilen bu modelin oluşturulan Melez Portföyler ve Geleneksel Portföyler ile performans karşılaştırmaları yapılmıştır. Çalışm anın sonuçları, geliştirilen modem yaklaşıma sahip modellerin, yüksek volatilite dönemleri için kullanılabilir olduğu ve başarılı performansı gösterebildiği ortaya konulmuştur.

In order to solve a number of real decision-making problems, over time, a number of multiple criteria decision-making methods have been proposed. The EDAS method is one of the newly proposed methods; its computational procedure can be identified as innovative and also based on verified approaches. An extension of the EDAS method adapted for the use of grey numbers is considered in this paper.

Nowadays decision making has a wide application in management, business, and engineering majors, thus several multiple criteria/attributes decision making (MCDM) methods have been directed by researchers to sort optimal decisions. These methods can be categorized into: outranking based, distance based, and pairwise comparisons based methods. On the other hand, due to the fact that there is uncertainty in the input data in a real-world situation, the approaches capable of handling uncertainties are encouraged to be employed to overcome the hesitancy in MCDM methods. Grey System Theory is one of the essential approaches to consider uncertainty because it is known to show a noteworthy performance when the input data is incomplete or partially known. Hence, the present study is a humble effort directed at executing a short review on grey MCDM methods based on the data from 2000 and 2018, a period of 19 years. Moreover, we have presented an analysis in this area based on the number of studies, available through the Google Scholar and Science Direct databases. Finally, the study identifies the most popular and least popular methods and thus guides future scholars in their choice of selecting models.

The adaptability of ISO 14001 is considered as one of the most useful tools for environmental sustainability and worldwide competitive advantage; however, the future of ISO 14001 certification faces some uncertainties because of its uneven acceptance in various countries. These uncertainties, if not properly managed, can hinder the implementation of business management systems in these countries. In order to guide policymakers in better management of ISO 14001 in future with certainty, this study aims to forecast the ISO 14001 certifications for 10 years for China, India, the USA, Italy, Japan, and Germany, the top six certified countries, through advanced mathematical modeling, namely grey models, even GM (1,1), discrete GM (1,1), and non-homogenous discrete grey model (NDGM). The benefits of mentioned models are ensured accuracy in assessment using small samples and poor information. Moreover, current research is a pioneer in the certifications growth analysis using the Synthetic Relative Growth Rate and Synthetic Doubling Time models. Finally, the empirical analysis indicated that China is constantly leading in terms of its ISO 14001 certifications till 2026 and the performance of developing countries was spectacular. Furthermore, the article has proposed some suggestions for the policymakers to make the environment more sustainable.

Regarded as one of the most effective tools to guide quality systems management, ISO 9001 is a valuable certification. Yet, the growth observed throughout the world by this standard provides a strong polarisation of interest in this practice by the companies. Our research goals are to analyze and forecast trends involving ISO 9001 certification of six countries, China, Italy, Germany, Japan, the United Kingdom, and India. We gathered ISO 9001 countrywide certification data over nine years from 2018 to 2026. The methods used in this study include Even GM (1, 1), Discrete GM (1, 1) and Non-homogeneous discrete grey model (NDGM) with an accompanying synthetic growth rate and synthetic doubling time grey models to investigate the comparison among these countries. The result reveals that Germany will likely continue to lead ISO 9001 certifications at a country level through 2026. We also find that Japan and UK required more time for ISO 9001 certification to double than other countries. Our forecasting of the uptake of the ISO 9001 standard is significant for the certification bodies to understand market diffusion and trends. Implications include this study providing valuable policy guidelines for decision-makers, and new opportunities for further research for scholars.

Purpose The purpose of this paper is to examine projects crashing based on the factors including cost, time, quality, risk and the law of diminishing returns. Design/methodology/approach The paper first investigated effective factors on project crashing then proposed a grey linear programming model. In the proposed grey linear programming model, the costs of quality of works that include the cost of conformance and non-conformance of deliverables in the project were studied. The results are presented for considering the existing uncertainties using positioned programming under the sensitivity analysis table and graphs. Findings The lack of consideration of project risks will reduce the project success probability in future. The proposed model reduces the existing uncertainties to a significant extent by covering the project risks completely. Based on the law of diminishing returns, after a certain point technically known as saturation point, the increase of resources does not lead to the reduction of time and may even have negative impacts. Finding the saturation point for each activity prevents the excessive allocation of resources that can lead to reduction of productivity. Practical implications The main duty of each project manager is finishing the project in the framework of the determined objectives. In most of the cases, after the preparation of the initial project schedule by the project team, it is seen that there is a need for the time reduction. This study has used a grey linear programming model for optimum crashing of project activities. In order to make the model more realistic and applicable, the authors endeavoured to consider most of the factors that are involved in doing a project. Originality/value In the present study, to the best of the authors’ knowledge the factors of time, cost, quality, risk and the law of diminishing returns are simultaneously considered in project crashing for the first time and the grey theory was used for considering the uncertainties of project parameters. Also, “the law of diminishing returns” has not been considered during crashing in the studies conducted so far.

The significance of adopting online service and using in the banking industry has attracted researchers' attention in the past decade. In such condition that banks use online services to provide easiness and safety in the internet banking transactions for their customers, it is natural that studying on the factors affecting customer satisfaction in internet banking system has utmost importance in banking industry, today. Hereupon, this research attempts to study the key factors affecting customer satisfaction in internet banking system to prioritizing based on cause and effect relationships. For this purpose, according to the literature, seven main factors were identified as most important factors affecting customer satisfaction in internet banking which totally include 27 measurement items. Then, to evaluate the cause and effect relationships of factors an online questionnaire link distributed to professors and students as a group of potential expert users of internet banking and finally 20 completed questionnaires collected. To analyze interactions between the factors using Grey-based DEMATEL method, first experts' opinions of grey numbers are converted to crisp numbers and all opinions are unified into a single view. Then the crisp numbers normalized in DEMATEL and total matrix of each factor is calculated. At the end, the values of R, D, R+D and R-D are calculated, which based on these criteria the cause and effect relationships of factors analyzed and factors affecting customer satisfaction in internet banking system prioritized.

This paper evaluates the human resource information systems provided by different vendors using two new hybrid multicriteria decision-making methods that require ordinal data as inputs. First, the grey-point-allocation full-consistency (Grey-PA-FUCOM) weighting method is proposed. The Grey-PA-FUCOM combines the simple point-allocation method widely used by human resource managers and the advanced FUCOM method widely accepted by scholars in grey system theory. Second, the grey-regime method, an extension of the classical regime method based on grey system theory, is used to account for the uncertainty in the evaluation. Next, the Grey-PA-FUCOM weights are applied in conjunction with the grey-regime scheme to evaluate the five vendors. Finally, to validate the results of this study, grey relational analysis with grey numbers, the grey weighted sum model, and a technique for order performance based on the similarity to the ideal solution with grey values are used.

Purpose – The purpose of this paper is to analyse the relationship between outpatient satisfaction and the
five constructs of healthcare projects’ service quality in Pakistan using Deng’s grey incidence analysis (GIA)
model, absolute degree GIA model (ADGIA), a novel second synthetic degree GIA (SSDGIA) model and two
approaches of decision-making under uncertainty.
Design/methodology/approach – The study proposes a new synthetic GIA model and demonstrates its
feasibility on data (N¼221) collected from both public and private sector healthcare projects of Punjab, the
most populous province of Pakistan, using a self-administered questionnaire developed using the original
SERVQUAL approach.
Findings – The results of decision analysis approach indicated that outpatients’ satisfaction from the private
sector healthcare projects is higher as compared to the public healthcare projects’. The results from the
proposed model revealed that tangibility and reliability play an important role in shaping the patient
satisfaction in the public and private sectors, respectively.
Originality/value – The study is pioneer in evaluating a healthcare system’s service quality using grey system
theory. The study proposes the SSDGIAmodel as a novelmethod to evaluate parameters comprehensively based
on their mutual association (given by absolute degree of grey incidence) and inter-dependencies (given by Deng’s
degree of grey incidence), and tests the new model in the given scenario. The study is novel in terms of its
analysis of data and modelling. The study also proposes a comprehensive structure of the healthcare delivery
system of Pakistan.

Purpose-The purpose of this paper is to survey and express the advantages and disadvantages of the existing approaches for solving grey linear programming in decision-making problems. Design/methodology/approach-After presenting the concepts of grey systems and grey numbers, this paper surveys existing approaches for solving grey linear programming problems and applications. Also, methods and approaches for solving grey linear programming are classified, and its advantages and disadvantages are expressed. Findings-The progress of grey programming has been expressed from past to present. The main methods for solving the grey linear programming problem can be categorized as Best-Worst model, Confidence degree, Whitening parameters, Prediction model, Positioned solution, Genetic algorithm, Covered solution, Multi-objective, Simplex and dual theory methods. This survey investigates the developments of various solving grey programming methods and its applications. Originality/value-Different methods for solving grey linear programming problems are presented, where each of them has disadvantages and advantages in providing results of grey linear programming problems. This study attempted to review papers published during 35 years (1985-2020) about grey linear programming solving and applications. The review also helps clarify the important advantages, disadvantages and distinctions between different approaches and algorithms such as weakness of solving linear programming with grey numbers in constraints, inappropriate results with the lower bound is greater than upper bound, out of feasible region solutions and so on.

Project success (and failure) leads to the success (and failures) of business/organizational strategies thus projects are becoming integral part of organizations operating in today's competitive environment (see, Serra, 2017; PMI, 2013). Today, project management is being applied in diverse range of professions and industries that includes both manufacturing and service sectors (Kerzner, 2009). Moreover, a competent and knowledgeable project manager is vital to project success (Hwang & Ng, 2013; PMI, 2013) and in a world where project failure rate is too high to ignore (Serra, 2017) understanding the mind and preferences of this extremely important individual becomes necessity. Project Management Institute (USA) distributes the project management knowledge into ten interlinked areas (PMI, 2013). The completeness or incompleteness of the number of these project management knowledge areas (PMKAs) can be debatable nevertheless the importance of these knowledge areas for project success is established across the board. The ten PMKAs are i. Project Integration Management (PIM) ii. Project Scope Management (PSM) iii. Project Time Management (PTM) iv. Project Cost Management (PCoM) v. Project Quality Management (PQM) vi. Project Human Resource Management (PHRM) vii. Project Communications Management (PCmM) viii. Project Risk Management (PRM) ix. Project Procurement Management (PPM) x. Project Stakeholder Management (PSHM) The current study views a project as a grey system and intends to evaluate the project management knowledge areas (PMKAs) in manufacturing and service industries by establishing relationships between the ten PMKAs and, then, prioritizing them, using the absolute degree grey incidence analysis (ADGIA) model and analytic hierarchy process (AHP). In this way, the study is pioneer in its evaluation of ten PMKAs. Data was collected, from thirty-two project management-related professionals, in Lahore, Pakistan. Since the sample size was small so application of the grey system theory was considered appropriate because, unlike statistical methods, the grey systems concepts (including GIA) work fine with small data samples as well. Absolute degree of grey incidence was calculated using the method proposed in Liu et al. (2016). To solve the problem using AHP, the simplest way adopted by Taha (2014) was followed. Literature suggests that complexity, risk, uncertainty and unpredictability are key attributes associated with a project, project environment and project management process. These are the attributes that distinguish a temporary organizational setup (project) from the permanent organizational setups (companies and firms) thus the application of grey system theory in project management discipline can be considered an appropriate initiative with huge scope of applicability within this discipline. The results reveal that Project Quality Management, the most important knowledge area, is most strongly related to Project Communication Management, and least strongly related to Project Integration Management. In manufacturing industry, Quality, Time and Scope related knowledge areas turned out to be the most important PMKAs and in the service sector, the knowledge areas associated with Cost, Quality and Communication are considered most important.

The purpose of this paper is developing a method to choose an appropriate Computerized Maintenance Management System (CMMS) using Multiple Criteria Decision Making (MADM) for a dairy company. Among different methods, the grey group TOPSIS and fuzzy group VIKOR methods were selected. TOPSIS is a Technique for order of Preference by Similarity to Ideal Solution and VIKOR technique is a method based on compromise programming. The data in this article were gathered using the interviews with the company's managers and elites in the field of maintenance. Then, out of five types of maintenance software, the best ones were selected using these two techniques and finally the results were compared with each other. In the selection process, 13 sub-criteria were introduced under 5 main criteria. These criteria were selected out of a huge number of criteria using the studies of others and by consulting with the company's managers and experts. We have tried to make the choices in a way that the majority of aspects could be considered. This paper helps the maintenance managers in decision-making related to choosing the CMMS software in uncertainty environment. Using two different fuzzy and grey approaches and comparing the results can lead to appropriate selection and improve the confidence in decision-making. Maintenance planning issues are among the important issues in industrial production systems. Maintenance systems have basically made remarkable progress in recent years. The increase of companies' competitive pressure on the one hand and the close relationship between maintenance activities and companies' core activities, on the other hand, have encouraged companies to use the software in order to manage their maintenance activities.

Dams are important engineering structures, therefore dams should be constructed with the rigors of safety in mind. In this paper, the vertical displacement of the crest of Keban Dam in Turkey, is determined using a grey prediction method. The grey prediction method is a method that produces satisfactory results when we do not have enough experience about a system behaviors. The purpose of this study is to examine the effectiveness of the grey prediction method in systems where a limited amount of data is available or known. In this study the Simple Exponential Smoothing (SES) method; a very well-known prediction method is used for comparison. The results from our investigation indicate that the grey prediction method produces better results, more in-keeping with true values.

Purpose-Tourism industry is a highly complex system surrounded by many uncertainties because of its innumerable connections with other supporting systems. Considering tourism, a grey system, the current study proposes optimistic-pessimistic method (OPM). This technique can aid in improving forecast accuracy of four tourism-related indicators, inbound tourism to China, outbound tourism from China, revenues collected through inbound tourism and expenses incurred on outbound tourism. Design/methodology/approach-The study integrates OPM into EGM and then using the secondary data collected from the World Bank database, predicts the four tourism-related indicators. The mean absolute percentage error steered the performance of the models. Findings-One of the main contributions of the study lies in its overall evaluation of one of the major travel and tourism countries of the world in light of four crucial indicators. The study highlights, four tourism-related indicators' recent information, contains more valuable information about the future. Originality/value-OPM represents a novel application of concept of whitenization of interval grey number in grey forecasting theory.

Abstract—The prediction of meteorological parameters at a meteorological station is an interesting and open problem. A firstorder linear dynamic model GM (1, 1) is the main component of the grey system theory. The grey model requires only a few previous data ...

Linear programming is being widely applied in various fields e.g., management sciences, operations research, economics and engineering. In real-world settings, the input data of linear programming models entail many uncertainties. Overlooking these uncertainties may lead to erroneous decision making. In the problems surrounding uncertainty and incomplete/partially known data, Grey System Theory (GST) is a suitable approach for data analysis. Accordingly, the current study is an attempt to propose a new method for solving grey linear programming problems. The grey linear programming methods proposed to date suffer from numerous drawbacks such as weakness of solving linear programming with grey numbers in constraints, inappropriate results with the lower bound is greater than upper bound, out-of feasible-region solutions and so on. To counter these drawbacks, the current study proposes a novel method of linear programming with grey parameters. Later, its solutions are compared with that of other alternative methods. Comparative analyses of the methods revealed the superiority of the proposed method over other methods in terms of quality of optimal solution and computational steps. As opposed to the other existing methods that usually comprise several stages, the proposed method has only three stages for solving grey linear programming problems and is therefore simple to work with.

This paper uses the grey fuzzy multiobjective programming to aid in decision making for the allocation of waste load in a river system under versatile uncertainties and risks. It differs from previous studies by considering a multicriteria objective function with combined grey and fuzzy messages under a cost benefit analysis framework. Such analysis technically integrates the prior information of water

Mounting environmental concerns have given rise to an increasing focus on renewable energies like biofuels. In 2018, three countries e China, the United States, and India e together emitted almost half (50.3%) of the world's CO 2 emissions (billion metric tons). The current study aims to forecast biofuels' production, consumption, and self-sufficiency in these top CO 2 emitting countries using a novel grey forecasting model. The study improves on an existing grey forecasting model by optimizing the model architecture (data accumulation operation and background value generation). The proposed forecasting model, EGM (1,1,a,q), is a generalized form of the even form of the grey forecasting model, and its relative performance turned out to be generally superior to that of the original model. The comparative analyses of the proposed model with two forecasting models revealed that the new model's forecast accuracy is generally better than those of others. The study finds, achieving self-sufficiency in both biofuels (fuel ethanol and biodiesel) would remain a challenge for China, while the United States and India would maintain their self-sufficiency in ethanol and biodiesel, respectively, at least till 2028. The study also argues that biofuel is more likely to be a complementary fuel rather than an alternative fuel. The study helps us understand how, in the next decade, the landscapes of biofuel production and consumption are changing, and concludes with significant policy implications.

The current study introduces a new technique for the analysis of uncertain systems and uncertain processes in geothermics/earth sciences. The method is the second synthetic grey relational analysis (SSGRA) model, which incorporated the advantages of both Deng's GRA model and the bidirectional absolute GRA model. The SSGRA model has been earlier successfully applied in project management and healthcare systems. The current study is a pioneer in demonstrating the feasibility of the SSGRA model in a geothermal environment. In the current study, the model was used to determine the associations between thermal conductivity and petrophysical parameters in an Algerian reservoir. The results revealed that thermal conductivity is most strongly associated with porosity followed by density and permeability. Their relationships are also discussed. The study concludes with valuable insights about the model and its application in engineering and natural sciences especially when the system contains uncertainty, which may arise either due to insufficient data or uncertain relationships among the parameters associated with the system or its processes.

This paper attempts to put forward a hybrid model which combines the advantages offered by grey systems theory, fuzzy theory and genetic algorithm, and tries to identify the causes that are influencing financial failure of a company. For this purpose, a knowledge matrix will be computed. Further, this matrix can be composed with a one-dimensional symptoms matrix for a certain company and so the causes that generate the anomalies can be identified. Knowing the causes, and managing them properly, we can improve company's financial situation and also lengthened its life on the market.

The problem of part supplier selection is a major concern for all manufacturers when seeking to enhance the
products’ quality and productivity. The objective of this paper is to propose an integrated genetic algorithm
based grey goal programming (G3) approach to solve the part supplier selection problem. The main factor in
part supplier selection is the assembly relation of the parts so as to find the suitable suppliers combination for
the parts of a product. We first identify the main factors affected on supplier selection. We then present a grey based
goal programming model to work as the fitness function to evaluate the suppliers with respect to the
total deviation the factors have from the ideal values. Since the objective is to find the best solution, a genetic
algorithm is used to solve this problem for faster and better evaluation. The novelty of this integrated
approach is to apply both qualitative and quantitative factors at once in one model and to use the grey theory
to cover the lack of information of qualitative factors in order to find a solution in a near real situation.

The examination of economic aspects of gas emissions and its consequences is very important, especially in terms of its volume at the current increasing trend. Therefore, the prediction of air pollution emissions of carbon dioxide can give the correct direction to policies adopted. Hence, studying and forecasting of gas emissions is necessary. The purpose of this paper is the prediction of CO 2 emissions based on Grey System and Autoregressive Integrated Moving Average and comparison of these two methods by RMSE, MAE and MAPE metrics. The results show the more accuracy of Grey system forecasting rather than other methods of prediction. Also, based on the estimated results, the amount of carbon dioxide emissions will reach up to 925.68 million tons in 2020 which shows an increase of 66 percent growth compared to 2010 which is highly significant.

The current study introduces a new technique for the analysis of uncertain systems and uncertain processes in geothermics/earth sciences. The method is the second synthetic grey relational analysis (SSGRA) model, which incorporated the advantages of both Deng’s GRA model and the bidirectional absolute GRA model. The SSGRA model has been earlier successfully applied in project management and healthcare systems. The current study is a pioneer in demonstrating the feasibility of the SSGRA model in a geothermal environment. In the current study, the model was used to determine the associations between thermal conductivity and petrophysical parameters in an Algerian reservoir. The results revealed that thermal conductivity is most strongly associated with porosity followed by density and permeability. Their relationships are also discussed. The study concludes with valuable insights about the model and its application in engineering and natural sciences especially when the system contain...

The adaptability of ISO 14001 is considered as one of the most useful tools for environmental sustainability and worldwide competitive advantage; however, the future of ISO 14001 certification faces some uncertainties because of its uneven acceptance in various countries. These uncertainties, if not properly managed, can hinder the implementation of business management systems in these countries. In order to guide policymakers in better management of ISO 14001 in future with certainty, this study aims to forecast the ISO 14001 certifications for 10 years for China, India, the USA, Italy, Japan, and Germany, the top six certified countries, through advanced mathematical modeling, namely grey models, even GM (1,1), discrete GM (1,1), and non-homogenous discrete grey model (NDGM). The benefits of mentioned models are ensured accuracy in assessment using small samples and poor information. Moreover, current research is a pioneer in the certifications growth analysis using the Synthetic Relative Growth Rate and Synthetic Doubling Time models. Finally, the empirical analysis indicated that China is constantly leading in terms of its ISO 14001 certifications till 2026 and the performance of developing countries was spectacular. Furthermore, the article has proposed some suggestions for the policymakers to make the environment more sustainable.