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Decision making is the task of selecting the most appropriate alternative among a finite set of possible alternatives with respect to some attributes. The attributes may be subjective or objective (or combination of both), depending upon the situation; requirements may also be conflicting. In practice, most of the real-world decision-making problems are based on subjective evaluation criteria which are basically ill-defined and vague. Since subjective human judgment bears ambiguity and vagueness in the decision making; application of grey numbers set theory may be proved fruitful in this context. The paper aims to discuss these issues.

Owing to the advantages of grey numbers set theory in tackling subjectivity in decision making; the crisp-TODIM needs to be extended by integrating with grey numbers set theory in order to facilitate decision making consisting of subjective data. Hence, the unified objective of this paper is to propose a grey-based TODIM approach in the context of decision making.

Application potential of grey-TODIM has been demonstrated through a case empirical robot selection problem. Result obtained thereof, has also been compared to that of existing grey-based decision support systems available in literature.

Application potential of grey-based decision support systems (grey-TOPSIS, grey analysis, grey-MOORA) have been highlighted in available literature resource. However, the shortcoming of these approaches is that they do not consider decision-makers’ risk attitude while decision making. TODIM method is derived from the philosophy of Cumulative Prospect Theory (CPT) which considers risk averting attitude of the decision maker in case of gain and risk seeking attitude in case of loss, while comparing dominance between two alternatives with respect to a particular criterion. Hence, this paper contributes a mathematical foundation of TODIM coupled with grey numbers set theory for logical decision making.

This study examines the potential of contracts as one of the supply chain coordination mechanisms under competitive conditions. It also investigates a two-echelon supply chain model with two manufacturers and two retailers to develop a competitive structure in grey stochastic demand.

Supply chain demand is considered as a stochastic phenomenon depending on the selling price of the product. Also, products can be replaced by market manufacturers. Each retailer faces the pricing of products from two manufacturers, leading to competition between downstream retailers. In the present study, the duopoly supply chain model was presented based on the wholesale price contract, revenue-sharing contract and quantity discount contract separately.

Grey optimization and analysis of their coordination were presented. The results showed the high performance of revenue-sharing contracts in the supply chain. Thus, manufacturers will give the next priority to quantity discount contracts.

Ordering is the main factor contributing to competitive decision-making. Meanwhile, decision-making along with ordering and pricing will be required due to the nature of the demand.

The purpose of this paper is to simplify the computation of parameter estimation in the grey linear regression model and solve the problem that the development coefficient could not be computed in some sequence data, such as short‐term traffic flow.

Starting from the limitation that can be identified in the equation and analyzing the range using the method to estimate parameters, this paper researches the modelling mechanism and the other forms which are equivalent with the original form. At the same time, this paper gives an estimation method and gets the relationship in various forms and the relationship between the model and GM(1,1) model.

For the grey linear regression model, there exists a new method of parameter identification and three other forms as follows: the original form, the Whitenization equation and the connotation form.

The method of parameter identification exposed in the paper expanded the scope of the application of the grey linear regression model, and it can be used to model and forecast the urban road short‐time traffic flow.

This paper has solved some complicated problems such as the parameter estimation computation in the grey linear regression model. In addition, three kinds of representation forms of the model and its relationship between the model and GM(1,1) have also been presented. Finally, its application of the model in a short‐term traffic flow prediction has shown its superiority.

This paper aims to develop an efficient measurement index evaluation system towards assessing suppliers' green performance practices. Apart from estimating overall performance index, the paper also aims to highlight application of decision‐support tools for selection of appropriate candidate supplier in green supply chain management context.

In order to tackle incompleteness and imprecision arising from assigning appropriateness rating as well as priority weights against subjective performance criteria‐attributes, use of grey numbers was proposed. An efficient grey‐based supplier appraisement platform was established. Application of Grey‐Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and COPRAS‐G method were reported to solve the supplier selection decision‐making problem. The theory of grey numbers was utilized here to facilitate such decision modeling.

Over the last two decades, growing concerns about ecosystem quality have stimulated to a renewed interest in environmentalism. Purchasing professionals should also be concerned and need to rethink purchasing strategies which have traditionally neglected environmental impacts. The “green” purchasing‐packaging in reducing and eliminating waste is a major concern in recent days. In order to help foster environmentally concerned purchasing strategies, this paper presents the findings of supplier evaluation strategy in an enterprise with enhanced degree of awareness and frequent applications of “green” purchasing. Environmental factors are identified that may reshape supplier evaluation decisions. The concept of grey numbers set has been adopted in this work. A case study reflects effectiveness of exploring grey relation theory in the context of green supplier evaluation.

The major contributions of this work have been summarized as follows: development and implementation of an efficient decision‐making tool to support green supplier evaluation; an overall green performance index evaluation platform has been introduced; concept of grey numbers has been efficiently explored to facilitate this decision‐making; the appraisement index system has been extended with the capability to search ill‐performing areas which require future progress; and the proposed appraisement system is capable of reducing the number of green attributes towards computing grey appropriateness index thereby transforming into lesser number of green capabilities, thus, facilitating applying decision‐making tools like grey‐TOPSIS and COPRAS‐grey method for appropriate supplier selection from a set of candidate suppliers.

Advanced manufacturing machines (AMMs) are searched as a momentous asset across the manufacturing societies for quenching and addressing the production units under economical circumstances, i.e. production of high-quality of goods under feasible cost. AMMs are significant in holding the managers against their rivals and competitors with high profit margins. The authors developed the decision support mechanism/portfolio (DSM-P) consist of knowledge-based cluster approach with a dynamic model. The purpose of research work is to measure overall economic worth of AMMs under objective and grey-imperfect (mixed) data by exploring the proposed DSM-P.

The authors developed the DSM-P that consist of knowledge-based cluster, three multi-criteria decision-making (MCDM) techniques-1-2-3 with complementary grey relational analysis-4(GRA), approach with a dynamic model (complied by technical plus cost and agility measures of AMMs). The proposed DSM-P enables the manager to map the overall economic worth of candidate AMMs under objective and grey-mixed data.

The presented DSM-P assist the managers for handling the selection problem of AMMs, i.e. CNCs, robots, automatic-guided vehicle, etc under mixed (objective cum grey) data. To enable the readers for intensely understand the work, the utility of proposed approach is displayed by illustrating a polar robot evaluation and selection problem. It is ascertained that the robot candidate-11 alternative is fulfilling the entire technical cum cost and agility measures.

The DSM-P provides more precise and reliable outcomes due to a usage of the dominance theory. Under the dominance theory, the ranks are obtained by MCDM techniques-1-2-3 are compared with ranks gathered by the GRA-4 under objective cum grey data, formed the novelties in presented research work. From a future perspective, the grey-based models in DSM-P can be built/extended/constructed more extensive and can be simulated by the same approach.

The radiation conduction coupling leads to particular problems due to computation time and high heat fluxes. Because of the hemispheric nature of the radiation, it is difficult to take into account symmetric or periodic conditions for the reduction of the modelled domain. We developed a finite element model of radiative heat transfers between grey diffuse surfaces with a nonparticipating medium with periodic or symmetric boundary conditions. The approaches used to decrease the computation time allowed the modelling of moving radiative surfaces. We introduced this model into a finite element convection diffusion code in order to simulate heat transfers in an electrical rotating engine. The main originality of this study lies in the use of periodic radiative conditions with moving surfaces and in the use of a method which is not based on the isothermal approximation.

This paper aims to propose an enhanced algorithm and used to decision-making that specifically focuses on the choice of a domain in the calculation of degree of greyness according to the principle of grey numbers operation. The domain means the emerging background of interval grey numbers, it is vital for the operational mechanism of such interval grey numbers. However, the criteria of selection of domain always remain same that is not only for the calculated grey numbers but also for the resultant grey numbers, which can be assumed as unrealistic up to a certain extent.

The existence of interval grey number operation based on kernel and the degree of greyness containing two calculation aspects, which are kernel and the degree of greyness. For the degree of greyness, it includes concepts of domain and calculation of the domain. The concepts of a domain are defined. The enhanced algorithm is also comprised of four deductive theorems and eight rules that are linked to the properties of the enhanced algorithm of the interval grey numbers based on the kernel and the degree of greyness.

Aiming to improve the algorithm of the degree of greyness for interval grey numbers, based on the variation of domain in the operation process, the degree of greyness of the operation result is defined in this paper, and the specific expressions for algebraic operations are given, which is relevant to the kernel, the degree of greyness and the domain. Then, these expressions are used to the algorithm of interval grey numbers based on the kernel and the degree of greyness, improving the accuracy of the operation results.

The enhanced algorithm in this paper can effectively reduce the loss of information in the operation process, so as to avoid the situation where the decision values are the same and scientific decisions cannot be made during the grey evaluation and decision-making process.

The objective of the study is to identify and analyse drivers of smart manufacturing using integrated grey-based approaches. The analysis facilitates industry practitioners in the identification of preference of drivers through which smart manufacturing can be implemented. These drivers are explored based on existing literature and expert opinion.

Modern manufacturing firms have been adopting smart manufacturing concepts to sustain in the global competitive landscape. Smart manufacturing incorporates integrated technologies with a flexible workforce to interlink the cyber and physical world. In order to facilitate the effective deployment of smart manufacturing, key drivers need to be analysed. This article presents a study in which 25 drivers of smart manufacturing and 8 criteria are analysed. Integrated grey Technique for Order Preference by Similarity to Ideal Solution (grey TOPSIS) is applied to rank the drivers. The derived ranking is validated using “Complex Proportional Assessment – Grey” (COPRAS-G) approach.

In total, 25 drivers with 8 criteria are being considered and an integrated grey TOPSIS approach is applied. The ranking order of drivers is obtained and further sensitivity analysis is also done.

In the present study, 25 drivers of smart manufacturing are analysed. In the future, additional drivers could be considered.

The study presented has been done with inputs from industry experts, and hence the inferences have practical relevance. Industry practitioners need to focus on these drivers in order to implement smart manufacturing in industry.

The analysis of drivers of smart manufacturing is the original contribution of the authors.

In present research, the authors conducted the massive literature review and collected the information, in regards to material handling system (MHS) to build a multi criteria MHS hierarchical module consists of ecological cum fiscal criteria. Moreover, similar literature review assisted the authors to resolve and eventually construct the effectual and robust approach. The purpose of this paper is to facilitate the managers for benchmarking the MHS alternatives operating under similar module via robust decision support system (DSS).

In present research, the proposed module dealt with ecological (subjective) and fiscal (objective) criteria, where subjective criteria associated with incompleteness, vagueness, imprecision, as well as inconsistency, solicited the discrete information in terms of Grey set via linguistic scale from experts panel. The objective information (capital) has been assigned by expert’s panel in terms of Grey set. To robustly evaluate and select the admirable MHS, three approaches named: degree of possibility, technique for order preference similar to ideal solution as well as Grey relational analysis fruitfully applied to connect and unite discrete information.

The performance evaluation of MHSs has been carried out under concert of individual fiscal criteria excluding ecological criteria in past researches. Moreover the previous developed DSS tackled sole approach under individual fiscal criteria. The authors found the broad applications of fuzzy sets except Grey set theory in the same context for measuring the performance of MHS alternatives. Aforesaid research gaps have been transformed into research objectives by incorporating the module for both fiscal cum ecological criteria. This research embraces a robust DSS, which has been explored to select the admirable MHS alternative.

An empirical case study has been carried out in order to demonstrate the legitimacy of holistic Grey-MCDM method, implemented over multi criteria MHS hierarchical module. Proposed DSS seems to be the best for organisations, which believe to appraise and select the MHS including fiscal as well as ecological criteria excluding individual fiscal criteria. Moreover, subjective cum objective or individual subjective or objective criteria can be extended with respect to varieties of MHSs.

The purpose of the article is to report a study on evaluation of smart manufacturing (SM) performance using a grey theory-based approach.

In total, 30 criteria and 79 attributes for SM performance have been developed. A grey theory-based approach has been used for SM performance evaluation. The grey index has been calculated, and weaker areas have been derived. Performance level of SM has been evaluated using the Euclidean distance approach.

The SM performance index is found to be (3.036, 12.296). The ideal grey performance importance index (GPII) is obtained as (3.025, 4.875). The level of visibility and traceability, vertical integration, lead time and configuration data espionage and control ability are strong performing attributes. Integration abilities of services and manufacturing systems, ability of self-control, worker and raw material productivity, collaboration among buyers and suppliers and dynamic scheduling are identified as weaker areas, and suggestions for improvement have been derived. SM performance level has been identified as “Good.”

Additional performance measures could be included as a part of evaluation. Practitioners can overcome weaker areas in the early phase. Management achieves confidence and practitioners attain success in implementation of SM in industry through the developed SM performance indexing system.

Identification of SM performance measures and analysis of SM performance is the original contribution of the authors. The developed approach assists practitioners and managers to focus more on specific areas for performance improvement.