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The degree of greyness may be regarded as a measure of cognitive uncertainty. Therefore, it is a part of the epistemological core of the grey systems theory. The theoretical importance of the degree of greyness concept is also due to its application in a range of uncertainty modelling methods: predictive, relational and decision-making methods. Greyness, being a result of cognitive uncertainty, was recently subjected to axiomatization in the form of grey space with the use of the classical sets theory. The purpose of this article is to develop a new approach to the degree of greyness, being consistent with the grey space concept.

In order to realise the article’s goals, the research is divided into three stages described in particular sections. The first section of the article presents a theoretical framework of the degree of greyness and the grey space. The second part includes the assumptions of the new degree of greyness concept, along with the mathematical models for the first, the second and the third degree of greyness. The third section contains numerical examples for each degree of greyness.

As a result of the research, a concept of a degree of greyness was created and it was linked with a concept of grey space. This new approach to the issue of the degree of greyness has allowed the analysing of this category in three dimensions dependent on an accepted reference base. As a result, a concept of concrete and abstractive grey numbers was introduced and relationships between these categories of numbers and the degree of greyness were determined.

The proposed approach to the issue of the degree of greyness is a theoretical unification of the previous considerations in this area. The proposed three dimensions of greyness degree will be derived from the grey space, so they will also be a function of quantity. Thus, the degree of greyness was linked with a classical set theory. An original input in this article is also a differentiation of concrete and abstractive grey numbers, which give a basis for deliberations connected with interpretation of grey numbers in the context of real applications.

The purpose of this paper is to develop a multi-item economic production quantity (EPQ) strategy under grey environment and space constraint. Since the “demand” cannot be predicted with certainty, it is assumed that data behave under grey environment and compare the proposed inventory model with other studies using crisp or fuzzy environments.

This paper is to optimise the cycle time and total cost of the multi-item EPQ inventory model. For this purpose, the Lagrangian coefficient is used to solve the constrained optimisation problem. The grey relational analysis approach and grey data are applied in developing the EPQ inventory model.

The results are compared with the analysis using crisp and fuzzy data. Sensitivity analysis is done to illustrate the effect of parameter variations on the optimal solution. The results of the study demonstrate that crisp data outperform the other two data in all scales problems in terms of cycle time and cost; grey data perform better in all scales problems than fuzzy data.

The contribution of this research is the use of grey data in developing the EPQ inventory model with space constraint.

The purpose of this paper is to solve the problems existing in traditional grey incidence models and advance several new grey incidence models based on visual angle of similarity and nearness.

Based on the definition of traditional grey incidence models, two novel grey incidence models, grey similar incidence model and grey close incidence model, are studied in this paper. The interrelations and influence can be measured by the new models with different visual angle of similarity and/or nearness, respectively. The grey similar incidence model is used mainly to measure the similitude degree of the geometric patterns of sequence curves. The grey close incidence model is used mainly to measure the nearness of the sequence curves in space. The properties of the new models are discussed. It is proved that the proposed models are simplified methods to calculate the similitude degree and the close degree of grey incidence models.

The results show that the two novel grey incidence models satisfy the grey incidence axiom properly. It is useful to calculate the similitude degree and the close degree of two different sequences, and the process of calculating is easier than with traditional grey incidence models.

The method exposed in the paper can be used to calculate every two sequences. The similitude degree and the close degree of two different sequences can be given out. The method can also be used to rank sequences of more than two.

The paper succeeds in constructing two novel grey incidence models. The properties of novel model are studied and it is undoubtedly a new development in grey systems theory.

Until now, many different varieties of grey relational grade methods had been proposed, and there are also many relevant publications. However, in one article published in 2007, which applied the previous grey relational grade to environmental protection fields and some results had been found. After studied it carefully, the author found that the grey relational grade in the paper was not the previous grey relational grade. According to the mathematics logic, it must first prove the proposed grey relational grade satisfies the four axioms in grey relational analysis, and then the author can say that the achieved results are reasonable and correct. The paper aims to discuss these issues.

The paper lists the rational and regular grey relational grade that had been published in the past, and used the four axioms in grey system theory to prove the Pai’s grey relational grade that satisfy the four axioms steps by steps.

Through the detail proof of the proposed grey relational grade in Pai’s paper, it indeed satisfies the four axioms in grey relational grade.

The paper had enhanced the correctness and reasonableness of that paper, and let the grey relational grade, which appear in Pai’s paper is legitimate and correct grey relational grade in grey system theory.

The paper had identified that Pai’s grey relational grade is a rational and regular grey relational grade in grey system theory, and it proves that the results in Pai’s paper are correct and reasonable.

During the service period of communication satellite systems, their performance is often degraded due to the depletion mechanism. In this paper, the grey system theory is applied to the multi-state system effectiveness evaluation and the grey Lz-transformation ADC (availability, dependability and capability) effectiveness evaluation model is constructed to address the characteristics of the communication satellite system such as different constituent subsystems, numerous states and the inaccuracy and insufficiency of data.

The model is based on the ADC effectiveness evaluation method, combined with the Lz transformation and uses the definite weighted function of the three-parameter interval grey number as a bridge to incorporate the possibility of system performance being greater than the task demand into the effectiveness solution algorithm. At the same time, using MATLAB (Matrix laboratory) to solve each state probability, the same performance level in the Lz transform is combined. Then, the system effectiveness is obtained by Python.

The results show that the G-Lz-ADC model constructed in this paper can accurately evaluate the effectiveness of static/dynamic systems and certain/uncertain system and also has better applicability in evaluating the effectiveness of the multi-state complex system.

The G-Lz-ADC effectiveness evaluation model constructed in this paper can effectively reduce the complexity of traditional effectiveness evaluation models by combining the same performance levels in the Lz-transform and solving the effectiveness of the system with the help of computer programming, providing a new method for the effectiveness evaluation of the complex MSS. At the same time, the weaknesses of the system can be identified, providing a theoretical basis for improving the system’s effectiveness.

The possibility solution method based on the definite weighted function comparing the two three-parameter interval grey numbers is constructed, which compensates for the traditional calculation of the probability based on numerical values and subjective preferences of decision-makers. Meanwhile, the effectiveness evaluation model integrates the basic theories of three-parameter interval grey number and its definite weighted function, Grey−Markov, grey universal generating function (GUGF), grey multi-state system (GMSS), etc., which is an innovative method to solve the effectiveness of a multi-state instantaneous communication satellite system.

The purpose of this paper is to propose a grey linear control system for regulating the price of China's real estate and provide the necessary support to assist the relevant management departments with their policy making.

A grey state equation of the real estate market price that can reflect both the market supply‐demand price mechanism and the production price mechanism is proposed based on the economic cybernetics. Also, the grey control linear theory is used to demonstrate the disequilibrium fluctuation control system for the China's real estate market with uncertain parameters.

The price disequilibrium fluctuation control system for China's real estate market has been in a critical state. The system would reach a balanced state in 2013, if the real estate price in 2010 and 2011 firstly decreased 244.41 yuan/m2 and 62.33 yuan/m2, respectively, and then increased 60.88 yuan/m2 in 2012. The disequilibrium state will continue for years before it reaches a balanced state.

Due to the complexity of operation of grey numbers, the present technique still cannot analyze the properties of the grey control system exactly and further research is needed.

The modelled results can help the relevant management departments steady China's real estate market by price regulation.

A new approach to study the price regulation system of a real estate market is proposed based on grey linear control theory.

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.

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.

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.

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.

This paper aims to construct a novel grey relational model based on grey number sequences and to solve the problems which exist in traditional grey relational models, in which the uncertain information cannot be described.

Based on the definition of traditional grey relational models, considering the limited information and knowledge, the algorithm of grey numbers was combined with the grey relational model. A general formula of grey operations and grey distance is defined. A novel grey relational model based on grey number sequences, named grey geometrical relational model, is proposed according to the definition of grey distance. Finally, several properties including parallel, multiple and order‐keeping about the proposed model are discussed.

The results show that the novel grey relational model satisfies the properties properly. It is useful to calculate the relational degree of two different grey number sequences. And the process of calculating is easier than traditional grey relational models.

The method exposed in the paper can be used to calculate every two sequences. The method can also be used to rank sequences of more than two.

The paper succeeds in constructing a novel grey relational model. The properties of novel model are studied and it is a new development in grey systems theory undoubtedly.

The purpose of this paper is to summarize the different types of grey information, explain the mechanism of grey system modeling and reconstruct the framework of grey system theory (GST).

GST has been developed for more than three decades; however, the framework of GST is still in an evolutionary process. This manuscript first explains grey information in detail, and then summarizes a series of grey system models under limited data and poor information. Figures and general steps for different types of grey system models are provided in this paper.

The findings in this paper clearly differentiate between grey information and other uncertainty information. The differences between grey system models and other uncertainty models are clearly explained. In addition, general steps for different grey system models are given which demonstrate the orientation of grey system modeling.

Theoretical framework is very important for developing a new theory. This paper clarified grey information and grey system-based modeling mechanism. It is very useful to understand and explain the systematic framework of GST and it contributes undoubtedly to make GST perfect.

Grey information is explained in terms of limited data and two types of grey numbers. Accordingly, all of the grey system models were divided into limited data-based grey system models and grey number-based grey system models.

The purpose of this paper is to propose a formative assessment framework to expose individual student's cognitive learning difficulties in English public speaking. The paper aims to provide student feedback and information during the teaching and learning process. A grey student-construct (S-C) chart is developed to represent the students’ cognitive mapping of the speech difficulties in relation to their overall speech conceptualization. This grey S-C chart can facilitate the instructors to ameliorate the classroom teaching and learning performance in English public speaking.

In total, 26 students in a class of English Speech and Rhetoric participate in the experiment – each student views the online video segments of a great speaker's speech, and then decides what segments would best support the speaking skill constructs and also reflects on his/her own difficulties in the same constructs. The grey relational analysis (GRA) method is used to analyze the empirical data. The individual student's construct localization grey relation grade values are calculated to rank the grey relation for both students and constructs. Accordingly, a grey S-C matrix is constructed and a grey S-C chart can thus be developed.

The grey S-C chart manifestly displays the cognitive difficulties in sequences of both students and constructs.

According to the grey S-C chart, the instructors may modify teaching strategies to enhance the overall classroom performance. The students may adjust learning strategies to eliminate their specific difficulties. Offering individualized advanced and remedial practices to those largely deviating from the norm is also possible.

The study is the first of its kind to apply the GRA method to expose individual student's cognitive learning difficulties in English public speaking. The grey S-C chart is novel in education literature, which can reveal individual student's learning difficulty patterns.