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To overcome the limitations of traditional multi-attribute decision making (MADM) methods, which only provide deterministic rankings of decision objects, this paper proposes a novel multi-attribute 3WD model. This model presents three-parameter interval grey number decision-theoretic rough sets (TPIGNDTRSs), aiming to offer a reasoned interpretation of loss functions in grey environments and ensure objective assessment of conditional probabilities.

Firstly, the traditional equivalence relation is replaced with the probabilistic dominance relation (PDR), categorizing decision objects into two state sets in DTRS for more objective conditional probabilities. Secondly, as the three-parameter interval grey number (TPIGN) introduces the most probable value on the basis of the traditional two-parameter interval grey number, it provides a more comprehensive method for describing grey information. Consequently, integrating TPIGN into DTRS refines the interpretations of loss functions in grey environments. Finally, by utilizing two main sorting techniques, relative kernel and degree of accuracy ranking and possibility ranking, two types of 3WD rules with TPIGNDTRSs, are constructed.

This study has successfully developed and validated a new multi-attribute 3WD model. The model was tested in two distinct domains: evaluating innovation efficiency in high-tech enterprises and recommending movies in a practical case. The findings reveal that the model can effectively integrate relevant information of high-tech enterprises, provide the government with enterprise-level assessments, and gather consumer preferences to recommend the most suitable movies.

This study treats the loss function as grey information in the 3WD model but overlooks the grey nature of evaluation values, limiting its applicability. Additionally, the model’s reliance on subjective expert judgments and historical data to establish the loss function may affect its objectivity. The implications of this research are that the novel model overcomes traditional MADM limitations, enhancing decision-making quality and efficiency in complex and grey scenarios. The model’s successful application in evaluating high-tech enterprises and recommending movies illustrates its dual value in both theory and practice.

Initially, the model proposed in this study is of significant importance for the development of the 3WD field, as it successfully addresses the challenges of uncertain loss functions and unknown conditional probabilities in grey information environments. Moreover, by integrating the 3WD model with MADM problems, it has broken through the bottlenecks of traditional MADM methods, offering new perspectives and strategies for solving MADM issues. Therefore, this research not only advances theoretical research but also provides powerful tools for practical applications.

In order to solve the decision-making problem that the attributive weight and attributive value are both interval grey numbers, this paper tries to construct a multi-attribute grey decision-making model based on generalized greyness of interval grey number.

Firstly, according to the nature of the generalized gresness of interval grey number, the generalized weighted greyness distance between interval grey numbers is given, and the transformation relationship between greyness distance and real number distance is analyzed. Then according to the objective function that the square sum of generalized weighted greyness distances from the decision scheme to the best scheme and the worst scheme is the minimum, a multi-attribute grey decision-making model is constructed, and the simplified form of the model is given. Finally, the grey decision-making model proposed in this paper is applied to the evaluation of technological innovation capability of 6 provinces in China to verify the effectiveness of the model.

The results show that the grey decision-making model proposed in this paper has a strict mathematical foundation, clear physical meaning, simple calculation and easy programming. The application example shows that the grey decision model in this paper is feasible and effective. The research results not only enrich the grey system theory, but also provide a new way for the decision-making problem that the attributive weights and attributive values are interval grey numbers.

The decision-making model proposed in this paper does not need to seek the optimal solution of the attributive weight and the attributive value, and can save the decision-making labor and capital investment. The model in this paper is also suitable for the decision-making problem that deals with the coexistence of interval grey numbers and real numbers.

The paper succeeds in realizing the multi-attribute grey decision-making model based on generalized gresness and its simplified forms, which provide a new method for grey decision analysis.

As some data to evaluate the efficiency of bank branches is qualitative or uncertain, only grey numbers should be used to calculate the efficiency interval. The combination of multi-stage models and grey data can lead to a more accurate and realistic evaluation to assess the performance of bank branches. This study aims to compute the efficiency of each branch of the bank as a grey number and to group all branches into four grey efficiency areas.

The key performance indicators are identified based on the balanced scorecard and previous research studies. They are included in the two-stage grey data envelopment analysis (DEA) model. The model is run using the GAMS program. The grey efficiencies are calculated and bank branches have been grouped based on efficiency kernel number and efficiency greyness degree.

As policies and management approaches for branches with less uncertainty in efficiency are different from branches with more uncertainty, considering the uncertainty of efficiency values of branches may be helpful for the policy-making of managers. The grey efficiency of branches of one bank is examined in this study using the two-stage grey DEA throughout one year. The branches are grouped based on kernel and greyness value of efficiency, and the findings show that considering the uncertainty of data makes the results more consistent with the real situation.

The performance of bank branches is modeled as a two-stage grey DEA, in which the efficiency value of each branch is obtained as a grey number. The main originality of this paper is to group the bank branches based on two grey indexes named “kernel number” and “greyness degree” of grey efficiency value.

We attempt to construct a grey three-way conflict analysis model with constraints to deal with correlated conflict problems with uncertain information.

In order to address these correlated conflict problems with uncertain information, considering the interactive influence and mutual restraints among agents and portraying their attitudes toward the conflict issues, we utilize grey numbers and three-way decisions to propose a grey three-way conflict analysis model with constraints. Firstly, based on the collected information, we introduced grey theory, calculated the degree of conflict between agents and then analyzed the conflict alliance based on the three-way decision theory. Finally, we designed a feedback mechanism to identify key agents and key conflict issues. A case verifies the effectiveness and practicability of the proposed model.

The results show that the proposed model can portray their attitudes toward conflict issues and effectively extract conflict-related information.

By employing this approach, we can provide the answers to Deja’s fundamental questions regarding Pawlak’s conflict analysis: “what are the underlying causes of conflict?” and “how can a viable consensus strategy be identified?”

This paper investigates a problem in a reverse logistics (RLs) network to decide whether to dispose of unsold goods in primary stores or re-commercialize them in outlet centers. By deducting the costs associated with each policy from its revenue, this study aims to maximize the profit from managing unsold goods.

A new mixed-integer linear programming model has been developed to address the problem, which considers the selling prices of products in primary and secondary stores and the costs of transportation, cross-docking and returning unwanted items. As a result of uncertain nature of the cost and time parameters, gray numbers are used to deal with it. In addition, an innovative uncertain solution approach for gray programming problems is presented that considers objective function satisfaction level as an indicator of optimism.

According to the results, higher costs, including transportation, cross-docking and return costs, make sending goods to outlet centers unprofitable and more goods are disposed of in primary stores. Prices in primary and secondary stores heavily influence the number of discarded goods. Higher prices in primary stores result in more disposed of goods, while higher prices in secondary stores result in fewer. As a result of the proposed method, the objective function satisfaction level can be viewed as a measure of optimism.

An integral contribution of this study is developing a new mixed-integer linear programming model for selecting the appropriate goods for re-commercialization and choosing the best outlet center based on the products' price and total profit. Another novelty of the proposed model is considering the matching percentage of boxes with secondary stores’ desired product lists and the probability of returning goods due to non-compliance with delivery dates. Moreover, a new uncertain solution approach is developed to solve mathematical programming problems with gray parameters.

The reported Kullback–Leibler (K–L) distance-based generalized grey target decision method (GGTDM) for mixed attributes is an asymmetric decision-making basis (DMB) that does not have the symmetric characteristic of distance in common sense, which may affect the decision-making result. To overcome the deficiency of the asymmetric K–L distance, the symmetric K–L distance is investigated to act as the DMB of GGTDM for mixed attributes.

The decision-making steps of the proposed approach are as follows: First, all mixed attribute values are transformed into binary connection numbers, and the target centre indices of all attributes are determined. Second, all the binary connection numbers (including the target centre indices) are divided into deterministic and uncertain terms and converted into two-tuple (determinacy and uncertainty) numbers. Third, the comprehensive weighted symmetric K–L distance can be computed, as can the alternative index of normalized two-tuple (deterministic degree and uncertainty degree) number and that of the target centre. Finally, the decision-making is made by the comprehensive weighted symmetric K–L distance according to the rule that the smaller the value, the better the alternative.

The case study verifies the proposed approach with its sufficient theoretical basis for decision-making and reflects the preferences of decision-makers to address the uncertainty of an uncertain number.

This work compares the single-direction-based K–L distance to the symmetric one and uses the symmetric K–L distance as the DMB of GGTDM. At the same time, different coefficients are assigned to an uncertain number’s deterministic term and uncertain term in the calculation process, as this reflects the preference of the decision-maker.

Educational policies, integrated practices, obliged strategies and notable benchmarks are always required by the higher educational institutions (HEIs) for operating business ventures into competent boundaries and to preside toward the overall new business density. The same are needed to be evaluated based on student's concerns for road-mapping sustainability. Accordingly, authors conducted present study to identify crucial quality characteristics (measures) under the origins of HEIs based on student's concerns using qualitative medium under Indian economy. The study is presenting critical dimensions and quality characteristics, which are seeking by the students for selecting HEIs for their studies.

Kano integrated-Grey-VIKOR approach is utilized in present study for road-mapping sustainability based on the determination of priority index and ranking. The study utilized three segments of methodology, where in the first segment, Kano technique is implicated to define priority index of quality characteristics. In the second segment, grey sets theory is implicated to capture the perceptions of the respondents. In the third segment, VIKOR technique is implicate to rank the HEIs.

The findings of the study will assist administrators in planning the prominent strategies that can embrace performance traits under HEI, which in turn will participate in growth and development of an economy. The findings have revealed “PPCS, ICMC, TSTR, PICM, AFEP, IMIS as Attractive performance characteristics,” “IEAF, OIAR, INET as One dimensional performance characteristics,” “QTCS, PORE, SIRD as Must-be performance characteristics” and “PQPE, PCTM as Indifferent performance characteristics.” Additionally, “Professional and placement characteristics of institute” is found as the most significant measure inspiring students for admiring engineering institutes. It is found that “Observance of institutional affiliation and recognition” and “Infrastructure, classroom management and control methods” are found as the second significant measures. “Patterns of question papers and evaluation medium” and “Personal characteristics of teacher and management” are found as the least competent characteristics admiring stakeholders for selecting HEI.

The present study can assist administrators in drafting refined policies and strategies for practising quality outputs by HEI. The study suggested critical quality characteristics, which in respond will aid in attracting more number of students toward educational institutes. A study under Indian context is demonstrated for presenting critical facts and attaining higher student's enrolment rates.

The goal of this article is to introduce the notion of a grey relation between grey sets using grey numbers.

This study uses the grey number to create novel ideas of grey sets. We suggest several operations that can be performed on it, including the union, intersection, join, merge, and composition of grey relations. In addition, we present the definitions of reflexive, symmetric, and transitive grey relations and analyze certain characteristics associated with them. Furthermore, we formulate the concept of the grey equivalence relation, apply it to the study of the grey equivalence class over the grey relation, and go over some of its features.

We present new algebraic aspects of grey system theory by defining grey relations and then analyzing their characteristic features.

This paper proposes a new theoretical direction for grey sets according to grey numbers, namely, grey relations. This paper proposes a new theoretical direction for grey sets according to grey numbers, namely, grey relations. As such, it can be applied to create rough approximations as well as congruences in algebras, topologies, and semigroups.

The presented notions are regarded as new algebraic approaches in grey system theory for the first time. Additionally, some fundamental operations on grey relations are also investigated. Consequently, different types of grey relations, such as reflexive, symmetric, and transitive relations, are discussed. Then, the grey equivalence class derived from the grey equivalence relation is demonstrated, and its properties are examined.

The objective of this paper is to formulate the precise meanings of grey graphs and examine some of their properties.

This article introduces innovative concepts of grey sets based on the grey number. We establish the grey graphs and examine their essential properties as isomorphisms of these graphs. Additionally, we explore the notion of a grey-complete graph and demonstrate certain properties of self-complementary grey-complete graphs.

We showcase novel facets of grey system theory through the establishment of the structures of grey graphs, and the subsequent analysis of their distinctive traits.

This article provides us with a new theoretical direction for grey system theory according to grey numbers. Thus, we present test examples that explain the routes between cities and the electrical wires between homes. Furthermore, the concept of grey graphs can be applied in several areas of engineering, computer science, neural networks, artificial intelligence, and medical diagnosis.

The proposed concepts are considered novel mathematical directions in grey system theory for the first time. Some operations of grey graphs are also explored.

This paper aims to optimize the air pressure regulation scheme of the aeroengine pressure test bench.

Based on the requirements of pressure regulation process and the operating mechanism of aeroengine pressure test bench, a grey performance evaluation index system is constructed. The combination of principal component analysis and grey theory is employed to assign weights to grey indexes. The grey target evaluation model is introduced to evaluate the performance of historical regulation processes, and the evaluation results are analyzed to derive optimization mechanism for pressure regulating schemes.

A case study based on monitoring data from nearly 300 regulation processes verifies the feasibility of the proposed method. On the one hand, the improved principal component analysis method can achieve rational weighting for grey indexes. On the other hand, the method comparison intuitively shows that the proposed method performs better.

The pressure test bench is a fundamental technical equipment in the aviation industry, serving the development and testing of aircraft engines. Due to the complex system composition, the pressure and flow adjustment of the test bench heavily rely on manual experience, leading to issues such as slow adjustment speed and insufficient accuracy. This paper proposes a performance evaluation method for the regulation process of pressure test bench, which can draw knowledge from historical regulation processes, provide guidance for the pressure regulation of test benches, and ultimately achieve the goal of reducing equipment operating costs.