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The purpose of this paper is to study the grey decision model and distance measuring method of general grey number.

First, intuitionistic grey number (IGN) set and an IGN are defined by grey number probability function. Second, each interval grey number in general grey number is represented by an IGN and converts the general grey number into an IGN set. Final, the operation of two general grey numbers is defined as the operation between IGN sets, and the distance measure of the general grey number is given.

Up to now, the method of measuring the distance and the grey decision model of general grey number is established. Thus, the difficult problem for set up decision mode of general grey number has been solved to a certain degree.

The method exposed in this paper can be used to integrate information form a different source. The method that a general grey number converted to a set of IGNs could be extended to the case of grey incidence analysis models, grey prediction models and grey clustering evaluation models, which includes general grey numbers, etc.

The concepts of IGN and IGN set are proposed for the first time in this paper; The operation of two general grey numbers can be defined as the operation between IGN sets. On this basis, the algorithm of IGN, the integration operator of IGN and the distance measure between IGN sets are given.

Enterprise Resource Planning (ERP) software which is a knowledge-based design on the interconnective communication of business units and information share, ensures that business processes such as finance, production, purchasing, sales, logistics and human resources, are integrated and gathered under one roof. This integrated system allows the company to make fast and accurate decisions and increases its competitiveness. Therefore, for an enterprise, choosing the suitable ERP software is extremely important. The aim of this study is to present new research on the ERP software selection process by clarifying the uncertainties and find suitable software in a computational way.

ERP selection problem design includes uncertainties on the expert opinions and the criteria values using intuitionistic fuzzy set theory and interval grey-numbers to MACBETH multi criteria decision making method. In this paper, a new interval grey MACBETH method approach is proposed, and the degree of greyness approach is used for clarifying the uncertainties. Using this new approach in which grey numbers are used, it is aimed to observe the changes in the importance of the alternatives. Moreover, the intuitionistic fuzzy set method is applied by considering the importance of expert opinions separately.

The proposed method is based on quantitative decision making derived from qualitative judgments. The results given under uncertain conditions are compared with the results obtained under crisp conditions of the same methods. With the qualitative levels of experts reflected in the decision process, it is clearly seen that ERP software selection problem area has more effective alternative decision solutions to the uncertain environment, and decision makers should not undervalue the unsteadiness of criteria during ERP software selection process.

This study contributes to the relevant literature by (1) utilizing the MACBETH method in the selection of the ERP software by optimization, and (2) validating the importance of expert opinions with uncertainties on a proper ERP software selection procedure. So, the findings of this study can help the decision-makers to evaluate the ERP selection in uncertain conditions.

The existing consensus reaching mechanisms ignore the influence of social triangle structure on the decision-makers’ (DMs') weights, and the consensus reaching process (CRP) fails to fully reflect the DMs' subjectivity and can be time consuming and costly. To solve these issues, a novel CRP for multi-criteria group decision-making (MCGDM) problems with intuitionistic grey linguistic numbers (IGLNs) is proposed in this paper.

First, a weight calculation method is proposed by analysing the triangle structure of DMs' social network and scale of adjacent nodes. Then, a consensus degree index based on three-level polygon area is defined and applied to identify the inconsistent DMs. Finally, the feedback mechanism based on particle swarm optimisation (PSO) algorithm under grey linguistic environment is developed, where subjective trust relationships in social network is utilised to determine the adjustment coefficient.

The advantages of the proposed method are highlighted by two practical applications of the evaluation of tunnel construction method and the selection of a hotel for the centralised isolation. Comparision analysis and numerical simulation are performed to reveal the effectiveness and applicability of the method.

The proposed model can not only reflect the effect of triangle structure in social network on DMs' weights, but also reduce the time and cost of decision-making.

The main contribution of this paper is to propose a new MCGDM model based on intuitionistic grey linguistic numbers, which can handle the problem of inconsistency of information more effectively.

This paper aims to solve the problem of public resource allocation among vulnerable groups by proposing a new method called uncertain α-coordination value based on uncertain cooperative game.

First, explicit forms of uncertain Shapley value with Chouqet integral form and uncertain centre-of-gravity of imputation-set (CIS) value are defined separately on the basis of uncertainty theory and cooperative game. Then, a convex combination of the two values above called the uncertain α-coordination value is used as the best solution. This study proves that the proposed methods meet the basic properties of cooperative game.

The uncertain α-coordination value is used to solve a public medical resource allocation problem in fuzzy coalitions and uncertain payoffs. Compared with other methods, the α-coordination value can solve such problem effectively because it balances the worries of vulnerable group’s further development and group fairness.

In this paper, an extension of classical cooperative game called uncertain cooperative game is proposed, in which players choose any level of participation in a game and relate uncertainty with the value of the game. A new function called uncertain α-Coordination value is proposed to allocate public resources amongst vulnerable groups in an uncertain environment, a topic that has not been explored yet. The definitions of uncertain Shapley value with Choquet integral form and uncertain CIS value are proposed separately to establish uncertain α-Coordination value.

Forecasting demand of emergency supplies under major epidemics plays a vital role in improving rescue efficiency. Few studies have combined intuitionistic fuzzy set with grey-Markov method and applied it to the prediction of emergency supplies demand. Therefore, this article aims to establish a novel method for emergency supplies demand forecasting under major epidemics.

Emergency supplies demand is correlated with the number of infected cases in need of relief services. First, a novel method called the Intuitionistic Fuzzy TPGM(1,1)-Markov Method (IFTPGMM) is proposed, and it is utilized for the purpose of forecasting the number of people. Then, the prediction of demand for emergency supplies is calculated using a method based on the safety inventory theory, according to numbers predicted by IFTPGMM. Finally, to demonstrate the effectiveness of the proposed method, a comparative analysis is conducted between IFTPGMM and four other methods.

The results show that IFTPGMM demonstrates superior predictive performance compared to four other methods. The integration of the grey method and intuitionistic fuzzy set has been shown to effectively handle uncertain information and enhance the accuracy of predictions.

The main contribution of this article is to propose a novel method for emergency supplies demand forecasting under major epidemics. The benefits of utilizing the grey method for handling small sample sizes and intuitionistic fuzzy set for handling uncertain information are considered in this proposed method. This method not only enhances existing grey method but also expands the methodologies used for forecasting demand for emergency supplies.

1. An intuitionistic fuzzy TPGM(1,1)-Markov method (IFTPGMM) is proposed.

2. The safety inventory theory is combined with IFTPGMM to construct a prediction method.

3. Asymptomatic infected cases are taken to forecast the demand for emergency supplies.

An intuitionistic fuzzy TPGM(1,1)-Markov method (IFTPGMM) is proposed.

The safety inventory theory is combined with IFTPGMM to construct a prediction method.

Asymptomatic infected cases are taken to forecast the demand for emergency supplies.

The purpose of this paper is to attempt supplier selection considering economic, environmental and social sustainability issues.

Subjective human judgment bears some kind of vagueness and ambiguity; fuzzy set theory has immense potential to overcome this. Owing to the advantage of intuitionistic fuzzy numbers set over classical fuzzy numbers set; three decision-making approaches have been applied here in intuitionistic fuzzy setting (namely, intuitionistic-TOPSIS, intuitionistic-MOORA and intuitionistic-GRA) to facilitate supplier selection in sustainable supply chain.

The stated objective of this research “to verify application potential of different decision support systems (in intuitionistic fuzzy setting) in the context of sustainable supplier selection” has been carried out successfully. A case empirical research has been conducted by applying three different decision-making approaches: intuitionistic fuzzy-TOPSIS, intuitionistic fuzzy-MOORA and intuitionistic fuzzy-GRA to an empirical data set of sustainable supplier selection problem. The ranking orders thus obtained through exploration of aforesaid three approaches have been explored and compared.

As compared to generalized fuzzy numbers, intuitionistic fuzzy numbers exhibit a membership degree, a non-membership degree and the extent of hesitation; a better way to capture inconsistency, incompleteness and imprecision of human judgment. Application potential of aforesaid three decision support approaches has been demonstrated in this reporting for a case sustainable supplier selection.

The purpose of the paper is to propose a new decision‐making method using grey systems theory with the attribute values of corresponding alternatives in the form of intuitionistic fuzzy numbers.

The uncertain degrees of different indices are determined by using the grey incidence analysis. Then, the mass functions of different alternatives in different indices are obtained by using the score function of intuitionistic fuzzy sets and the uncertain degrees of different indices. Information can be fused in accordance with the D‐S combination rule and the best alternative is calculated accordingly. Finally, a numerical example is utilized to illustrate that a satisfied solution can be obtained and the uncertainty can be decreased.

The results are convincing: the new decision‐making method, by combining the D‐S theory of evidence, can well deal with decision‐making problems with the attribute values of corresponding alternatives in the form of intuitionistic fuzzy sets. From the numerical example, it is seen that the uncertainty can be decreased by using the new method.

The method exposed in the paper can be used to help the decision maker make a fast and accurate decision when facing decision problems with the attribute values of corresponding alternatives in the form of intuitionistic fuzzy sets.

The paper succeeds in proposing a decision‐making method by using the D‐S theory of evidence and one of the newest developed theories: grey systems theory.

In the literature, many multi attributes decision making (MADM) models allow evaluation of the alternatives considering their current or last performance. However, in some MADM problems, not only current performance of alternatives but also their past performance should be taken into account in order to select the most appropriate alternative. For this reason, the purpose of this paper is to develop four procedures to evaluate the alternatives in MADM problems with multi terms.

This study uses dynamic operators to aggregate the evaluation in different terms and then, grey relational analysis (GRA) and technique for order preference by similarity to ideal solution (TOPSIS) methods are utilized to determine the most appropriate alternative. Thus, four procedures which consist of these operators and methods are developed to evaluate the alternatives in multi terms.

Some numerical examples are presented for the proposed procedures in multi-terms. Moreover, these four procedures are compared with other four procedures. The analyses of the results show that dynamic aggregation operators based on intuitionistic fuzzy set (IFS) and interval valued intuitionistic fuzzy sets (IVIFS) with GRA and TOPSIS can be used jointly for MADM problems in which alternatives are evaluated for different terms.

One of the significant mistakes faced in some MADM problems is to take into account the current performance of alternatives or is to ignore their past performance. The right selection depends on past and current performance of the alternatives. The novelty of this study is to propose four procedures for solving MADM problems in multi terms based on IFS and IVIFS using dynamic aggregation operators and GRA and TOPSIS methods.

The purpose of this paper is to establish a novel conflict analysis model so that it can well describe and deal with the real conflict problems.

In order to overcome the shortcomings that the agents have only three attitudes with respect to the conflict issues in Pawlak conflict information system, so that it is too stiff to describe and portray the real conflict problems, the thought and methodology of the intuitionistic fuzzy set is employed to soften the agents’ attitudes of the conflict issues, and then a novel conflict analysis model is constructed. This method, to begin with, the intuitionistic fuzzy number is used to express the opposition and support degree with respect to the conflict issues from agents, and then the similarity measure method is utilized to define conflict coefficient; what is more, the conflict degrees between any two agents can be obtained, and then the alliances are determined by setting different threshold values. Finally, an example illustrates the validity and rationality of the proposed method.

The novel conflict analysis model proposed in the paper can well describe and resolve a real-life conflict problems such as the conflict of national territory, employee and employer.

The proposed model can only do with the conflict problems in which there do not exit the correlations among conflict issues, while it does not cope with the conflict problems with the mutually interrelated conflict issues.

The paper succeeds in softening the Pawlak conflict analysis information system, and describing and dealing with the actual conflict problems.

Selection of resilient suppliers has attracted the attention of researchers in the past one decade. The devastating effect of COVID-19 in emerging economies has provided great impetus to the selection of resilient suppliers. Under volatile and uncertain business scenarios, supplier selection is often done under imprecise and incomplete information, making the traditional decision-making methods ineffective. The purpose of this paper is to demonstrate the application of a fuzzy decision-making method for resilient supplier selection.

A group of three decision makers was considered for evaluating various alternatives (suppliers) based on their performance under different primary, sustainability and resilience criteria. Experts' opinion about each criterion and alternative was captured in linguistic terms and was modelled using fuzzy numbers. Then, an algorithm for solving resilient supplier selection problem based on the trapezoidal intuitionistic fuzzy technique for order preference by similarity to ideal solution (TrIFTOPSIS) was introduced and demonstrated through a case study.

A closeness coefficient was used to rank the suppliers based on their distances from intuitionistic fuzzy positive-ideal solution and intuitionistic fuzzy negative-ideal solution. Finally, the proposed fuzzy decision making model was applied to a real problem of supplier selection in the clothing industry.

The presented TrIFTOPSIS model provides an effective route to prioritise and select resilient suppliers under imprecise and incomplete information. This is the first application of intuitionistic fuzzy multi-criteria decision-making for resilient supplier selection.