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The purpose of this paper is to combine the interval grey number algorithm with a project scheduling model, so as to solve the interval grey number based project scheduling problem.

According to the grey system theory, if we could not clearly collect the right value of an activity while obtaining the upper and lower boundaries of the activity duration time, we can find activity duration time as interval grey number. This paper tries to combine interval grey number with project scheduling problem. The general definition of interval grey number was given. And then the linear operations of independent interval grey number and non-independent interval grey number were further defined. Interval grey number based project scheduling model and its algorithm were further proposed. Finally, a numerical case was adopted to test the effectiveness of the proposed method.

The results show that grey project scheduling and grey critical path method could be established under interval grey number measured activities.

Scheduling problem was widely used in project planning and control. This manuscript attempted to combine interval grey number with project scheduling so as to explain the flexible deadline in a special project. It is truly in accordance with the requirements for real applications.

This paper proposed linear operations of independent and non-independent interval grey numbers, and proposed a interval grey number based project scheduling model. Valuable contribution is to combine interval grey numbers with project scheduling and it is meaningful to make a useful strategy in a flexible condition of project scheduling.

Supplier selection is a complex multiple criteria decision (MCDM) problem which directly depends on decision makers’ choice. Some decisions are getting involved with linguistic variables and they are not mathematically operable. To solve a typical decision problem through MCDM techniques, a number or a numerical interval should be defined. The purpose of this paper is to focus on that numerical interval and in a case of supplier selection, the aim is to close the decisions to the real number that the decision maker mentions and this number is in a numerical interval.

The proposed method deals with grey relational analysis (GRA) and develops it by applying triangular fuzzy numbers. The grey numbers have two defined bounds; the proposed method defines two fuzzy bounds for each grey attribute. In the proposed method, the fuzzy membership function has been employed for each bounds of grey attribute to make them to fuzzy bounds with two undefined bounds. Also to make comparison, with employing of TOPSIS technique, both of the grey fuzzy combination decision matrix and the original grey decision matrix are obtained.

The results indicate that, except to the ideal solutions, the grey relation coefficient for each alternative is too close to each other. Indeed, they are too close to zero. Applying the proposed method in problem of supplier selection shows the difference between two selected supplier in proposed method and the original grey method.

As mentioned heretofore this paper aims to make decision makers’s decision more accurate and actually there is no other researches which used this combination method.

The purpose of this paper is to propose an uncertainty representation and information measurement method for characterizing grey numbers, estimating their internal laws and solving how to generate them based on available information data in the real world.

This paper attempts to present a new mathematical methodology in the field of grey numbers. The generalized grey number is defined at first with the concept of information elements and information samples. Then, the probability function of a grey number is proposed to describe the internal law of the grey number. By finding the feasible information elements from information samples, the probability calculation method for the true value of a grey number is presented. Finally, some numerical examples and comparisons are carried out to assess the efficiency and performance.

The results show that the uncertainty representation and information measurement method is effective in characterizing and quantifying grey numbers based on available information data.

Uncertain information is widespread in practical applications. In this manuscript, the grey number is represented and its information is measured through some existing data in discrete or interval forms, which provides a grey information concept that utilizes information elements to represent uncertainty in the real world.

The proposal presents a novel data-driven method to generate a grey number representation from available data rather than the classical whitening weight function constructed from experience, and the dynamic evolution process of a grey number is measured by the increase of information samples.

To explore a more effective method to study the information content of grey numbers.

An axiomatic approach is used for the measurement of information content of a given grey number.

A new definition for information content of grey numbers is introduced. And, relevant results are proven.

This work fills the vacancy on how to measure the information value contained in a grey number.

The purpose of this paper is to construct an interval grey number NGM(1,1) direct prediction model (abbreviated as IGNGM(1,1)), which need not transform interval grey numbers sequences into real number sequences, and the Markov model is used to optimize residual sequences of IGNGM(1,1) model.

A definition equation of IGNGM(1,1) model is proposed in this paper, and its time response function is solved by recursive iteration method. Next, the optimal weight of development coefficients of two boundaries is obtained by genetic algorithm, which is designed by minimizing the average relative error based on time weighted. In addition to that, the Markov model is used to modify residual sequences.

The interval grey numbers’ sequences can be predicted directly by IGNGM(1,1) model and its residual sequences can be amended by Markov model. A case study shows that the proposed model has higher accuracy in prediction.

Uncertainty and volatility information is widespread in practical applications, and the information can be characterized by interval grey numbers. In this paper, an interval grey numbers direct prediction model is proposed, which provides a method for predicting the uncertainty information in the real world.

The main contribution of this paper is to propose an IGNGM(1,1) model which can realize interval grey numbers prediction without transforming them into real number and solve the optimal weight of integral development coefficient by genetic algorithm so as to avoid the distortion of prediction results. Moreover, the Markov model is used to modify residual sequences to further improve the modeling accuracy.

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

First, the concept of generalised grey number based on grey system theory is given in this paper. Second, from the perspective of kernel and degree of greyness of general grey number, the method of measuring the distance of general grey number and its properties are given. At the same time, the concepts of the kernel expectation and the kernel variance of the general grey number are proposed.

Up to now, the method of measuring the distance and sorting of general grey number is established. Thus, the difficult problem for set up sorting 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. Distance measuring and sorting method of general grey number could be extended to the case of grey algebraic equation, grey differential equation and grey matrix which includes general grey numbers, etc.

The concepts of the kernel expectation and the kernel variance of the general grey number are proposed for the first time in this paper; the novel sorting rules of general grey numbers were also constructed.

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.

The purpose of this paper is to explain the connotation of grey number, which is the basic unit of grey mathematics and the key to establish the mathematic framework of grey system theory.

From the grey hazy set, the paper re‐defines grey number and the operation of grey‐number element, then some properties are obtained. Based on them, the operation of grey‐matrix element is given. The general definition of grey function and its operation are also proposed.

The connotation of grey number is elaborated and the elementary framework of grey mathematics can be established.

The researched object, objective and techniques of grey system theory have not been logically proposed and they may influence the comprehension of grey system theory. The obtained results of grey mathematics may significantly promote its development.

The paper can enable managers to control the complex system with missing information by using the quantitative approaches.

Grey mathematics may become a branch of mathematics to deal with proximate calculation.

The purpose of this paper is to present a mixed integer programming model for simple assembly line balancing problems (SALBP) with Type 1 when the annual demand and task durations are uncertain and encoded with grey numbers.

Grey theory and grey numbers are used for illustrating the uncertainty of parameters in an SALBP, where the objective is to minimize the total number of workstations. The paper proposes a 0-1 mathematical model for SALBP of Type 1 with grey demand and grey task durations.

The uncertainty of the demand and task durations are encoded with grey numbers and a well-known 0-1 mathematical model for SALBP of Type 1 is modified to find the minimum number of workstations in order to meet both the lower and upper bounds of the uncertain demand. The results obtained from the proposed mathematical model show a task-workstation assignment that does not distribute precedence relations among tasks and workstations and the sum of task durations in each single workstation is less than or equal to the grey cycle time.

The grey theory and grey numbers have not been previously used to identify uncertainties in assembly line balancing problems. Therefore, this study provides an important contribution to the literature.

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.