Prediction model of interval grey number based on DGM(1,1)

In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.By mining the geometric features of interval grey number sequences on a two-dimensional surface,all the interval grey numbers are converted into real numbers by means of certain algorithm,and then the prediction model is established based on those real number sequences.The entire process avoids the algebraic operations of grey number,and the prediction problem of interval grey number is usefully solved.Ultimately,through an example＇s program simulation,the validity and practicability of this novel model are verified.

CALCULATION FOR KERNEL OF INTERVAL GREY NUMBER BASED ON BARYCENTER APPROACH

The kernel of interval grey number is most likely the real number,which can be used to represent whitenization value of interval grey number.A novel method for calculating kernel of interval grey number is constructed based on the geometric barycenter of whitenization weight function in the two-dimensional coordinate plane,and the calculation of kernel is converted to the calculation of barycenter in geometric figures.The method fully considers the effect of all information contained in whitenization weight function on the calculation result of kernel,and is the extension and perfection of the existing methods in the scope of application.

Dynamic Multi-Attribute Decision Analysis on Three-Parameter Interval Grey Number of Upper(Lower)Deviation Quasi-Normal Distribution

Aiming at the dynamic multi-attribute decision making problem where the weight of each decision stage and attribute weight are completely unknown and the attribute value is unknown distributed three-parameter interval grey number,a threeparameter interval grey number dynamic multiattribute grey target decision making method with attribute value following quasi-normal distribution is proposed.Firstly,the position relationship between the“center of gravity”point and the kernel of the threeparameter interval grey number is discussed.According to the characteristicthat the attribute value obeys the quasi-normal distribution,anew weight isgiventothe“centerof gravity”point,and a new distance measure formula of the three-parameter interval grey number is defined.Secondly,according to the principle of maximum entropy,the objective programming model is constructed to determine the stage weight and attributeweight.Then,the schemes aresorted according to thesize of the comprehensive bull's-eye distance Finally an example is given to illustrate the effectiveness of the decision model.

Grey clustering evaluation based on AHP and interval grey number

Purpose–The purpose of this paper is to propose a grey clustering evaluation model based on analytic hierarchy process(AHP)and interval grey number(IGN)to solve the clustering evaluation problem with IGNs.Design/methodology/approach–First,the centre-point triangular whitenisation weight function with real numbers is built,and then by using interval mean function,the whitenisation weight function is extended to IGNs.The weights of evaluation indexes are determined by AHP.Finally,this model is used to evaluate the flight safety of a Chinese airline.The results indicate that the model is effective and reasonable.Findings–When IGN meets certain conditions,the centre-point triangular whitenisation weight function based on IGN is not multiple-cross and it is normative.It provides a certain standard and basis for obtaining the effective evaluation indexes and determining the scientific evaluation of the grey class.Originality/value–The traditional grey clustering model is extended to the field of IGN.It can make full use of all the information of the IGN,so the result of the evaluation is more objective and reasonable,which provides supports for solving practical problems.

Environmental stress level evaluation approach based on physical model and interval grey association degree

Associating environmental stresses （ESs） with built-in test （BIT） output is an important means to help diagnose intermittent faults （IFs）. Aiming at low efficiency in association of traditional time stress measurement device （TSMD）, an association model is built. Thereafter, a novel approach is given to evaluate the integrated environmental stress （IES） level. Firstly, the selection principle and approach of main environmental stresses （MESs） and key characteristic parameters （KCPs） are presented based on fault mode, mechanism, and ESs analysis （FMMEA）. Secondly, reference stress events （RSEs） are constructed by dividing IES into three stress levels according to its impact on faults; and then the association model between integrated environmental stress event （IESE） and BIT output is built. Thirdly, an interval grey association approach to evaluate IES level is proposed due to the interval number of IES value. Consequently, the association output can be obtained as well. Finally, a case study is presented to demonstrate the proposed approach. Results show the proposed model and approach are effective and feasible. This approach can be used to guide ESs measure, record, and association. It is well suited for on-line assistant diagnosis of faults, especially IFs.

A New DGM(1,1)Model with a Grey Parameter and Its Application

In the DGM(1, 1) model modeling process, the influencing factors are uncertain. But the solution of DGM(1, 1) model with uncertain information is unique, which conflicts with the nonuniqueness principle of solution in grey theory. In view of this situation, this paper makes an in-depth analysis of the meaning of grey action quantity β_(2) in DGM(1, 1) model and regards β_(2) as an interval grey number. The maximum possibility whitenization value is given to estimate the kernel of grey number,and the typical possibility function is constructed to describe the possibility of grey number taking different values. A new DGM(1, 1) model with a grey parameter is then proposed, whose simulation results are interval grey numbers. The proposed model is compatible with the DGM(1, 1) model in model structure and simulation results. Finally, the practical example results show the applicability and effectiveness of the proposed model.