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/meth...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.展开更多
In this paper,we construct the addition formulae for several integrable hierarchies,including the discrete KP,the q-deformed KP,the two-component BKP and the D type Drinfeld–Sokolov hierarchies.With the help of the H...In this paper,we construct the addition formulae for several integrable hierarchies,including the discrete KP,the q-deformed KP,the two-component BKP and the D type Drinfeld–Sokolov hierarchies.With the help of the Hirota bilinear equations and τ functions of different kinds of KP hierarchies,we prove that these addition formulae are equivalent to these hierarchies.These studies show that the addition formula in the research of the integrable systems has good universality.展开更多
基金supported by National Natural Science Foundation of China under the project of 71601050 and Civil Aviation Administration of China Science Planned Projects under the project of MHRD20150211.
文摘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.
基金Supported by the Zhejiang Provincial Natural Science Foundation under Grant No.LY15A010004the National Natural Science Foundation of China under Grant Nos.11201251,11571192+2 种基金the Natural Science Foundation of Ningbo under Grant No.2015A610157supported by the National Natural Science Foundation of China under Grant No.11271210K.C.Wong Magna Fund in Ningbo University
文摘In this paper,we construct the addition formulae for several integrable hierarchies,including the discrete KP,the q-deformed KP,the two-component BKP and the D type Drinfeld–Sokolov hierarchies.With the help of the Hirota bilinear equations and τ functions of different kinds of KP hierarchies,we prove that these addition formulae are equivalent to these hierarchies.These studies show that the addition formula in the research of the integrable systems has good universality.
