TOPSISEvaluation Method on″Have Both Hardand Soft″Systems

1　Topsis Synthetical Evaluation MethodIn multiobjective decision making,if schemes are limit in number,then Topsis method isoften used.It can arrange order to each decision making scheme which is its advantage,Topsis method is as follows:1 ) Construct decision making matrix AA =x1 1 x1 2 … x1 mx2 1 x2 2 … x2 mxn1 xn2 … xnmHere,xijis value of j-th for i-th appraisal object,i=1 ,2 ,… ,n,j=1 ,2 ,… ,m.2 ) Construct normal decision making matrix YY =y1 1 y1 2 … y1 my2 1 y2 2 … y2 myn1 y…     

A New Approach to Solving Nonlinear Programming

1　 IntroductionConsider a class of nonlinear programming problems as follows:max F( x1 ,x2 ,… ,xn)s.t.ai1 x1 ai2 x2 … ainxn=bi,i =1 ,2 ,… ,pai1 x1 ai2 x2 … ainxn bi,i =p 1 ,… ,mSuch nonlinear programming problems are wildly applied to the areas of engineering,economic management and even policy decision of the government,e.g.over-bounderyanalysis ofthe economy.Unfortunately,so far there is nota systemetic method to solvingsuch nonlinear programming problems.Only for some pro…     

Error Analysis in Frequency Domain for Linear Multipass Algorithms

1. INTRoDUCTIONConsider the dyntalc systemdridt = Ax Bu (1)y = Cx Du (2)whre u is the inPut VaIable; y is the output wriab1e, and x = (x', x2,...,x")" is the state vahale. A, B, Cand D are n x n, n x r, l x n, l x r constant matrices, respectively The transfer function H(s) of equabo (1)and (2) is given bywhere H(s) and oi(i = 0, 1,..., n) are l x r matrices; pi, i = 0, 1,... 1 n are real nUIners. lt can be seen thathe sca1ar relation between every pair of input comPoneni ui and …     

STRONG CONSISTENCY OF THE PERIODIC SMOOTHING SPLINES

Consider the regression model Y_i=u(x_i)+ε_i,i=1,2,…,n,where u(x)∈W_(2,per)~2[0,1],x_i=(i-1)/n,{ε_i}(?)are i.i.d,random variables.We use the periodic smoothing spline u_(λp)(x)toestimate u(x).Under certain conditions,strong consistency results of u_(λp)(x)are obtained,i.e.,forall 0相似文献   

A Class of Optimization Method for Bilevel Multi-objective Decision Making Problem with the Help of Satisfactoriness

1　 IntroductionWe discuss the following bilevel multi-objective decision making problemmaxx F( x,y) ( 1 a)s.t. G( x,y)≤ 0 ( 1 b)maxyifi( x,yi) ,　 i =1 ,… ,p ( 1 c)s.t. gi( x,gi)≤ 0 ,　 i =1 ,… ,p ( 1 d)where F( x,y) =( F1 ( x,y) ,… ,FM( x,y) ) ,M≥ 2 .x=( x1 ,x2 ,… ,x N) Tand yi=( yi1 ,… ,yin) Tstand for the decision variable of the upper-level decision maker and the decision variable ofthe lower-level i-th decision making unit;y=( y T1 ,… ,y Tp) T;letn =∑pi=1ni;F∶ Rn N → RM…     

A New Generating Method and Its Application

1 .INTRODUCTIONGreyforecastingisoneoftheimportantelementsinthegreytheory .Ithasbeenusedinmanyfields[1 ,3] ,andalltheseapplicationsarebasedonagreymodel.Intheprocessofmodelbuilding ,usuallytherawse riesismanagedbyaccumulatedgeneratingoperation(AGO) ,thatis,letx(0 ) =(x(0 ) ( 1 ) ,x(0 ) ( 2 ) ,… ,x(0 ) (n) )bearawseries,andx(1 ) =(x(1 ) ( 1 ) ,x(1 ) ( 2 ) ,… ,x(1 ) (n) )isone orderaccumulatedgeneratingseriesofx(0 ) ,wherex(1 ) (k) = Ki=1x(0 ) (i) ,k=1 ,2 ,… ,nIfx(0 ) (k)≥ 0 ,obviously ,…     

A New Convergence Result of Gauss－Newton Methods for the Complementarity Problem

1　 IntroductionL et F∶Rn→Rnbe continuously differentiable.The nonlinear complementarity problem isto find a solution of the following system of equations and inequalities:x 0 ,F( x) 0 ,x TF( x) =0or,equivalently,xi 0 ,Fi( x) 0 ,xi Fi( x) =0 ,　 i =1,… ,nWe denote this problem by NCP( F) .When F is an affine function and is of the formF( x) =Mx qM is an n× n real matrix and q∈ Rn,the complementarity problem is referred to as thelinear complementarity,denoted by L CP( M,q) .N…     

NONMRAMETRIC AND SEMIPARAMETRICREGRESSION MODELS WITH LOCALLYGENERALIZED GAUSSIAN ERROR

1.IntroductionLetpbeanaturalnumberandAbeacompactsetinW,K(")~g(xj")) e(")ti~1)2,...5acwherexln),x;n),''t.in)EAaredesignpoints,gisanunknownfunction,ej")arerandomerrors.Georgiovil]definedg.(x)~fWu.(x)K(")asanestimateofg,whereWei(x)=i=1Wei(x,xl"),xln),''5x;…     

混合基表示下的大数比较算法及其最优性

本文给出了大数在混合基表示下的比较算法,主要结论为:设X=b_(n 1)P_nP_(n-1)…P_1 … b_2p_1 b_1,其中{p_i}两两互素,则对于计算{b_i}的任何算法,计算b_(n 1)所花的时间大于计算b_1,b_2,… ,b_n所花时间的总和.从而利用计算b_1,b_2,…,b_n的最优算法进行两个大数的比较,本文提出的比较算法是最优的.     

EDGE CONDITION FOR A HAMILTONIAN BIPARTITE GRAPH TO BE BIPANCYCLIC

Let G be a hamiltonian, bipartite graph on 2n vertices, where n>3. It isshown that if e(G)>n(n-1)/2 + 2 then G contains cycles of every possible even length.This improves a result of Entringer and Schmeichel.