A Modified Approach to Construct the Supermatrix of ANP for the Circular System with Inner Independence
ANP 内部独立循环系统超矩阵构造的改进方法

In analytic network process(ANP),how to construct reasonably the supermatrix of evaluated problem is a vital technical core.For the evaluation problem of circular system with inner independence(CSII),an important submatrix of the supermatrix,i.e.,the influence matrix of alternatives to goals(IMAG),is constructed in ANP by the same way as the other submatrices,that is,by way of point estimates.This constructing pattern does not reasonably reflect the characteristic of high imprecision existing in holistic logic judgments,required in the IMAG constructing by the nolism thought.To overcome the above drawback,this paper suggests that experts should adopt interval estimates to reflect their relative preferences,instead of adopting point estimates.With the above suggestion concerneol,a modified approach to construct the supermatrix based on the methodology of data envelopment analysis is presented.Applied to a specific example,the modified approach is validated to be scientific and reasonable and can be well applied to real world ranking problems of CSII.