Data Perturbations of Matrices of Pairwise Comparisons

被引：2

作者：

András Farkas

Pál Rózsa

机构：

[1] IMC Graduate School of Business,Department of Production and Operations Research

[2] Budapest,Department of Computer Science

[3] Technical University of Budapest,undefined

来源：

Annals of Operations Research | 2001年 / 101卷

关键词：

Density Matrix; Analytic Hierarchy Process; Characteristic Polynomial; Comparison Matrix; Output Analysis;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

This paper deals with data perturbations of pairwise comparison matrices (PCM). Transitive and symmetrically reciprocal (SR) matrices are defined. Characteristic polynomials and spectral properties of certain SR perturbations of transitive matrices are presented. The principal eigenvector components of some of these PCMs are given in explicit form. Results are applied to PCMs occurring in various fields of interest, such as in the analytic hierarchy process (AHP) to the paired comparison matrix entries of which are positive numbers, in the dynamic input–output analysis to the matrix of economic growth elements of which might become both positive and negative and in vehicle system dynamics to the input spectral density matrix whose entries are complex numbers.

引用

页码：401 / 425

页数：24

共 19 条

[1] Ding J.(2001)On the spectrum and pseudoinverse of a special bordered matrix Linear Algebra and its Applications 333 11-20
[2] Pye W.C.(1973)The description of road surface roughness Journal of Sound Vibrations 26 175-183
[3] Dodds C.J.(1981)On eigenvectors and adjoints of modified matrices Linear and Multilinear Algebra 10 235-247
[4] Robson J.D.(1999)Transitive matrices and their applications Linear Algebra and its Applications 302–303 423-433
[5] Elsner L.(1977)A scaling method for priorities in hierarchical structures Journal of Math. Psychology 15 234-281
[6] Rózsa P.(1986)Axiomatic foundation of the analytic hierarchy process Management Sci. 32 841-855
[7] Farkas A.(1987)The analytic hierarchy process–what it is and how it is used Mathematical Modeling 9 161-176
[8] Rózsa P.(1949)Adjustment of an inverse matrix corresponding to changes in a given column or a given row of the original matrix Ann. Math. Statist. 21 124-127
[9] Stubnya E.(1953)A balanced growth under constant returns to scale Econometrica 21 172-186
[10] Saaty T.L.(1986)Saaty's consistency analysis: an application to problems in static and dynamic input–output models Socio–Economic Planning Sciences 20 173-180

← 1 2 →