A MATHEMATICAL TREATMENT OF INCONSISTENCY IN THE ANALYTIC HIERARCHY PROCESS

被引：23

作者：

DADKHAH, KM ^{[1
]}

ZAHEDI, F ^{[1
]}

机构：

[1] UNIV MASSACHUSETTS,DEPT MANAGEMENT SCI,BOSTON,MA 02125

来源：

MATHEMATICAL AND COMPUTER MODELLING | 1993年 / 17卷 / 4-5期

关键词：

D O I：

10.1016/0895-7177(93)90180-7

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

This paper presents a simple mathematical exposition foor some of theorems regarding the treatment of inconsistency in AHP. It provides a rigorous mathematical proof that the largest eigenvalue reaches its global minimum when the input matrix is consistent. Furthermore, the paper provides an algorithm for moving towards consistency and shows mathematically why the algorithm works.

引用

页码：111 / 122

页数：12

共 25 条

[1]

[Anonymous], 2019, MATRIX DIFFERENTIAL, DOI DOI 10.1002/9781119541219.CH5

[2] APPROACHES TO CONSISTENCY ADJUSTMENT [J].

BLANKMEYER, E .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1987, 54 (03) :479-488

[3]

Brazilai J., 1987, OPERATION RES LETT, V6, P131

[4] COMPARISON OF 2 METHODS FOR DETERMINING THE WEIGHTS OF BELONGING TO FUZZY-SETS [J].

CHU, ATW ;

KALABA, RE ;

SPINGARN, K .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1979, 27 (04) :531-538

[5]

CRAWFORD GB, 1985, R25721AF RAND CORP R

[6] THE APPROACH TO CONSISTENCY IN THE ANALYTIC HIERARCHY PROCESS [J].

DETURCK, DM .

MATHEMATICAL MODELLING, 1987, 9 (3-5) :345-352

[7]

ELSNER L, 1986, LINEAR ALGEBRA APPL, V80, P200

[8] THE THEORY OF RATIO SCALE ESTIMATION - SAATY ANALYTIC HIERARCHY PROCESS [J].

HARKER, PT ;

VARGAS, LG .

MANAGEMENT SCIENCE, 1987, 33 (11) :1383-1403

[9] DERIVATIVES OF THE PERRON ROOT OF A POSITIVE RECIPROCAL MATRIX - WITH APPLICATION TO THE ANALYTIC HIERARCHY PROCESS [J].

HARKER, PT .

APPLIED MATHEMATICS AND COMPUTATION, 1987, 22 (2-3) :217-232

[10]

Lancaster P., 1985, THEORY MATRICES

← 1 2 3 →