INTERVAL WEIGHTED COMPARISON MATRICES-A REVIEW

Nowadays, interval comparison matrices (ICM) take an important role in decision making under uncertainty. So it seems that a brief review on solution methods used in ICM should be useful. In this paper, the common methods are divided into four categories that are Goal Programming Method (GPM), Linear Programming Method (LPM), Non-Linear Programming Method (NLPM) and Statistic Analysis (SA). GPM itself is divided also into three categories. This paper is a review paper and is written to introduce the mathematical methods and the most important applications of ICM in decision making techniques.

[1]  Patrick T. Harker,et al.  The Analytic hierarchy process : applications and studies , 1989 .

[2]  Bruce L. Golden,et al.  Applications of the Analytic Hierarchy Process: A Categorized, Annotated Bibliography , 1989 .

[3]  Luis G. Vargas,et al.  Preference simulation and preference programming: robustness issues in priority derivation , 1993 .

[4]  T. L. Saaty.  A Scaling Method for Priorities in Hierarchical Structures , 1977 .

[5]  Luis G. Vargas,et al.  Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios , 1984 .

[6]  Ralph E. Steuer,et al.  Multiple criteria decision making combined with finance: A categorized bibliographic study , 2003, Eur. J. Oper. Res..

[7]  S. Lipovetsky.  The synthetic hierarchy method: An optimizing approach to obtaining priorities in the AHP , 1996 .

[8]  J. Barzilai.  Deriving weights from pairwise comparison matrices , 1997 .

[9]  N. Bryson,et al.  An action learning evaluation procedure for multiple criteria decision making problems , 1997 .

[10]  Jian-Bo Yang,et al.  A two-stage logarithmic goal programming method for generating weights from interval comparison matrices , 2005, Fuzzy Sets Syst..

[11]  Ozan Çakir,et al.  Post-optimality analysis of priority vectors derived from interval comparison matrices by lexicographic goal programming , 2008, Appl. Math. Comput..

[12]  M. P. Biswal,et al.  Preference programming and inconsistent interval judgments , 1997 .

[13]  F. Downton,et al.  Introduction to Mathematical Statistics , 1959 .

[14]  Hideo Tanaka,et al.  Interval priorities in AHP by interval regression analysis , 2004, Eur. J. Oper. Res..

[15]  Yuzhong Zhang,et al.  Deriving Interval Weights from Interval Comparison Matrices based on Consistency Test , 2007 .

[16]  Stan Lipovetsky,et al.  Interval estimation of priorities in the AHP , 1999, Eur. J. Oper. Res..

[17]  Ami Arbel,et al.  Approximate articulation of preference and priority derivation , 1989 .

[18]  Jian-Bo Yang,et al.  Interval weight generation approaches based on consistency test and interval comparison matrices , 2005, Appl. Math. Comput..

[19]  Stan Lipovetsky,et al.  Robust estimation of priorities in the AHP , 2002, Eur. J. Oper. Res..

[20]  Ying-Ming Wang,et al.  A goal programming method for obtaining interval weights from an interval comparison matrix , 2007, Eur. J. Oper. Res..

[21]  Antonie Stam,et al.  On multiplicative priority rating methods for the AHP , 2003, Eur. J. Oper. Res..

[22]  R. Hämäläinen,et al.  Preference programming through approximate ratio comparisons , 1995 .

[23]  F. Lootsma.  SCALE SENSITIVITY IN THE MULTIPLICATIVE AHP AND SMART , 1993 .