Testing the efficiency of two pairwise comparison methods in discrete multiple criteria problems

We test the efficiency of two pairwise comparison methods. The methods studied are Salminen''s piecewise linear prospect theory (PLP) method and the convex cone method by Korhonen, Wallenius, and Zionts (KWZ). The PLP method is based on a piecewise linear difference function. The KWZ method assumes a quasi-concave utility or value function. These methods are tested using randomly generated data sets with 50, 100, 150, and 200 alternatives and from 2 up to 6 criteria. The DM''s preference statements are simulated using linear, quadratic, and Chebycheff value functions and piecewise linear difference functions. Both methods lose their efficiency very rapidly with increasing number of criteria. Our results indicate that pairwise comparison methods are not as efficient as reported in literature.

[1]  Jyrki Wallenius,et al.  A Progressive Algorithm for Modeling and Solving Multiple-Criteria Decision Problems , 1986, Oper. Res..

[2]  Jyrki Wallenius,et al.  Further Developments and Tests of a Progressive Algorithm for Multiple Criteria Decision Making , 1993, Oper. Res..

[3]  M. Murat Koksalan,et al.  An Interactive Approach for Choosing the Best of a Set of Alternatives , 1992 .

[4]  Behnam Malakooti.  Theories and an exact interactive paired-comparison approach for discrete multiple-criteria problems , 1989, IEEE Trans. Syst. Man Cybern..

[5]  P. Salminen.  Solving the discrete multiple criteria problem using linear prospect theory , 1994 .

[6]  Risto Lahdelma,et al.  SMAA - Stochastic multiobjective acceptability analysis , 1998, Eur. J. Oper. Res..

[7]  S. Zionts,et al.  Solving the Discrete Multiple Criteria Problem using Convex Cones , 1984 .

[8]  S. Zionts,et al.  An approach for solving discrete alternative multiple criteria problems involving ordinal criteria , 1988 .

[9]  Murat Köksalan,et al.  Interactive Approaches for Discrete Alternative Multiple Criteria Decision Making with Monotone Utility Functions , 1995 .

[10]  Stanley Zionts,et al.  A multiple criteria method for choosing among discrete alternatives , 1981 .

[11]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[12]  Murat Köksalan,et al.  An approach to and computational results on testing the form of a decision maker's utility function , 1995 .

[13]  Srinivas Y. Prasad,et al.  Use of Convex Cones in Interactive Multiple Objective Decision Making , 1997 .

[14]  Pekka Korhonen,et al.  Testing the Form of a Decision-maker's Multiattribute Value Function Based on Pairwise Preference Information , 1989 .