A new approach for weight derivation using data envelopment analysis in the analytic hierarchy process

Abstract

Recently, some researches have been carried out in the context of using data envelopment analysis (DEA) models to generate local weights of alternatives from pairwise comparison matrices used in the analytic hierarchy process (AHP). One of these models is the DEAHP. The main drawback of the DEAHP is that it generates counter-intuitive priority vectors for inconsistent pairwise comparison matrices. To overcome the drawbacks of the DEAHP, this paper proposes a new procedure entitled Revised DEAHP, and it will be shown that this procedure generates logical weights that are consistent with the decision maker's judgements and is sensitive to changes in data of the pairwise comparison matrices. Through a numerical example, it will be shown that the Revised DEAHP not only produces correct weights for inconsistent matrices but also does not suffer from rank reversal when an irrelevant alternative is added or removed.

Keywords:

• data envelopment analysis
• analytic hierarchy process
• DEAHP
• rank reversal

Acknowledgements

The authors thank the anonymous reviewer for valuable suggestions and comments.

Notes

1 For more details, please see Appendix A.

2 According to Saaty (2000), a consistency ratio of 0.1 or less is considered acceptable.

3 Epsilon is an infinitesimal non-Archimedean value. In other words, it is a very small positive value. Here, definitions of Archimedean and infinitesimal are presented as below. Archimedean: A number series is Archimedean if, (∀x) (∀y) (∃n) (0<x<y → y<nx) well-behaved numbers are Archimedean. Take any two numbers, however far apart they are. Then there is some number that you can multiply the smaller by to give a result greater than the larger. Non-standard analysis introduces infinitesimals of which this is not true. Infinitesimal: A function or variable continuously approaching zero as a limit (a variable with a limit of zero).

4 For benefit of the readers, a model with solution for matrix A has been represented in Appendix B.