نکاتی پیرامون رویکردی جدید برای اشتقاق وزن با استفاده از تحلیل پوششی داده ها در فرآیند تحلیل سلسله مراتبی

DEAHP as a weight derivation procedure for analytic hierarchy process (AHP) has been found suffering from some significant drawbacks. Recently, Mirhedayatian and Saen (2011) [5] proposed a new procedure entitled Revised DEAHP for AHP weight derivation [S.M. Mirhedayatian, R.F. Saen, A new approach for weight derivation using data envelopment analysis in the analytic hierarchy process, Journal of the Operational Research Society 62 (2011) 1585–1595]. This paper provides a detailed note to reveal that (1) the Revised DEAHP cannot derive true weights from perfectly consistent pairwise comparison matrices, (2) it may produce irrational weights for inconsistent pairwise comparison matrices, (3) it still suffers from rank reversal problem when an efficient decision criterion or alternative is added or removed, (4) the use of the super-efficiency model in data envelopment analysis (DEA) for AHP weight derivation is redundant and meaningless when there exist multiple decision criteria or alternatives that are efficient in a pairwise comparison matrix, and (5) it may produce a completely reversed ranking that is totally opposite to the rank obtained by the eigenvector method in the case of hierarchical structures, leading to a wrong decision being made.

How to derive priorities from pairwise comparison matrices has been being an important research topic in the analytic hierarchy process (AHP) and has been extensively investigated. Quite a number of approaches have been suggested and DEAHP is one of them, which was proposed by Ramanathan [1]. Such a method, however, has been found suffering from some significant drawbacks such as producing irrational weights for inconsistent pairwise comparison matrices. Detailed analyses and theoretical improvements can be found in [2], [3] and [4]. Recently, Mirhedayatian and Saen [5] also analyzed the drawbacks of DEAHP that had been analyzed by Wang and Chin [2] and Wang et al. [3] and [4] and proposed a new procedure which they called Revised DEAHP for AHP weight derivation. Instead of the use of the CCR model [6] for AHP weight derivation, the Revised DEAHP applies the super-efficiency model [7] in data envelopment analysis (DEA) to improve the discriminating power of the DEAHP. In this paper, we provide a detailed note to illustrate with numerical examples the significant drawbacks that the Revised DEAHP suffers from. The remainder of the paper is organized as follows. Section 2 briefly reviews the Revised DEAHP procedure. Section 3 examines the drawbacks that the Revised DEAHP suffers from. Section 4 concludes the paper with a brief summary.

The use of DEA models for AHP weight derivation has become a new direction of AHP research, but not every DEA model can be used for AHP weight derivation. In this paper, we have provided a detailed note to illustrate the significant drawbacks suffered from by the Revised DEAHP, a recently proposed procedure by Mirhedayatian and Saen [5] for AHP weight derivation. Our illustrations have revealed that (1) the Revised DEAHP cannot derive true weights from perfectly consistent pairwise comparison matrices, (2) the Revised DEAHP may produce irrational weights for inconsistent pairwise comparison matrices, (3) the Revised DEAHP suffers from the rank reversal problem when an efficient decision criterion or alternative is added or removed, (4) the use of super-efficiency model in DEA for AHP weight derivation is redundant and meaningless when there exists multiple decision criteria or alternatives in a pairwise comparison matrix to be efficient, and (5) the Revised DEAHP may produce a completely reversed ranking that is totally opposite to the rank obtained by the eigenvector method in the case of hierarchical structures, leading to a wrong decision being made. These drawbacks clearly show that the use of the Revised DEAHP for AHP weight derivation is inappropriate. There is no guarantee that the Revised DEAHP can produce logical weights and correct decision conclusions. Its applications should be very cautious. Finally, we point out that as a competing approach of the AHP, the primitive cognitive network process (P-CNP) developed by Yuen [9], [10] and [11] has also been integrated with data envelopment analysis. Interested readers may refer to Yuen [12] for details.