"Ranking Irregularities When Evaluating Alternatives by Using Some ELECTRE Methods"
February 2008, Vol. 36, No. 1, pp. 45-63.
Xiaoting Wang and Evangelos Triantaphyllou
The ELECTRE II and III methods enjoy a wide acceptance in solving multi-criteria decision-making (MCDM) problems.
Research results in this paper reveal that there are some compelling reasons to doubt the correctness of the
proposed rankings when the ELECTRE II and III methods are used. In a typical test we first used these methods
to determine the best alternative for a given MCDM problem. Next we randomly replaced a non-optimal alternative
by a worse one and repeated the calculations without changing any of the other data. Our computational tests revealed
that sometimes the ELECTRE II and III methods might change the indication of the best alternative. We treat such phenomena
as rank reversals. Although such ranking irregularities are well known for the additive variants of the AHP method, it is the
very first time that they are reported to occur when the ELECTRE methods are used. These two methods are also evaluated in
terms of two other ranking tests and they failed them as well. Two real-life cases are described to demonstrate the
occurrence of rank reversals with the ELECTRE II and III methods. Based on the three test criteria presented in this paper,
some computational experiments on randomly generated decision problems were executed to test the performance
of the ELECTRE II and III methods and an examination of some real-life case studies are also discussed. The results of
these examinations show that the rates of the three types of ranking irregularities were rather significant in both the
simulated decision problems and the real-life cases studied in this paper.
Multi-criteria decision-making, ranking irregularities, ELECTRE methods,
the Analytic Hierarchy Process (AHP), multiplicative AHP.