Ranking range model in multiple attribute decision making: A comparison of selected methods

Multiple attribute decision making (MADM) approaches have been investigated extensively for ranking the alternatives related to multiple attributes. In most existing MADM approaches, attribute weights play a key role due to the fact that the ranking of alternatives may changes with attribute weights vector. Ranking range can be used to measure the lower and upper bounds of all possible rankings of alternatives when attribute weights are varying. In the paper, we investigate the ranking range for the selected seven popular MADM approaches: Weighted averaging (WA), weighted geometric averaging (WGA), ordered weighted averaging (OWA), ordered weighted geometric averaging (OWGA), TOPSIS, PROMETHEE and ELECTRE. Through determining the ranking ranges of alternatives, associated with attribute weights, in the selected seven approaches, we present several desirable properties of the ranking range. Then, we design the simulation experiments with either random or real data to compare the ranking range for selected seven MADM approaches. Interestingly, the experiment results clearly show that TOPSIS>ELECTRE>PROMETHEE(similar to)WA>WGA>OWA>OWGA in the average sense, where '>' denotes the larger ranking range, and '(similar to)' denotes no difference in the ranking range. A larger ranking range means an easier to manipulate the ranking of alternatives, and also means a worse robustness of a MADM approach.

Automated summary

The paper investigates the ranking range of seven popular MADM approaches, presents desirable properties of the ranking range, and compares the ranking range through simulation experiments with either random or real data. The experiment results clearly show that TOPSIS>ELECTRE>PROMETHEE(similar to)WA>WGA>OWA>OWGA in the average sense. A larger ranking range means it is easier to manipulate the ranking of alternatives, but also indicates worse robustness of a MADM approach.