Materials selection involves a multiattribute decision making whereby materials engineers choose optimal materials among more than two alternatives on the basis of more than two attributes.
Technique for order preference by similarity to ideal solution (TOPSIS) is a well-known multi attribute decision making (MADM) method and it has been widely used in materials selection.
It is based on the principle that the best alternative must have the shortest distance from the positive ideal solution (PIS) and the farthest distance from the negative ideal solution (NIS).
However, the TOPSIS has a non-negligible drawback: rank reversal. It refers to the change in the ranks of the alternatives when one alternative is removed from or added to the list of alternatives.
Although many works have been conducted, the MADM methods such as TOPSIS still suffer from rank reversal, and it is necessary to give further study to perfectly overcome it.
According to the traditional TOPSIS, when the composition of the alternatives is changed, the normalized decision-matrix is changed. The PIS and the NIS are determined from the maximum or minimum value among the attribute values of the present alternatives. When the alternative with maximum or minimum value is removed or added, the PIS and the NIS are changed. Hence, the distances from the alternatives to the PIS and the NIS are changed, and the relative closeness values are also changed, and therefore, rank reversal may be generated.
To overcome the rank reversal, the normalization method and the determination method of the PIS and the NIS should be irrelevant to the composition of alternatives. Therefore, there is a need to improve the normalization method and the determination method of the PIS and NIS.
The normalization of decision-matrix by the linear max-min normalization method can solve this problem.
The application of the improved TOPSIS without rank reversal to select the best absorbent layer material for thin film solar cells (TFSCs) showed that it could fully overcome rank reversal and that it could be applied to many real materials selection problems in practice.
You can find more information about this in “Materials selection method using improved TOPSIS without rank reversal based on linear max-min normalization with absolute maximum and minimum values” presented by Yang Won Chol, a researcher at the Faculty of Materials Science and Technology, to the SCI Journal “Materials Research Express”.