Fuzzy Multi-attribute Grey Relational Analysis Using DEA and AHP

This research applies the method of grey relational analysis (GRA) for multiple attribute decision making (MADM) problems in which the attribute weights are completely unknown and attribute values take the form of fuzzy numbers. In order to obtain the attribute weights, this research proposes an integrated data envelopment analysis (DEA) and analytic hierarchy process (AHP) approach. According to this, we define two sets of weights in a domain of grey relational loss, i.e., a reduction in grey relational grade, between each alternative and the ideal alternative. The first set represents the weights of attributes with the minimal grey relational loss in DEA. The second set represents the priority weights of attributes, bounded by AHP, with the maximal grey relational loss. Using a parametric goal programming model, we explore the various sets of weights in a defined domain of grey relational loss. This may result in various ranking positions for each alternative in comparison to the other alternatives. An illustrated example of a nuclear waste dump site selection is used to highlight the usefulness of the proposed approach.