Ranking alternatives in a preferential voting system using fuzzy concepts and data envelopment analysis

In this paper, a new method for aggregating the opinions of experts in a preferential voting system is proposed. The method, which uses fuzzy concept in handling crisp data, is computationally efficient and is able to completely rank the alternatives. Through this method, the number of votes for certain rank position that each alternative receives are first grouped together to form fuzzy numbers. The nearest point to a fuzzy number concept is then used to introduce an artificial ideal alternative. Data envelopment analysis is next used to find the efficiency scores of the alternatives in a pair-wise comparison with the artificial ideal alternative. Alternatives are rank based on these efficiency scores. If the alternatives are not completely ranked, a weight restriction method also based on fuzzy concept is used on the un-discriminated alternatives until they are completely ranked. Two examples are given for illustration of the method.

► Fuzzy concepts are used even though data are crisp.
► Alternatives are ranked based on their ‘distance’ to an artificial alternative.
► ‘Distance’ is determined by the efficiency score of a pair-wise DEA model.
► Un-discriminated alternatives are further treated by a weight restriction DEA model.
► Thus, a computationally efficient and strongly discriminating method is proposed.