Since fuzzy numbers represent vague numeric values, they may overlap with each other. So, the comparison between fuzzy numbers may be vague. For this reason, in a set of fuzzy numbers, the rank of a fuzzy number and the k-th largest fuzzy number are vague. In this paper, to determine the rank of a fuzzy number and the k-th largest fuzzy number in a set of fuzzy numbers, a fuzzy set based method is proposed. The proposed method uses a given greater-than relation defined on the set of fuzzy numbers. The rank of a fuzzy number is described with a fuzzy set of the ranks that the fuzzy number can take, and the k-th largest fuzzy number with a fuzzy set of fuzzy numbers which can be k-th ranked.
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