A method for describing the rank of a fuzzy number and the k-th largest fuzzy number with fuzzy sets

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.