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1999•Unpublished venueRequires access

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

Jee-Hyong Lee, Hyung Lee-Kwang, Keon Myung Lee

Open publisher page 1 citations

Abstract

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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What this paper is about

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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Available abstract

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.

Key concepts: Fuzzy number, Fuzzy set operations, Fuzzy classification, Mathematics, Defuzzification, Type-2 fuzzy sets and systems, Fuzzy mathematics, Fuzzy logic

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