Journal of Central South University

, Volume 25, Issue 5, pp 1116–1128

# Combining TOPSIS and GRA for supplier selection problem with interval numbers

Article

## Abstract

Supplier selection can be regarded as a typical multiple attribute decision-making problem. In real-world situation, the values of the alternative attributes and their weights are always being nondeterministic, and as a result of this, the values are considered interval numbers. In addition, the common approach to measure the similarity between alternatives through their distance suffers from some minor shortcomings. To address these problems, this study develops a novel hybrid decision-making method by combining the technique for order preference by similarity to an ideal solution (TOPSIS) with grey relational analysis (GRA) for supplier selection with interval numbers. By introducing the intervals theory, the extensions of Euclidean distance and grey relational grade are defined. And then a new comprehensive closeness coefficient is constituted for supplier alternatives evaluation based on the interval Euclidean distance and the interval grey relational grade, which could indicate the distance-based similarity and the shape-based similarity simultaneously. A numerical example is taken to validate the flexibility of the proposed method, and result shows that this method can tackle the uncertainty in real-world supplier selection and also help decision makers to effectively select optimal suppliers.

## Key words

supplier selection interval number grey relational analysis (GRA) technique for order preference by similarity to an ideal solution (TOPSIS)

# 区间条件下基于理想决策法与灰关联分析的供应商选择方法

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