In this paper, a novel fuzzy linear assignment method is developed for multi-attribute group decision making problems. Since uncertain nature of many decision problems, the proposed method incorporates various concepts from fuzzy set theory such as fuzzy arithmetic and aggregation, fuzzy ranking and fuzzy mathematical programming into a fuzzy concordance based group decision making process. Fuzziness in the group hierarchy and quantitative type criteria are also taken into account. In order to present the validity and practicality of the proposed method, it is applied to a real life multi-criteria spare part inventory classification problem. The case study has demonstrated that the proposed method is easy to apply and able to provide effective spare parts inventory classes under uncertain environments. In addition to the practical verification by the company experts, the proposed method is also compared with some of the commonly used fuzzy multi-attribute decision making methods from the literature. According to the comparison of the results, there is an association between classes of spare parts obtained by the proposed method and the benchmarked methods. (C) 2016 Elsevier B.V. All rights reserved.