In this paper, new concepts such as multi-granularity soft rough sets and multi-granularity soft relative attribute reduction are introduced. Basic properties of multi-granularity soft rough approximations are presented and illustrated by examples. A multi-granularity soft decision system is constructed based on multi-granularity soft rough sets. Furthermore, an algorithm for multi-attribute decision-making problems is proposed. Finally, the validity of this method is proved by the application of the component retrieval problem.
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