Pairs mining targets to mine pairs relationship between entities such as between stocks and markets in financial data mining. It has emerged as a kind of promising data mining applications. Due to practical complexities in the real-world pairs mining such as mining high dimensional data and considering user preference, it is challenging to mine pairs of interest to traders in business situations. This paper presents fuzzy genetic algorithms to deal with these issues. We introduce a fuzzy genetic algorithm framework to mine pairs relationship, and propose strategies for the fuzzy aggregation and ranking of identified pairs to generate final optimum pairs for decision making. The proposed approaches are illustrated through mining stock pairs and stocktrading rule pairs in stock market. The performance shows that the proposed approach is promising for mining pairs helpful for real trading decision making.