Data mining is the process of extracting desirable knowledge or interesting patterns from existing databases for specific purposes. Most of the previous approaches set a single minimum support threshold for all the items and identify the relationships among transactions using binary values. In real applications, different items may have different criteria to judge their importance. In the past, we proposed an algorithm for extracting appropriate multiple minimum support values, membership functions and fuzzy association rules from quantitative transactions. It used requirement satisfaction and suitability of membership functions to evaluate fitness values of chromosomes. The calculation for requirement satisfaction might take a lot of time, especially when the database to be scanned could not be totally fed into main memory. In this paper, an enhanced approach, called the fuzzy cluster-based genetic-fuzzy mining approach for items with multiple minimum supports (FCGFMMS), is thus proposed to speed up the evaluation process and keep nearly the same quality of solutions as the previous one. It divides the chromosomes in a population into several clusters by the fuzzy k-means clustering approach and evaluates each individual according to both their cluster and their own information. Experimental results also show the effectiveness and the efficiency of the proposed approach.