Trading strategies can be divided into two categories, i.e., those with momentum characteristic and those that appear contrarian. The characteristics of trading strategies have been widely studied; however, there has been relatively little work on the characteristics of stocks. Furthermore, there is no standard approach to the classification of stocks in terms of momentum and contrarian. This article presents a fuzzy momentum contrarian uncertain characteristic system for the classification and quantification of stock characteristics. Random trading, stop-loss, and take-profit mechanisms are first used to identify characteristics, and then, a novel profitability index with a type-2 fuzzy set module is used to quantify them. In the experiments, 41 stocks on the Taiwan 50 index were deemed suitable for momentum strategies, whereas nine stocks were deemed suitable for contrarian strategies. An uphill relationship between profitability index and trading performance is observed, which produced correlation coefficients of 0.148–0.539 and a classification accuracy of 52.0–60.0%. However, the proposed system greatly improved classification performance, resulting in correlation coefficients of 0.572–0.722 with an accuracy of 63.6–84.5%. In the real-world application, the proposed system outperforms the benchmark among all datasets and increases the profitability by 1.5 times on the Taiwan 50 dataset. These results clearly demonstrate the efficiency of the proposed system in the quantification and classification of stocks suited to momentum- and contrarian-type trading strategies and also in the real-world applications.