A new method to measure the distance between fuzzy singletons (FSNs) is presented. It first fuzzifies a crisp number to a generalized trapezoidal fuzzy number (GTFN) using the Mamdani fuzzification method. It then treats an FSN as an impulse signal and transforms the FSN into a new GTFN by convoluting it with the original GTFN. In so doing, an existing distance measure for GTFNs can be used to measure distance between FSNs. It is shown that the new measure offers a desirable behavior over the Euclidean and weighted distance measures in the following sense: Under the new measure, the distance between two FSNs is larger when they are in different GTFNs, and smaller when they are in the same GTFN. The advantage of the new measure is demonstrated on a fuzzy forecasting trading system over two different real stock markets, which provides better predictions with larger profits than those obtained using the Euclidean distance measure for the same system.

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In this work we are proposing a trading system where fuzzy logic is applied not only for defining the trading rules, but also for managing the capital to invest. In fact, two fuzzy decision support systems are developed.The first one uses fuzzy logic to design the trading rules and to apply the stock market technical indicators.The second one enhances this fuzzy trading system adding a fuzzy strategy to manage the capital to trade.Additionally, a new technical market indicator that produces short and long entry signals is introduced. It is based on the MACD (Moving Average Convergence Divergence) indicator. Its parameters have been optimized by genetic algorithms. The proposals are compared to a classical non-fuzzy version of the proposed trading systems and to the Buy-and-Hold strategy. Results favor our fuzzy trading system in the two markets considered, NASDAQ100 and EUROSTOXX. Conclusions suggest that the use of fuzzy logic for capital management is promising and deserves further exploration.