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 measures for the same system.

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基于卷积的模糊单调距离测度及其在模式识别中的应用

提出了一种测量模糊单调之间的距离的新方法。它首先使用Mamdani模糊化方法将清脆数模糊化为广义梯形模糊数（GTFN）。然后，它将FSN视为脉冲信号，然后通过将其与原始GTFN卷积而将其转换为新的GTFN。这样做，可以将用于GTFN的现有距离量度用于测量FSN之间的距离。结果表明，新度量在以下意义上比欧几里得度量和加权距离度量具有理想的行为：在新度量下，两个FSN在不同GTFN中时的距离较大，而在相同GTFN中时则较小。 GTFN。在两个不同的实际股票市场上的模糊预测交易系统上证明了新措施的优势，