Abstract Alpha-cut representation of fuzzy sets has been used as a basis for fuzzy numbers ranking in some applications but rarely used for defuzzification of rule-based systems or fuzzy controllers. Moreover, such alpha-cut defuzzification (called ACD here) is not yet formally linked to the membership function (MF) or to the common MF-based defuzzification methods, namely the centroid. The ACD can be considered as a generalisation of the similar algorithms in fuzzy numbers to any fuzzy set. A close-form formula for ACD is developed that involves both MF and its derivative, which shows that ACD reflects both static and dynamic aspects of a fuzzy set. Moreover, formal links between ACD and some MF-based defuzzification methods are shown. Through two groups of experiments, the utility of the new method is compared with centroid defuzzification. Particularly, we examined how the ACD significantly outperforms the centroid for noisy time-series prediction. Finally, the computation complexity of ACD is shown to be about the same as the centroid method, for convex fuzzy sets. Our tests suggest that ACD can be considered as a viable alternative defuzzification method for fuzzy system designers.

中文翻译：

---

在基于规则的系统中用于去模糊化的 Alpha-cut 表示

摘要 模糊集的 Alpha-cut 表示在一些应用中被用作模糊数排序的基础，但很少用于基于规则的系统或模糊控制器的去模糊化。此外，这种 alpha-cut 去模糊化（这里称为 ACD）还没有正式链接到隶属函数（MF）或常见的基于 MF 的去模糊化方法，即质心。ACD 可以被认为是模糊数中类似算法对任何模糊集的推广。开发了 ACD 的闭式公式，它涉及 MF 及其导数，这表明 ACD 反映了模糊集的静态和动态方面。此外，还显示了 ACD 和一些基于 MF 的去模糊化方法之间的正式联系。通过两组实验，将新方法的效用与质心去模糊化进行了比较。特别是，我们研究了 ACD 如何在噪声时间序列预测方面显着优于质心。最后，对于凸模糊集，ACD 的计算复杂度与质心方法大致相同。我们的测试表明，ACD 可以被视为模糊系统设计者的一种可行的替代去模糊化方法。