Abstract The Average Cumulative representation of fuzzy intervals is connected with the possibility theory in the sense that the possibility and necessity functions are substituted by a pair of non decreasing functions defined as the positive and negative variations in the Jordan decomposition of a membership function. In this paper we motivate the crucial role of ACF in determining the membership function from experimental data; some examples and simulations are shown to state the robustness of the proposed construction.

中文翻译：

---

用经验分位数函数逼近隶属函数

摘要 模糊区间的平均累积表示与可能性理论相联系，因为可能性函数和必要性函数被一对定义为隶属函数的 Jordan 分解中的正负变化的非递减函数所替代。在本文中，我们激发了 ACF 在根据实验数据确定隶属函数方面的关键作用；显示了一些示例和模拟来说明所提议结构的稳健性。