Purpose

This study aims to propose, as the first time, the interval type-2 adaptive network-fuzzy inference system (ANFIS) structure, which is given better results compared to previously presented in the open literature. So, the ANFIS can be used effectively for training of interval type-2 fuzzy logic system (IT2FLS) parameters.

Design/methodology/approach

Karnik–Mendel algorithm (KMA) is modified to use in interval type-2 ANFIS. The modified Karnik–Mendel algorithm (M-KMA) is implemented to change the uncertain ANFIS parameters into known ones. In this way, the interval type-2 ANFIS removes uncertainties of IT2FLS. Therefore, the interval type-2 ANFIS is reduced to a simple one, i.e. less mathematical operation required. Only consequent parameters are trained, and the consequent parameters are chosen in the form of crisp.

Findings

By applying the mentioned procedure, it can be shown that interval type-2 ANFIS has generally better results compared to type-1 ANFIS. However, it was noticed that the worst results obtained in the case of interval type-2 ANFIS are equal to the best result obtained in the case of type-1 ANFIS. Therefore, users in this field can use this approach in solving nonlinear problems.

Practical implications

The interval type-2 ANFIS can be used as controller for highly nonlinear systems such as air vehicles.

Originality/value

As stated in the open literature, it is ineffective to use ANFIS for IT2FLS. In this study, the KMA is modified for IT2FLS, and it is seen that the ANFIS can be used effectively for IT2FLS.

中文翻译：

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基于改进型 Karnik-Mendel 算法的区间类型 2 ANFIS 和类型 1 ANFIS 的比较

目的

本研究旨在首次提出区间 2 型自适应网络模糊推理系统 (ANFIS) 结构，与先前在公开文献中提出的结果相比，该结构得到了更好的结果。因此，ANFIS 可以有效地用于训练区间 2 型模糊逻辑系统 (IT2FLS) 参数。

设计/方法/方法

Karnik–Mendel 算法 (KMA) 被修改为在区间类型 2 ANFIS 中使用。改进的 Karnik-Mendel 算法 (M-KMA) 用于将不确定的 ANFIS 参数更改为已知参数。这样，区间类型 2 ANFIS 消除了 IT2FLS 的不确定性。因此，区间类型 2 ANFIS 被简化为简单的，即所需的数学运算较少。只训练后续参数，并以清晰的形式选择后续参数。

发现

通过应用上述程序，可以表明，与类型 1 ANFIS 相比，区间类型 2 ANFIS 通常具有更好的结果。然而，注意到在区间类型 2 ANFIS 情况下获得的最差结果等于在类型 1 ANFIS 情况下获得的最佳结果。因此，该领域的用户可以使用这种方法来解决非线性问题。

实际影响

间隔类型 2 ANFIS 可用作高度非线性系统（如飞行器）的控制器。

原创性/价值

正如公开文献中所述，将 ANFIS 用于 IT2FLS 是无效的。在本研究中，针对 IT2FLS 修改了 KMA，可以看出 ANFIS 可以有效地用于 IT2FLS。