Images are always contaminated by noise, increasing uncertainty. Fuzzy set (FS) theory is a useful tool for dealing with uncertainty in images. When comparing with the FS, an intuitionistic fuzzy set (IFS) can better describe the blurred characteristic in images due to the membership, nonmembership, and hesitation degrees. However, when applied to an image segmentation, the IFS cannot completely overcome the influence of noise. With the aim of performing noisy image segmentation under several criteria, this paper defines a noise robust IFS (NR-IFS) for an image and then presents a novel noise robust multiobjective evolutionary intuitionistic fuzzy clustering algorithm (NR-MOEIFC). A majority dominated suppressed similarity measure using the neighborhood statistics and the competitive learning is proposed to obtain the NR-IFS representation for the image corrupted by noise. Then, the NR-IFS is fully used to motivate the whole process of multiobjective evolutionary clustering: first, computing a three-parameter intuitionistic fuzzy distance measure; second, constructing intuitionistic fuzzy fitness functions; third, designing a nonuniform intuitionistic fuzzy mutation operator; and forth, defining an intuitionistic fuzzy cluster validity index to select the optimal solution from the final nondominated solution set. The histogram statistics of NR-IFS are adopted in the NR-MOEIFC to greatly reduce the computational complexity. Experimental results on Berkeley and real magnetic resonance images reveal that the NR-MOEIFC behaves well in noise robustness and segmentation performance while requiring a low time cost.

中文翻译：

---

基于直觉模糊信息的噪声鲁棒多目标进化聚类图像分割

图像总是被噪音污染，增加了不确定性。模糊集 (FS) 理论是处理图像不确定性的有用工具。与FS相比，直觉模糊集（IFS）可以更好地描述图像中由于隶属度、非隶属度和犹豫度而产生的模糊特征。然而，当应用于图像分割时，IFS 不能完全克服噪声的影响。为了在多个标准下执行噪声图像分割，本文定义了图像的噪声鲁棒 IFS（NR-IFS），然后提出了一种新的噪声鲁棒多目标进化直觉模糊聚类算法（NR-MOEIFC）。提出了使用邻域统计和竞争学习的多数支配抑制相似性度量，以获得被噪声破坏的图像的 NR-IFS 表示。然后，充分利用NR-IFS来激发多目标进化聚类的整个过程：首先，计算三参数直觉模糊距离测度；第二，构造直觉模糊适应度函数；第三，设计非均匀直觉模糊变异算子；第四，定义一个直觉模糊聚类有效性指数，从最终的非支配解集中选择最优解。NR-MOEIFC采用了NR-IFS的直方图统计，大大降低了计算复杂度。