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The main purpose of this paper is to label one face to which it refers using a commonly accepted concept or linguistic term that corresponds to a given face class. Therefore, a facial semantic description method based on the axiomatic fuzzy set (AFS) theory is proposed. Firstly, the facial geometric features are defined based on the landmarks, such as distance features, angle features and scale features, etc. And then the salient features are selected via AFS feature selection method, and the fuzzy linguistic terms are defined the selected features. Thirdly, the facial descriptions which can characterize the salient characteristics are extracted via a clustering scheme in the framework of AFS theory. Multiple experiments are done on Chinese ethnic face database including <italic>Korean</italic>, <italic>Uyghur</italic> and <italic>Zhuang</italic>. The experimental results demonstrate that AFS feature selection can obtain higher accuracies via AFS clustering algorithm for each ethnic group than that via mRMR. Furthermore, compared with <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-means, FCM and Minmax <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-means, AFS clustering algorithm obtains the highest accuracies for each ethnic group, which verifies the efficacy of the proposed semantic extractor. Consequently, one comparative experimental results verify the consistency between the extracted semantic description method and the facial physical characteristics in physical anthropology. Also the facial semantics would be very useful to further describe some facial action units or facial expressions, which can be further used for affection analysis of images as well as semi-automatic action unit/facial expression annotation.

Notice of Retraction: Interpretable Facial Semantic Extractor Based on Axiomatic Fuzzy Set