Neutrosophic extended triplet group is a new algebra structure and is different from the classical group. In this paper, the notion of generalized neutrosophic extended triplet group is proposed and some properties are discussed. In particular, the following conclusions are strictly proved: (1) an algebraic system is a generalized neutrosophic extended triplet group if and only if it is a quasi-completely regular semigroup; (2) an algebraic system is a weak commutative generalized neutrosophic extended triplet group if and only if it is a quasi-Clifford semigroup; (3) for each $n\in Z^{+},n\ge 2,(Z_n,\otimes )$ is a commutative generalized neutrosophic extended triplet group; (4) for each $n\in Z^{+},n\ge 2,(Z_n,\otimes )$ is a commutative neutrosophic extended triplet group if and only if $n=p_1{p}_2\cdots p_m$ , i.e., the factorization of n has only single factor.

With the rapid development of the Internet, there are a large number of high-dimensional multi-label data to be processed in real life. To save resources and time, semi-supervised multi-label feature selection, as a dimension reduction method, has been widely used in many machine learning and data mining. In this paper, we design a new semi-supervised multi-label feature selection algorithm. First, we construct an initial similarity matrix with supervised information by considering the similarity between labels, so as to learn a more ideal similarity matrix, which can better guide feature selection. By combining latent representation with semi-supervised information, a more ideal pseudo-label matrix is learned. Second, the local manifold structure of the original data space is preserved by the manifold regularization term based on the graph. Finally, an effective alternating iterative updating algorithm is applied to optimize the proposed model, and the experimental results on several datasets prove the effectiveness of the approach.