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Unconstrained human-hand motions that consist grasp motions and in-hand manipulations lead to a fundamental challenge that many algorithms have to face in both theoretical and practical development, mainly due to the complexity and dexterity of the human hand. There is no effective solution reported to recognize in-hand manipulations, although recognition algorithms have been proposed to recognize grasp motions in constrained scenarios. This paper proposes a novel unified fuzzy framework of a set of recognition algorithms: time clustering, fuzzy active axis Gaussian mixture mode, and fuzzy empirical copula, from numerical clustering to data dependence structure in the context of optimally real-time human-hand motion recognition. Time clustering is a fuzzy time-modeling approach that is based on fuzzy clustering and Takagi--Sugeno modeling with a numerical value as output. The fuzzy active axis Gaussian mixture model effectively extract abstract Gaussian pattern to represent components of hand gestures with a fast convergence. A fuzzy empirical copula utilizes the dependence structure among the finger joint angles to recognize the motion type. The proposed algorithms have been evaluated on a wide range of scenarios of human-hand recognition: 1) datasets that include 13 grasps and ten in-hand manipulations; 2) single subject and multiple subjects; and 3) varying training samples. The experimental results have demonstrated that the proposed framework outperforms the hidden Markov model (HMM) and Gaussian mixture model in terms of both effectiveness and efficiency criteria.