Most existing multi-view clustering algorithms typically rely on hard or fuzzy partitioning, which makes it difficult to effectively model the uncertainty and imprecision inherent in the clustering process. In addition, multi-view data often exhibit high dimensionality and complex structures, leading to substantial computational costs during clustering. To address these issues, this paper proposes a novel multi-view clustering algorithm that integrates Nonnegative Matrix Factorization (NMF) with Weighted Evidential C-Means (WECM). Through a synergistic design at the theoretical level, the proposed method achieves a deep coupling of dimensionality reduction, credal partitioning, and view weighting, thereby improving clustering accuracy while reducing computational complexity. Specifically, NMF is first employed to obtain low-dimensional representations of each view, extracting discriminative latent features and alleviating computational burden; then, within the framework of belief function theory, a global credal partition is generated to effectively handle uncertainty caused by potential conflicts and inconsistencies among views; finally, an adaptive view weighting mechanism with Shannon entropy regularization is introduced, enabling the joint optimization of view weights, feature representations, and credal assignments. Experimental results on six real-world datasets and two large-scale datasets demonstrate that the proposed WECM-NMF algorithm outperforms several state-of-the-art multi-view clustering methods.