The fuzzy rough set theory is considered an effective tool for attribute reduction in decision information tables containing continuous numerical attributes. Nevertheless, algorithms based on this approach perform poorly when handling noisy and inconsistent data. Additionally, these algorithms have high computational complexity and storage requirements for decision information tables with a large number of dimensions. To address this issue, we initially present a new extension called the fuzzy neighborhood rough set. This model is effective in limiting the influence of noisy objects in fuzzy neighborhood information granules and narrowing the computational space. Based on the advantages of the model, we continue to develop a new measure to evaluate the classification ability of fuzzy neighborhood information granules. Finally, we define a new reduct and design a hybrid approach algorithm to extract an optimal subset from the decision table. Experimental results have demonstrated the effectiveness of the proposed algorithm compared to several methods based on the fuzzy rough set approach.