In collaborative filtering recommendations, part of studies mainly focus on quantitatively learning user preferences based on explicit rating information. However, due to the uncertainty and complexity of decision-making scenarios, user preferences usually express ambiguity and diversity. Therefore, to fully capture user preferences from both qualitative and quantitative perspectives and improve the accuracy and reliability of recommendations, we propose a novel fuzzy neural collaborative filtering for recommender systems. Firstly, we qualitatively divide user preferences into fine-grained categories based on picture fuzzy set and transform the rating matrix into four preference degree matrices. Then, we employ Bernoulli matrix factorization to independently learn preference features of each submatrix to obtain picture fuzzy numbers. To enhance the adaptability of picture fuzzy set in recommender systems, we design an improved scoring function based on picture fuzzy number to effectively distinguish differences in user preference levels. In addition, we use a simple deep neural framework to quantitatively extract global preferences of users and fuse it with fine-grained preferences of users to thoroughly predict user preferences. Experiments on four benchmark datasets show that the proposed model outperforms other comparison methods in terms of recommendation accuracy. Compared with the closest competitor method, our model has the highest improvements of 5.08% and 4.04% in the metrics HR@10 and NDCG@10, respectively.