In this paper, with respect to reviewing and comparing existing social networks’ datasets, we introduce SNEFL dataset: the first social network dataset that includes the level of users’ likes (fuzzy like) data in addition to the likes between users. With users’ privacy in mind, the data has been collected from a social network. It includes several additional features including age, gender, marital status, height, weight, educational level and religiosity of the users. We have described its structure, analysed its features and evaluated its advantages in comparison with other social network datasets. On top of that, using unique feature of SNEFL dataset (fuzzy like) for the first time a rule-based algorithm has been developed to detect involuntary celibates (Incels) in social networks. Despite Incels activities in online social networks, until now no study on computer science has been performed to identify them. This study is the first step to address this challenge that society is facing today. Experimental results show that the accuracy of the proposed algorithm in identifying Incels among all social network users is 23.21% and among users who have fuzzy like data is 68.75%. In addition to the Incel detection, SNEFL dataset can be used by researchers in different fields to produce more accurate results. Some study areas that SNEFL dataset can be used in are network analysis, frequent pattern mining, classification and clustering.