Predicting missing links and links that may occur in the future in social networks is an attention grabbing topic amid the social network analysts. Owing to the relationship between human-based system and social sciences in this field, granular computing can help us to model the systems more effectively. The present study aims to propose two new similarity indices, based on granular computing approach and fuzzy logic. It also presents a new hybrid model for creating synergy between various link prediction models. Results show that fuzzy system analysis, in comparison with the crisp approach, can make more effective predictions through better expression of network characteristics. The indices are tested on collaboration networks. It is found that the accuracy of predictions is significantly higher than the crisp approach. It can modify the models for computing the strength of the links and/or predicting the evolutions of the social networks.