To provide timely and appropriate assistance, robots must have the capability of proactively understanding a user's personal needs, the so-called human intention inference. In human-human interaction, humans have a natural and implicit way to infer others' intentions by selecting correlated context features and interpreting these features based on their life experience. However, robots do not have this capability and it is not realistic to build an explicit formula to associate human intentions with context. In this article, a novel fuzzy context-specific intention inference method is developed for human-like implicit human intention inference. With a fuzzy manner, context features are converted into discrete context statuses, which are similar to human subjective feelings. An intention-centered common sense database is developed consisting of correlated fuzzy context statuses, object affordances, and their relationship with human intentions. With this database, a Fuzzy Naïve Bayesian Network algorithm is adopted for implicit intention inference. Home scenario results validated the fuzzy context-specific intention inference methods reliability and lab scenario results validated the fuzzy context-specific intention inference methods effectiveness and robustness. This work is expected to develop intuitive and effective human-robot interaction, consequently enhancing the adoption of assistive technologies and improving the independence of the disabled and elderly in activities of daily living.