Social media has replaced traditional journalism, such as television and newspapers, by a large proportion. Social media data presents an incredible opportunity for governments and organizations to understand the public's response to a news event, which is critical for government organizations to make informed decisions. News events are made up of a series of related sub-events. These sub-events determine the flow and dynamics of the entire news event. Hence, monitoring the public's response to each sub-event is crucial. This work proposes a framework to classify microblogs that discuss news sub-events into eight dimensions of emotion: Happy, Sad, Fear, Anger, Cynical, Neutral, Positive and Negative. This work introduces a cynical emotion that attempts to catch skepticism and sarcastic emotions, which are highly common in news-based events. Not limited to news events and microblogs, this framework can be utilized on any public response monitoring system without much changes. The proposed framework employs a bi-layered composite fuzzy mechanism. The emotions are represented as fuzzy sets. The fuzzy membership score of a microblog towards each fuzzy set is generated by integrating neural-network-based pre-trained word vector similarity, thesaurus-based similarity, and linguistic hedge information for each word. Fuzzy inference is then employed to identify the predominant emotion expressed in a microblog. This work is compared against state-of-the-art BERT models and demonstrates a remarkably high level of precision.