Risk assessment takes place depending on the expertise and subjective linguistic assessments of experts. Expert judgements are collected via a questionnaire or an interview including qualitative data. Pessimistic or optimistic status of experts can affect their perceptions on risk. Furthermore, expert judgments are affected by questions' structure based on whether it is a positive type question (e.g., 'What is the occurrence probability of the accident?) or a negative type question (e.g., 'What is the non-occurrence probability of the accident?). All of these cases create uncertainties in the risk assessment process. For this reason, there are various studies using fuzzy risk analysis models to address these uncertainties in risk assessment. However, there is not any risk assessment tool that considers the uncertainties caused by the factors mentioned above, simultaneously. Therefore, in this paper, we introduce the concept of decomposed fuzzy sets (DFS) to model human thoughts and perceptions in a more realistic and detailed way through optimistic and pessimistic membership functions. We present the basic operations on decomposed fuzzy sets and their properties. To demonstrate the utility of the proposed method, the method is applied to operational risk analysis in business processes. The data used in the application are collected from the managerial board of a construction company. The application results and advantages of the proposed method are presented together with a comparative analysis.