This study aims to define the relationship between risk degrees and risk indexes on different functional structures with the assumption that risk degrees may not always present a linear relationship with the risk indexes. In this way, risk indexes suitable for expert evaluation of working conditions and computed using three different membership functions are determined. Among the membership functions used, one is preferred as linear and the others are preferred as non-linear. Additionally, a new fuzzy risk assessment (RA) algorithm is developed using these three membership functions. With this new fuzzy RA algorithm, a more flexible and precise process becomes available, while information loss during the determination of the risk index of danger sources is prevented. As a result, non-linear increasing membership function is selected as most suitable for the expression of the relationship between risk degrees and risk indexes.