In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition; that is to say, an element either belongs or does not belong to the set. In contrast, fuzzy sets theory are sets whose elements have degrees of membership.
These steps apply fuzzy logic techniques for developing a causal model that relates the risk to its key drivers or indicators. Then, the causal model is then used to develop a distribution of losses based on expectations for the levels of its key drivers.
- Specify Key Risk Indicators. For each top risk, several key risk indicators (KRIs) are specified.
- Calibrate Fuzzy. Linguistic descriptors such as High, Low, Medium, Small, Large, for example, are assigned to a range of values for each KRI and the loss amount. These descriptors will form the basis for capturing expert input on the impact of KRIs on the loss amount.
- Specify Impact of KRIs on Loss Amount. Having specified the risk and its KRIs, the logical next step is to specify how the loss amount varies as a function of the KRIs. Experts provide fuzzy rules in the form of “if … then” statements that relate loss amounts to various levels of KRIs based on their knowledge and experience.
- Calculate Expected Loss Amount. Since the fuzzy rules cover all possible combinations of KRI levels, the estimated loss amount can be calculated for the current levels of each KRI. A fuzzy calculator applies the math based on the fuzzy rules to generate the expected loss.
- Calculate Distribution of Losses. A probability distribution of expected losses next year can be derived by representing the KRIs as a probability distribution of their levels expected next year.