A fuzzy mapping framework for risk aggregation based on risk matrices

Extant research has focused upon assessing individual risks with the aid of risk matrices. Although risk aggregation is an important issue in risk management, aggregation of risks measured by risk matrices remains unresolved despite the wide usage of risk matrices. This paper proposes a framework to resolve the problem. We start from modifying the two notions of non-aggregatability of risk matrices, namely, qualitative description of inputs and non-comparability of different types of consequences. Then, we explicate the strong connection between risk matrices and fuzzy sets and propose that the transformation from risk matrices to fuzzy sets clear some confusions encountered in the aggregation process. A framework which covers membership analysis, composing different risk and defuzzification of the aggregated membership function, is proposed to aggregate different risks. In the framework, we pay maximum attention to accurate estimation of memberships of different risks. Besides, technical problems of composition and defuzzification are solved in detail. At last, an illustrative example is presented to show the feasibility of our method where we report the ranking of the aggregated risks of different scenarios.