Supporting risk management decision making by converting linguistic graded qualitative risk matrices through interval type-2 fuzzy sets

Abstract

Risk matrices are widely used to present results of qualitative and semi-quantitative risk assessment for risk management decision making. There are different types of risk matrix category definitions according to the function and risk acceptance criteria. This paper reviews some general weaknesses of current risk matrices and proposes a method to improve the reading ambiguity of linguistically graded qualitative risk matrices. Main topic of this paper is the type of risk matrix that grades event consequence and frequency categories in linguistic terms. Because different people understand the meaning of these terms differently, the aim is to convert subjective quantified term inputs produced by a number of experts independently as much as possible to objective values creating at the same time a clearer and more discriminative result. In other words, the method involves asking various expert users independently to estimate numerical intervals of linguistic grades of event consequence and frequency on a continuous scale while maintaining risk acceptance levels. It is applying a second-generation fuzzy logic technique to express linguistic terms in numbers, called computing with words. This interval type-2 fuzzy system has evolved lately as a decision-making support tool and appears to be well suited to handle uncertainty intrinsic to qualitative linguistic grades, fusing different individual expert estimates in an objective way and to facilitate the reading resolution by introducing gliding numerical scales instead of discrete categories. Examples are given to illustrate the method as well as the use of the technique to aggregate a number of different qualitative risk matrix types into one unified risk matrix. The latter is useful in case a corporate-wide risk matrix exists to standardize risk management across the company, but older versions may still be around which should be fused with the newer ones.