Development of Risk Measurement Instrumentarium in Modeling of Uncertainty Using the Fuzzy Set Approach

Abstract

The article is aimed at developing a methodical apparatus for risk measurement using the fuzzy set theory in order to formalize uncertainty. The problem field of research is limited to a situation where an economic indicator that serves as a decision-making criterion is described by a fuzzy number, understanding the latter as a fuzzy value with normal and convex membership function. Based on the interval (by the levels of membership) method of presenting a fuzzy assessment of the criterion indicator, the publication considers such indicators of the risk degree as average absolute deviation, average range of variation, half-deviation (average absolute half-deviation), the average one-sided variation. The versions of the last two indicators, formulated in the study in terms of the fuzzy-set methodology, are the result of the refinement of their prototypes proposed in previous publications of the author. As evidence of the logical correctness of the revised versions of the half-deviation and the average one-sided variation are the corresponding equalities, which reflect the relationship of these indicators with the indicators of the average absolute deviation and average range variation, respectively. In general, the results of the proposed study should be regarded as separate components of a single system of instrumental means for quantifying the risk degree in a fuzzy data situation, the formation of which has not yet been completed and suggests further development.

Keywords

• uncertainty
• fuzziness
• risk degree
• average absolute deviation
• average variation
• half-deviation
• average one-sided variation