Problemi Ekonomiki (Jun 2017)
The Fuzzy Adaptation of Probabilistic Risk Indicators
Abstract
The aim of the article is to develop fuzzy tools for measuring risk based on adaptation of corresponding indicators developed within the methodology of the probability theory. The study is limited to the situations where the economic indicator, which performs the function of a decision criterion and is an object of the analysis of the degree of risk, is modeled by a fuzzy number, and the latter is to be understood as a fuzzy value with a normal and convex membership function. Also in this case there applied the interval method, which describes fuzzy estimation of the criterion index by membership degrees. Within the framework of implementing the goal set, there consistently considered a number of probabilistic indicators of risk degree: mean absolute deviation, semideviation, coefficient of unfavorable deviations, ratio of expected losses (losses). For the latter, a modified version is proposed, in which the expected favorable and unfavorable deviations of the values of the criterion index are estimated taking into account the probability of their occurrence due to which it was called the weighted expected loss ratio. For the initial and modified version of the expected loss ratio, their fuzzy adaptations are formulated. According to the known property of the semideviation index, in the situation of probabilistic uncertainty the values of the coefficient of unfavorable deviations and the weighted expected loss ratio coincide. If the analyzed criterion index is described by a fuzzy estimate, the use of fuzzy adaptations of these coefficients in the general case leads to different results. It is also revealed that the fuzzy adaptation of the coefficient of unfavorable deviations coincides with the indicator of the degree of risk on the basis of a combined (hybrid) version of the possibility measure.
