Development of a Fuzzy Set Apparatus for Risk Measurement: the Case of Simultaneous Fuzziness of the Criterion Indicator and its Standard

Abstract

The article deals with the development of a methodological apparatus for quantifying the degree of economic risk in modeling uncertainty with the usу of fuzzy set theory. The study implements the task of further development of a fuzzy set method for risk measurement based on a probabilistic analogy for a case of simultaneous fuzziness of estimates of the criterion economic indicator (criterion) and its standard, which allow for a presentation form that is interval in terms of levels of membership ( levels). As part of this, an appropriate calculation model is formulated. Furthermore, the work pays attention to the situation when both the criterion and its standard are modeled by fuzzy values with a high degree of arbitrariness of their structure, which does not allow an interval, in terms of levels of membership, way of representing them. Within the methodological approach, based on the probabilistic analogy, a possible computational design is proposed for this purpose. Along with the above mentioned, the study distinguishes as practically significant a combined situation, when the structure for fuzzy assessment of the criterion economic indicator is characterized with a high degree of randomness, while the assessment of its standard assumes a presentation form that is interval in terms of membership level. Moreover, possible calculation model is formulated for the above statement of the problem under study. As a promising area for further scientific research on the problem field considered in the article, there identified studying and developing tools to support decision-making in management of economic systems that allow handling simultaneously different types of uncertainty.

Keywords

• uncertainty
• fuzziness
• risk
• risk measurement
• probability measure