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Computing the Risk Indicators in Fuzzy Systems

Computing the Risk Indicators in Fuzzy Systems

Irina Georgescu
Copyright: © 2012 |Volume: 5 |Issue: 4 |Pages: 22
ISSN: 1938-7857|EISSN: 1938-7865|EISBN13: 9781466615045|DOI: 10.4018/jitr.2012100105
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MLA

Georgescu, Irina. "Computing the Risk Indicators in Fuzzy Systems." JITR vol.5, no.4 2012: pp.63-84. http://doi.org/10.4018/jitr.2012100105

APA

Georgescu, I. (2012). Computing the Risk Indicators in Fuzzy Systems. Journal of Information Technology Research (JITR), 5(4), 63-84. http://doi.org/10.4018/jitr.2012100105

Chicago

Georgescu, Irina. "Computing the Risk Indicators in Fuzzy Systems," Journal of Information Technology Research (JITR) 5, no.4: 63-84. http://doi.org/10.4018/jitr.2012100105

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Abstract

The modeling of complex risk situations imposes the existence of multiple ways to represent the risk and compare the risk situations between them. In probabilistic models, risk is described by random variables and risk situations are compared by stochastic dominance. In possibilistic or credibilistic models, risk is represented by fuzzy variables. This paper concerns three indicators of dominance associated with fuzzy variables. This allows the definition of three notions of fuzzy dominance: dominance in possibility, dominance in necessity and dominance in credibility. These three types of dominance are possibilistic and credibilistic versions of stochastic dominance. Each type offers a modality of ranking risk situations modeled by fuzzy variables. In the paper some properties of the three indicators of dominance are proved and relations between the three types of fuzzy dominance are established. For triangular fuzzy numbers formulas for the computation of these indicators are obtained. The paper also contains a contribution on a theory of risk aversion in the context of credibility theory. Using the credibilistic expected utility a notion of risk premium is defined as a measure of risk aversion of an agent in front of a risk situation described by a fuzzy variable and an approximate calculation formula of this indicator is proved.

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