A Risk Aversion under Fuzzy Set and System Environment

Abstract

Risk aversion play an important role in economics, finance, psychology
and especially decision making. This research conduct a study using random data by
proving Arrow-Pratt measures using Jensen-type operators. The methodology is
based on the objectives. The methodology includes formulating utility functions
under decision making, triangular and trapezoidal fuzzy number is introduced to
reduce the complexity of determining the utility function of a decision maker, proving
Pratt’s theorem for possibilistic risk aversion associated with fuzzy number, a utility
function and weighting function under Jensen type operators and also risk premium
was set defining as a measure of risk aversion discovered and explain using the
possibilistic expected value using Arrow-Pratt formula The results and discussion
yields all the three objectives based on the methodology done in the previous section.
The main notions are the possibilistic risk premium and the possibilistic relative risk
premium associated with a fuzzy number and a utility function using Arrow-Pratt
theorems with Jensen type operators under risk aversion.