A model for determining the utility function using Fuzzy numbers

• Author: Lixandroiu D.
• Pages: 469-478

Bulletin of the Transilvania University of Braşov

Series V: Economic Sciences • Vol. 8 (57) No. 2 - 2015

A model for determining the utility function

using Fuzzy numbers

Dorin LIXNDROIU1

Abstract: This paper proposes an interactive model for determining the utility function of

the decision maker. The model is based on the estimation of the certainty equivalent, which is

estimated by the decision maker as a trapezoidal fuzzy number.

Key-words: utility function, fuzzy numbers, St. Petersburg paradox

1. Introduction

The concept of utility, which is used in the economic decision-making theory to

compare different evaluation variants, is defined as a subjective measure depending

on the decision-making factor.

In order to model an individual’s behaviour regarding certain risky choices,

the utility function was introduced. The construction of the utility function has to

satisfy the rationality axioms defined in 1947 by von Neumann and Morgenstern in

their Theory of Games and Economic Behavior and presented in Ionescu et al.

(1999).

But the expectation utility theory actually begins with Daniel Bernoulli, who,

in a memo addressed to the Science Academy in Saint Petersburg in 1738, criticized

the criterion of the mathematic expectation introduced by Pascal and proposed a

new decision rule by introducing the utility function, a derivative and strictly

increasing function, which should measure the individual’s satisfaction.

The utility function expresses the decision maker's estimation as regards the

risk and the interest in the additional marginal gains that can be achieved.

The concept of utility is based on the risk aversion usually manifested by the

decision maker and his level of wealth.

Generally, in many economic models, the argument for the utility function is

the capital (income, profit) of the given individual.

It is supposed that he makes decisions that bring about the maximization of

the value of the mathematical expectation of his utility.

1 Transilvania University of Braşov, lixi.d@unitbv.ro