ON TRUNCATED MEASURES OF INCOME INEQUALITY FROM A FUZZY PERSPECTIVE

In most statistical analysis, inequality or extent of variation in income is represented in terms of certain summary measures. But some authors argued that the concept of inequality is vague and thus cannot be measured as an exact concept. Therefore, fuzzy set theory provides naturally a useful tool for such circumstances. In this paper we have introduced a real-valued fuzzy method of illustrating the measures of income inequality in truncated random variables based on the case where the conditional events are vague. To guarantee certain relevant properties of these measures, we first selected three main families of measures and obtained their closed formulas, then used two simulated and real data set to illustrate the usefulness of derived results.