Document Type: Research Paper


Department of Statistics, Faculty of Mathematics ~and Computer Shahid Bahonar University of Kerman Kerman, Iran


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


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