Fuzzy measurement of income inequality: a class of fuzzy inequality measures

The typical practice of income inequality evaluation is by using inequality indices. Yet there is no “best” measure of inequality as we know it, and hence, any conclusion based on an inequality index must be subject to some doubts. Some authors even argued that the concept of inequality, by its very nature, is vague, and thus, cannot be measured like an exact concept. Motivated by these considerations, this paper studies axiomatic fuzzifications of inequality measures. Consequently, a systematic method of viewing the conclusions of inequality comparisons in terms of truth value statements is developed. Furthermore, it is shown that this method (or in fact, any other fuzzy inequality measure) can be used to construct confidence intervals for the crisp conclusions of inequality indices.