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.I wish to thank Kaushik Basu, Larry Blume, Gary Fields, Tapan Mitra, Maurice Salles, Anthony Shorrocks, Sinan Unur, the participants of the 1993 Midwest Mathematical Economics Conference held in University of Wisconsin at Madison and those of the 2nd International Meeting of the Society for Social Choice and Welfare held at University of Rochester, and two anonymous referees for insightful comments and suggestions. Janos Aczel and Karol Baron kindly provided some help about a mathematical problem I faced, I am grateful to them. Needless to mention, however, the usual disclaimer applies.