Fuzzy set based intra-urban inequality indicator

Intra-urban inequality is not strictly defined and therefore cannot be measured accurately. The literature shows that the measurement of inequality varies depending on the judgment of the experts and that this judgment can be realized in several ways. Taking this into account, the capabilities created using fuzzy set theory and consensus schemes can be useful in the process of measuring inequality. The objective of their use is twofold. First, analyze the degree to which experts diverge on an ill-defined phenomenon such as inequality. Second, build a fuzzy set based Intra-Urban Inequality Indicator (F-II-I). The results of the present research show that F-II-I is adequate to represent the intra-urban inequality. The experts involved agree 93% on the weight of the inequality variables. The correlation coefficient and the proportion of outliers between the F-II-I and the Average Monthly Income per Household is 0.61 and 0.06, respectively. The degree of uncertainty associated with the different ways of normalizing and aggregating the F-II-I variables was 0.11. The pattern of inequality represented by F-II-I is consistent with similar studies and with the World Bank's Poverty Line. This research contributes to the practice as it combines methods and techniques that make it possible to measure phenomena without strict definition and to consider conflicting opinions expressed in different ways. As a theoretical contribution, this research demonstrates a certain degree of a satisfactory definition of intra-urban inequality. Besides, even if this definition's limits remain unclear, there is a reasonable consensus degree on specific aspects of inequality.