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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. [ABSTRACT FROM AUTHOR]

This study examines a general scheme of multicriteria decision-making under uncertainty based on quantitative and qualitative information. In its original form, the general scheme uses qualitative information at the final decision stage, only if the quantitative information is unable to generate unique solutions. Considering that many problems require objectives based on qualitative information at all decision stages, the results of Ramalho et al. (2019) can provide such solutions. However, the processing of qualitative information in Ramalho et al. (2019) is based on applying a very simple approach to aggregating individual preferences without analyzing any type of consensus information. Therefore, the present study sets out to show that representative combinations of initial data, states of nature or scenarios can be constructed by using qualitative information directly, based on aggregating individual preferences after achieving the necessary consensus. In particular, a new scheme for consensus construction is proposed. Using this scheme enables negative points inherent in traditional approaches to be avoided and uncertainty levels to be reduced when estimating coefficients of objective functions based on qualitative information. An illustrative example is presented to demonstrate the results that the new proposal can achieve. [ABSTRACT FROM AUTHOR]