ABSTRACT

In this paper, we adopt a general framework that allows to fully rank distributions of partially ordered variables. Building on concepts from the poset and fuzzy set theories, we incorporate a modified (rank-based) fuzzification technique into Hammond-type distribution function. This methodology allows to take into account the inherent incomparability among some attribute profiles and establish a firm ranking of distributions based on two dominance criteria. First, an extended fuzzy Hammond criterion that ranks distributions based on their degree of dominance while emphasizing within-distribution inequality. Second, a social welfare criterion that ranks distributions in a crisp fashion while placing more weight on overall efficiency. The resulting matrices satisfy the three desirable properties of dominance analysis; viz. consistency, transitivity, and anti-symmetry. We illustrate our proposed methodology using two applications: one on ill-health distributions and the other on well-being distributions using data from the Middle East, North Africa, and Sub-Saharan Africa. Both applications yield a full ranking of countries based on ill-health and well-being, respectively.