Unidimensional Development Ranking and Fuzzy Lorenz Dominance

  • Asis Kumar BanerjeeEmail author
Part of the Themes in Economics book series (THIE)


This chapter is devoted to an attempt at extending the unidimensional theory of development ranking so as to reduce the possibility of ranking failures. For this purpose, we borrow from the theory of fuzzy sets in mathematics and use the notion of fuzzy Lorenz dominance relation. The approach of modelling Lorenz dominance by a fuzzy binary relation was proposed in the 1980s. The idea does not seem to have been followed up actively in the subsequent literature. The fuzzy dominance relation proposed in the chapter is a follow-up on this line of research. It is, however, different from the earlier suggestions. Moreover, if the idea of Lorenz dominance is “fuzzified”, it would be natural to fuzzify the notion of development ranking itself. Indeed, this is what we do in this chapter. It is seen that such fuzzy development rankings can also be used to induce crisp (i.e. non-fuzzy) development rankings. The ranking methods developed in this chapter seem to be able to reduce the preponderance of the problem of ranking failures that arises frequently under the crisp (i.e. non-fuzzy) approach. In particular, it is shown that if two economies have the same per capita income, we shall now always be able to rank them in terms of development. While that is not the case when per capita incomes differ, completeness of the ranking is achieved under weaker conditions than in crisp theory.


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© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.University of CalcuttaKolkataIndia

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