Fuzzy Poverty Indices
Keywords:
crisp indices, fuzzy indices, fuzzy membership functions, headcount ratio, income gap ratioAbstract
This article considers how conventional poverty indices may best be extended to a fuzzy environment in which the traditional “crisp” (or dichotomous) poverty assignment is replaced by a membership function m taking values in the unit interval. Suitable analogues are proposed for a variety of standard index properties such as monotonicity, transfer preference, decomposability and scale invariance. It is shown that, in certain circumstances, a unique fuzzy index can be associated with any given conventional index family, and that the fuzzy index may be interpreted as the expected value of the conventional indices. Furthermore, the fuzzy indices not only inherit all the principal index properties of its crisp sub-family, but may also exhibit additional desirable characteristics.
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