The Fuzzy Set Approach to Multidimensional Poverty: the Case of Italy in the 1990s
The Fuzzy Set Approach to Multidimensional Poverty: the Case of Italy in the 1990s
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多维贫困的模糊集方法：20 世纪 90 年代意大利的案例
DOI：
10.1057/9780230582354_2
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
V. Verma
中科院分区：
文献类型：
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作者：
G. Betti;B. Cheli;A. Lemmi;V. Verma
大多数用于贫困分析的方法都有两个主要局限性：（i）它们是单维的，即仅参考低收入或消费支出等贫困指标；（ii）它们需要通过所谓的贫困线将人口分为贫困人口和非贫困人口。如今，许多作者认识到贫困是一种复杂的现象，不能简化为单一的货币维度。这就需要采取多维方法，将分析扩展到各种生活条件的非货币指标。随着信息的增多，这种多维度的分析确实变得越来越可行，这反过来又促使许多国家开展了涵盖生活条件各个方面的调查。相比之下，人们很少关注传统方法的第二个局限性，即严格的贫困/非贫困二分法，其结果是，大多数关于贫困衡量的文献仍然基于贫困阈值的使用。然而，无可争议的是，如此明确的划分会导致信息丢失，并消除两个极端之间存在的细微差别——一方面是实质性福利，另一方面是明显的物质困难。换句话说，贫困应被视为程度问题，而不是人口中个人存在或不存在的一种属性。 Cerioli 和 Zani (1990) 早期尝试将这一概念纳入方法论层面（以及多维框架），他们从 Zadeh (1965) 发起的模糊集理论中汲取灵感。给定一个由元素 x X 组成的集合 X，X 的任意模糊子集 A 定义如下：A{x, mA (x)}，其中 mA (x): X→[0, 1] 称为模糊子集 A 中的隶属函数 (mf.)。mA (x) 值表示 x 在 A 中的隶属程度。因此，mA (x) 0 表示 x 不属于 A，而 mA (x) 1 表示 x 完全属于 A。当 0 mA (x) 1 时，x 部分属于 A，并且它对 A 的隶属度随着 mA (x) 越接近 1 而成比例增加。
Most of the methods designed for the analysis of poverty share two main limitations:(i) they are unidimensional, ie refer to only one proxy of poverty such as low income or consumption expenditure;(ii) they need to dichotomize the population into the poor and the non-poor by means of the so-called poverty line. Nowadays many authors recognize that poverty is a complex phenomenon that cannot be reduced to the sole monetary dimension. This leads to the need for a multidimensional approach that consists in extending the analysis to a variety of non-monetary indicators of living conditions. Such a multidimensional analysis has indeed become increasingly feasible as more information has become available, and this in turn has induced many countries to launch surveys covering the various aspects of living conditions. By contrast, little attention has been devoted to the second limitation of the traditional approach, viz the rigid poor/non-poor dichotomy, with the consequence that most of the literature on poverty measurement continues to be based on the use of poverty thresholds.Yet it is undisputable that so clear-cut a division causes a loss of information and removes the nuances that exist between the two extremes–substantial welfare on the one hand and distinct material hardship on the other. In other words, poverty should be considered a matter of degree rather than as an attribute that is simply present or absent for individuals in the population. An early attempt to incorporate this concept at the methodological level (and in a multidimensional framework) was made by Cerioli and Zani (1990) who drew inspiration from the theory of Fuzzy Sets initiated by Zadeh (1965). Given a set X of elements x X, any fuzzy subset A of X is defined as follows: A{x, mA (x)}, where mA (x): X→[0, 1] is called the membership function (mf.) in the fuzzy subset A. The value mA (x) indicates the degree of membership of x in A. Thus mA (x) 0 means that x does not belong to A, whereas mA (x) 1 means that x belongs to A completely. With 0 mA (x) 1, x belongs to A partially and its degree of membership of A increases in proportion to the proximity of mA (x) to 1.