Analyzing Multidimensional Well-Being

Chapter 4Fuzzy Set Approaches to the Measurement of Multidimensional Poverty

4.1 Introduction

It often becomes impossible to gain sufficient information on achievement levels in different dimensions of well-being. This, therefore, may make the poverty status of a person quite ambiguous. To understand this, consider a person who has sufficiently high income so that he can certainly be regarded as income-rich. It is likely that he will remain rich if his income reduces by a tiny amount. But if this tiny reduction process continues, he will be poor after some time. In the process of these sequential reductions, we may classify him as “marginally poor” or “borderline poor” at some stage. However, there may not be a clear borderline or line of demarcation that will unambiguously partition the population into sets of poor and rich. Therefore, the predicate “poor” may often involve vagueness. Often, the respondents may be reluctant to supply correct data on achievement levels, particularly, on income and wealth holdings. There can be a wide range of threshold limits for achievement levels, which may be socially acceptable. The possibility that there is lack of relevant information on achievement quantities indicates that there is a degree of unclearness in the concept of poverty.

Now, if there is some vagueness in a concept, then vagueness is preserved by a clear-cut representation of that ambiguous concept. Fuzzy set theory has been introduced an equipment for tackling problems in ...