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In the traditional literature of poverty measurement, a kind of demarcation line separates the poor from the rich persons. An individual is poor if his or her income does not exceed a well defined income threshold. If the amount of income is one cent higher than this threshold, the respective person belongs to the subset of rich people within the society. The author's intention is to offer some tools in order to overcome this traditionally sharp distinction between poor and rich. Furthermore other indicators of poverty exist which also contribute to a gradual transition from poor to rich. This smooth transition can be achieved by means of the theory of fuzzy sets which does not possess sharp boundaries.