Extension of an inequality index for fuzzy-valued attributes

In previous papers (Gill 1979, 1982; Gill et al., 1989) we have introduced an inequality index for real-valued attributes, which is closely related to Shannon´s entropy (or diversity). In practice, situations arise in which attributes involved in an inequality measurement are more appropriately quantified by means of fuzzy values. In this communication we present a fuzzy index of inequality for fuzzy-valued attributes that has been obtained from the preceding one on the basis of Zadeh´s extension principle. An analysis of the behavior of this fuzzy index is finally included, and this analysis makes use of some well-known ranking procedures