Comparing different approaches to entropy for Interval Valued Fuzzy Sets

In a general sense, entropy is a measure of disorder. When adapted to information theory, the considered disorder is mostly related to information uncertainty, and in particular to randomness. Finally, when applied to fuzzy sets, this disorder is interpreted also in terms of uncertainty, but now the uncertainty relates to fuzziness. Consequently the fuzzy entropy of a fuzzy set defines how fuzzy is the set. Since its introduction, different approaches to fuzzy entropy has been considered. Those approaches usually measure the distance from the considered fuzzy set, to a minimum entropy set. In general, the minimum entropy set is a crisp set, but when analysing fuzzy entropy in the different extensions of fuzzy sets (interval valued, intuitionistic, type-2 and so on) this is not always the case. The present paper will concentrate on Interval Valued Fuzzy Sets, considering the different definitions of entropy that has been introduced, and analysing them in terms of the set used for comparison and the way to measure the distance. As a result, a certain ordering among the considered measures will be achieved.