Abstract
A first generalization of Shannon entropy of random variables has been suggested by Renyi, and later other authors derived a new family of generalized entropies referred to as structural entropy of order s and structural entropy of order (r, s). In the present paper we shall combine this theory with our approach to information of deterministic mappings, and we shall so obtain a new family of structural entropies for deterministic functions, which can be helpful to take account of measurement errors, or uncertainty in definition. As a special case, we apply this model to fuzzy sets, as we show how it is especially suitable to deal with the useful case when the membership function itself is fuzzy.
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