STRUCTURAL ENTROPIES OF ORDERsAND OF ORDER (r, s) FOR DETERMINISTIC FUNCTIONS WITH AN APPLICATION OF FUZZY SET THEORY
Guy Jumarie · Cybernetics & Systems · 1990
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.