A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory

A functional defined on the class of generalized characteristic functions (fuzzy sets), called “entropy≓, is introduced using no probabilistic concepts in order to obtain a global measure of the indefiniteness connected with the situations described by fuzzy sets. This “entropy≓ may be regarded as a measure of a quantity of information which is not necessarily related to random experiments.Some mathematical properties of this functional are analyzed and some considerations on its applicability to pattern analysis are made