A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory
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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.
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