Entropy, distance measure and similarity measure of fuzzy sets and their relations

The axiom definitions of entropy, distance measure and similarity measure of fuzzy sets are systematically given and basic relations between these measures are discussed. The concepts of σ- (resp. sub-σ-)entropy, σ- (resp. sub-σ-)distance measure and σ- (resp. sub-σ-)similarity measure are proposed, and some examples of them are listed. The relations between σ- (resp. sub-σ-)entropy, σ- (resp. sub-σ-)distance measure and σ- (resp. sub-σ-)similarity measure are obtained.