The generalized additivity,transformation theorem and the defect of additivity for fuzzy measures

Based on the concept of generalized additivity proposed in this paper,the generalized additivity for two popular types of non-additive measures are studied.Simultaneously,the characteristic theorem for generalized additivity fuzzy measures is given,that is,the relationship between generalized additivity and ordinary additivity is presented.Furthermore,the error estimates between generalized additivity and ordinary additivity are discussed.