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2010•Journal of Shandong UniversityRequires access

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

Ting Xie

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Abstract

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.

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What this paper is about

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.

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Available abstract

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.

Key concepts: Additive function, Mathematics, Transformation (genetics), Fuzzy logic, Applied mathematics, Extension (predicate logic), Mathematical analysis, Computer science

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