J4 ›› 2010, Vol. 45 ›› Issue (10): 53-60.

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

GONG Zeng-tai, XIE Ting   

  1. College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2009-09-02 Online:2010-10-16 Published:2010-10-19

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 words: fuzzy measures; generalized additivity; the defect of additivity

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