Signed Fuzzy-Valued Measures and Radon-Nikodym Theorem of Fuzzy-Valued Measurable Functions
β Scribed by Chen Degang; Zhang Liguo
- Publisher
- Springer
- Year
- 2003
- Weight
- 126 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0129-2021
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In this paper, the concept of fuzzy-valued fuzzy measures is introduced at first and then, based on the generalized fuzzy integral given by Wu et al. [Fuzzy Sets and Systems 57 (1993) 219], the generalized fuzzy integral of fuzzy-valued functions with respect to fuzzy-valued fuzzy measures is define
Radon-Nikodym theorem is established on fuzzy number measures in Banach spaces, Vitali-Hahn-Saks theorem is generalized to set valued measures and fuzzy number measures.
This is a subsequent paper of [9]. By using the concepts of fuzzy number fuzzy measures [9] and fuzzy-valued functions [10], a theory of fuzzy integrals of fuzzy-valued functions with respect to fuzzy number fuzzy measures is built up. So far, it is a more general one following Sugeno's [5].