Extension is an important way to construct fuzzy measures on a σ-ring (Appendix A, Definition A.14). However, not all fuzzy measures defined on a ring ℛ can be extended onto the σ-ring ℱ(ℛ). The following is a sample of fuzzy measure for which a required extension does not exist.
KeywordsProbability Distribution Function Extension Theorem Absolute Continuity Fuzzy Measure Classical Measure
Unable to display preview. Download preview PDF.
- Wang, Zhenyuan [ 1985b ], Extension of possibility measures defined on an arbitrary nonempty class of sets. Proceeding of the First IFSA Congress, Palma de Mallorca.Google Scholar
- Wang, Zhenyuan [ 1985c ], Extension of consonant belief functions defined on an arbitrary nonempty class of sets. Publication 54 de la Groupe de Recherche Claude François Picard, C.N.R.S., France, 61–65.Google Scholar
- Wang, Zhenyuan [1985e], Semi-lattice structure of all extensions of possibility measure and consonant belief function. In: Feng and Liu [ 1985 ], 332–336.Google Scholar
- Wang, Zhenyuan , Some recent advances on the possibility measure theory. In: Bouchon and Yager [ 1987 ], 173–175.Google Scholar
- Wang, Zhenyuan, and Zhang, Zhipeng [ 1984a ], An extension theorem on generalized possibility measure. Kexue Tongbao, 15, 959 (in Chinese).Google Scholar
- Qiao Zhong, On the extension of possibility measures, Fuzzy Sets and Systems 32 (1989) 315–320.Google Scholar
- Wang, Zhenyuan [ 1981 ], Une class de mesures floues-les quasi-mesures. BUSEFAL, 6, 28–37.Google Scholar
- Qiao Zhong, Transformation theorems of abstract integrals on fuzzy sets, Proc. 2nd Joint IFSA-EC EURO-WG, Vienna (1988) 50–53.Google Scholar
- Song, Renming [ 1984a ], The extensions of a class of fuzzy measures. Journal of Hebei University, 2, 97–101 (in Chinese).Google Scholar