• Zhenyuan Wang
  • George J. Klir


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 can be extended onto the σ-ring (). The following is a sample of fuzzy measure for which a required extension does not exist.


Probability Distribution Function Extension Theorem Absolute Continuity Fuzzy Measure Classical Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Wang, Zhenyuan [ 1985a ], Asymptotic structural characteristics of fuzzy measure and their applications. Fuzzy Sets and Systems, 16, 277–290.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 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
  3. 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
  4. 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
  5. Wang, Zhenyuan [ 1986b ], Semi-lattice isomorphism of the extensions of possibility measure and the solutions of fuzzy relation equation. In: Cybernetics and Systems ‘86, ed. by R. Trappl, Kluwer, Boston, 581–583.CrossRefGoogle Scholar
  6. Wang, Zhenyuan [1987], Some recent advances on the possibility measure theory. In: Bouchon and Yager [ 1987 ], 173–175.Google Scholar
  7. Wang, Zhenyuan, and Zhang, Zhipeng [ 1984a ], An extension theorem on generalized possibility measure. Kexue Tongbao, 15, 959 (in Chinese).Google Scholar
  8. Wang, Zhenyuan, and Zhang, Zhipeng [ 1984b ], On the extension of possibility measures. BUSEFAL, 18, 26–32.zbMATHGoogle Scholar
  9. Qiao Zhong, On the extension of possibility measures, Fuzzy Sets and Systems 32 (1989) 315–320.Google Scholar
  10. Wang, Zhenyuan [ 1981 ], Une class de mesures floues-les quasi-mesures. BUSEFAL, 6, 28–37.Google Scholar
  11. Wang, Zhenyuan [ 1990a ], Absolute continuity and extension of fuzzy measures. Fuzzy Sets and Systems, 36, 395–399.MathSciNetzbMATHCrossRefGoogle Scholar
  12. Qiao Zhong, Transformation theorems of abstract integrals on fuzzy sets, Proc. 2nd Joint IFSA-EC EURO-WG, Vienna (1988) 50–53.Google Scholar
  13. Song, Renming [ 1984a ], The extensions of a class of fuzzy measures. Journal of Hebei University, 2, 97–101 (in Chinese).Google Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Zhenyuan Wang
    • 1
  • George J. Klir
    • 1
  1. 1.State University of New York at BinghamtonBinghamtonUSA

Personalised recommendations