Skip to main content

Required Background in Set Theory

  • Chapter
Fuzzy Measure Theory
  • 361 Accesses

Abstract

Let X be a nonempty set. Unless otherwise stated, all sets that we consider are subsets of X. X is called the universe of discourse. The elements of X are called points. X may contain finite, countably infinite, or uncountably infinite number of points. A set that consists of a finite number of points x 1, x 2, ...., x n (or, a countably infinite number of points x 1, x 2, ...) may be denoted by {x 1, x 2, ..., x n } ({x 1, x 2, ...}, respectively). A set containing no point is called the empty set, and is denoted by Ø.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

  1. Halmos, P. R. [ 1967 ], Measure Theory. Van Nostrand, New York.

    Google Scholar 

  2. Wang, Zhenyuan, and Zhang, Zhipeng [ 1984a ], An extension theorem on generalized possibility measure. Kexue Tongbao, 15, 959 (in Chinese).

    Google Scholar 

  3. Wang, Zhenyuan, and Zhang, Zhipeng [ 1984b ], On the extension of possibility measures. BUSEFAL, 18, 26–32.

    MATH  Google Scholar 

  4. Liu, Guiting, and Wang, Zhenyuan [ 1985 ], An extension theorem on consonant belief function. Kexue Tongbao, 9, 718–719 (in Chinese).

    Google Scholar 

  5. Wang, Zhenyuan [ 1990b ], Structural characteristics of fuzzy measure on S-compact spaces. International Journal of General Systems, 17, 309–316.

    Article  MATH  Google Scholar 

  6. Qiao, Zhong [ 1990 ], On fuzzy measure and fuzzy integral on fuzzy set. Fuzzy Sets and Systems, 37, 77–92.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer Science+Business Media New York

About this chapter

Cite this chapter

Wang, Z., Klir, G.J. (1992). Required Background in Set Theory. In: Fuzzy Measure Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5303-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-5303-5_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-3225-9

  • Online ISBN: 978-1-4757-5303-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics