Skip to main content
Springer Nature Link
Log in

A Quantitative View on Quasi Fuzzy Numbers

  • Chapter
  • First Online:
Combining Experimentation and Theory

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 271))

  • 707 Accesses

Abstract

In this paper we generalize the principles of possibilistic mean value, variance, covariance and correlation of fuzzy numbers to a more general class of fuzzy subsets of the real line: to quasi fuzzy numbers.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

Similar content being viewed by others

References

  1. Carlsson, C., Fullér, R.: On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems 122, 315–326 (2001); doi:10.1016/S0165-0114(00)00043-9

    Article  MATH  MathSciNet  Google Scholar 

  2. Carlsson, C., Fullér, R.: Fuzzy Reasoning in Decision Making and Optimization. Studies in Fuzziness and Soft Computing Series, vol. 82. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  3. Carlsson, C., Fullér, R., Majlender, P.: On possibilistic correlation. Fuzzy Sets and Systems 155, 425–445 (2005); doi:10.1016/j.fss.2005.04.014

    Article  MATH  MathSciNet  Google Scholar 

  4. Chanas, S., Nowakowski, M.: Single value simulation of fuzzy variable. Fuzzy Sets and Systems 25, 43–57 (1988); doi:10.1016/0165-0114(88)90098-X

    Article  MATH  MathSciNet  Google Scholar 

  5. Dubois, D., Prade, H.: The mean value of a fuzzy number. Fuzzy Sets and Systems 24, 279–300 (1987); doi:10.1016/0165-0114(87)90028-5

    Article  MATH  MathSciNet  Google Scholar 

  6. Dubois, D., Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York (1988)

    MATH  Google Scholar 

  7. Dubois, D.: Possibility theory and statistical reasoning. Computational Statistics & Data Analysis 51, 47–69 (2006); doi:10.1016/j.csda.2006.04.015

    Article  MATH  MathSciNet  Google Scholar 

  8. Fullér, R., Majlender, P.: On weighted possibilistic mean and variance of fuzzy quantitives. Fuzzy Sets and Systems 136, 363–374 (2003); doi:10.1016/S0165-0114(02)00216-6

    Article  MATH  MathSciNet  Google Scholar 

  9. Fullér, R., Majlender, P.: On interactive fuzzy quantitives. Fuzzy Sets and Systems 143, 355–369 (2004); doi:10.1016/S0165-0114(03)00180-5

    Article  MathSciNet  Google Scholar 

  10. Fullér, R., Mezei, J., Várlaki, P.: An improved index of interactivity for fuzzy numbers. Fuzzy Sets and Systems (to appear); doi:10.1016/j.fss.2010.06.001

    Google Scholar 

  11. Goetschel, R., Voxman, W.: Elementary Fuzzy Calculus. Fuzzy Sets and Systems 18, 31–43 (1986); doi:10.1016/0165-0114(86)90026-6

    Article  MATH  MathSciNet  Google Scholar 

  12. Larsen, P.M.: Industrial applications of fuzzy logic control. International Journal of Man–Machine Studies 12, 3–10 (1980), doi:10.1016/S0020-7373(80)80050-2

    Article  Google Scholar 

  13. Mamdani, E.H.: Advances in the linguistic synthesis of fuzzy controllers. International Journal of Man–Machine Studies 8(6), 669–678 (1976), doi:10.1016/S0020-7373(76)80028-4

    Article  MATH  Google Scholar 

  14. Yager, R.R.: A procedure for ordering fuzzy subsets of the unit interval. Information Sciences 24, 143–161 (1981); doi:10.1016/0020-0255(81)90017-7

    Article  MATH  MathSciNet  Google Scholar 

  15. Yoshida, Y., Yasuda, M., Nakagami, J.-I., Kurano, M.: A new evaluation of mean value for fuzzy numbers and its application to American put option under uncertainty. Fuzzy Sets and Systems 157, 2614–2626 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  16. Zadeh, L.A.: Concept of a linguistic variable and its application to approximate reasoning, I, II, III. Information Sciences 8, 199–249, 301–357 (1975); 9, 43–80 (1975)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IAMSR, Åbo Akademi University, Joukahaisenkatu 3-5, FIN-20520, Åbo, Finland

    Christer Carlsson & Robert Fullér

  2. Turku Centre for Computer Science, Joukahaisenkatu 3-5, FIN-20520, Åbo, Finland

    József Mezei

Authors
  1. Christer Carlsson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert Fullér
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. József Mezei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christer Carlsson .

Editor information

Editors and Affiliations

  1. European Center for Soft Computing, Mieres, Asturias, 33600, Spain

    Enric Trillas

  2. , Computing and Decision Sciences, Coolidge Fellow GE Global Research, NY, 12309, USA

    Piero P. Bonissone

  3. , Edificio Científico-Tecnológico, European Centre of Soft Computing, Calle Gonzalo Gutiérrez Quirós S/N Mieres, Asturias, 33600, Spain

    Luis Magdalena

  4. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, Warsaw, 01--447, Poland

    Janusz Kacprzyk

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Carlsson, C., Fullér, R., Mezei, J. (2012). A Quantitative View on Quasi Fuzzy Numbers. In: Trillas, E., Bonissone, P., Magdalena, L., Kacprzyk, J. (eds) Combining Experimentation and Theory. Studies in Fuzziness and Soft Computing, vol 271. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24666-1_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24666-1_16

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24665-4

  • Online ISBN: 978-3-642-24666-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics