Skip to main content
SpringerLink
Log in

Possibilistic Optimization Tasks with Mutually T-Related Parameters: Solution Methods and Comparative Analysis

  • Chapter
Fuzzy Optimization

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 254))

Abstract

The problems of possibilistic linear programming are studied in the article. Unlike in other known related publications, t-norms are used to describe the interaction (relatedness) of fuzzy parameters. Solution methods are proposed, models of possibilistic optimization are compared for different t-norms.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
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.

References

  1. Dubois, D., Prade, H.: Possibility theory. Tr. from french. Moskva. Radio i svyaz (1990) (in Russian)

    Google Scholar 

  2. Ermolyev, Y.M.: Methods of stochastic programming. — M.: Nauka, in Russian (1976) (in Russian)

    Google Scholar 

  3. Soldatenko, I.S.: On weighted sum of mutually T W -related fuzzy variables. Vestnik of Tver State University. Applied Mathematics 5(33), 63–77 (2007) (in Russian)

    Google Scholar 

  4. Yazenin, A.V.: To the problem of fuzzy goal achievement level maximization. Izvestia RAN. Theory and Systems for Control 4, 120–123 (1999) (in Russian)

    MathSciNet  Google Scholar 

  5. Yazenin, A.V.: Fuzzy variables and fuzzy mathematical programming. In: Proceedings of inter-republican scientific conference “Models of alternatives choosing in a fuzzy environment”, pp. 57–59. Riga polytechnical institute, Riga (1984) (in russian)

    Google Scholar 

  6. Yazenin, A.V.: Models of fuzzy mathematical programming. In: Proceedings of inter-republican scientific conference “Models of alternatives choosing in a fuzzy environment”, pp. 51–53. Riga polytechnical institute, Riga (1984)

    Google Scholar 

  7. Yazenin, A.V.: Fuzzy mathematical programming. Kalinin State University, Kalinin (1986) (in Russian)

    Google Scholar 

  8. De Baets, B., Marková-Stupňanová, A.: Analytical expressions for the addition of fuzzy intervals. Fuzzy Sets and Systems 91, 203–213 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  9. Dubois, D., Prade, H.: Additions of interactive fuzzy numbers. IEEE Trans. Automat. Control 26, 926–936 (1981)

    Article  MathSciNet  Google Scholar 

  10. Dubois, D., Prade, H.: Fuzzy numbers: an overview. In: Bezdek, J. (ed.) Analysis of Fuzzy Information, vol. 2, pp. 3–39. CRC-Press, Boca Raton (1988)

    Google Scholar 

  11. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)

    MATH  Google Scholar 

  12. Hong, D.H.: Parameter estimations of mutually T-related fuzzy variables. Fuzzy Sets and Systems 123, 63–71 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  13. Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Position paper I: basic analytical and algebraic properties. Fuzzy Sets and Systems 143, 5–26 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Position paper II: general constructions and parameterized families. Fuzzy Sets and Systems 145, 411–438 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  15. Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Position paper III: continuous t-norms. Fuzzy Sets and Systems 145, 439–454 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  16. Liu, B.: Uncertain programming. Wiley and Sons, New York (1999)

    Google Scholar 

  17. Mesiar, R.: A note to the T-sum of L − R fuzzy numbers. Fuzzy Sets and Systems 79, 259–261 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  18. Mesiar, R.: Computation of L − R-fuzzy numbers. In: Proc. 5th Internat. Workshop on Current Issues in Fuzzy Technologies, Trento, Italy, pp. 165–176 (1995)

    Google Scholar 

  19. Mesiar, R.: Shape preserving additions of fuzzy intervals. Fuzzy Sets and Systems 86, 73–78 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  20. Mesiar, R.: Triangular-norm-based addition of fuzzy intervals. Fuzzy Sets and Systems 91, 231–237 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  21. Nahmias, S.: Fuzzy Variables. Fuzzy Sets and Systems 1, 97–110 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  22. Nguyen, H.T., Walker, E.A.: A first cours in fuzzy logic. CRC Press, Boca Raton (1997)

    Google Scholar 

  23. Rao, M., Rashed, A.: Some comments on fuzzy variables. Fuzzy Sets and Systems 6, 285–292 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  24. Yazenin, A.V.: Fuzzy and stochastic programming. Fuzzy Sets and Systems 22, 171–180 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  25. Yazenin, A.V.: On the problem of possibilistic optimization. Fuzzy Sets and Systems 81, 133–140 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  26. Yazenin, A.V., Wagenknecht, M.: Possibilistic optimization. Brandenburgische Technische Universitat, Cottbus, Germany (1996)

    Google Scholar 

  27. Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Technologies, Tver State University, Tver, Russia

    Alexander Yazenin & Ilia Soldatenko

Authors
  1. Alexander Yazenin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ilia Soldatenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathemaitical and Statistical Sciences, University of Colorado Denver, PO Box 173364, 80217-3364, Colorado, Denver, USA

    Weldon A. Lodwick

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

    Janusz Kacprzyk

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Yazenin, A., Soldatenko, I. (2010). Possibilistic Optimization Tasks with Mutually T-Related Parameters: Solution Methods and Comparative Analysis. In: Lodwick, W.A., Kacprzyk, J. (eds) Fuzzy Optimization. Studies in Fuzziness and Soft Computing, vol 254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13935-2_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-13935-2_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13934-5

  • Online ISBN: 978-3-642-13935-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation