Skip to main content

Abstract

The concept of Z-numbers introduced by Prof. L. Zadeh created the new approach to decision-making problem. Use of Z-information for describing and calculating uncertain information was more convenient and decision making under Z-information was more adequate. Zadeh’s achievements on base of Z-information became a source of motivation for other researchers.

In this paper we propose the solution method for Zadeh’s “fast way” problem under Z-information. This solution method is based on Z-dynamic programming approach. To illustrate this problem under Z-information, the numerical example is analyzed.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight 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

References

  1. Klein, C.M.: Fuzzy shortest paths. Fuzzy Sets Syst. 39, 27–41 (1991)

    Article  MathSciNet  Google Scholar 

  2. Lin, K., Chen, M.: The fuzzy shortest path problem and its most vital arcs. Fuzzy Sets Syst. 58(5), 343–353 (1994)

    MathSciNet  Google Scholar 

  3. Liu, S.T., Kao, C.: Network flow problems with fuzzy arc lengths. IEEE Trans. Syst. Man Cybern.: Part B 34, 765–769 (2004)

    Article  Google Scholar 

  4. Mares, M., Horak, J.: Fuzzy quantities in networks. Fuzzy Set. Syst. 10, 135–155 (1983)

    Article  Google Scholar 

  5. Okada, S., Gen, M.: Fuzzy shortest path problem. Comput. and Indust. Eng. 27, 465 (1994)

    Article  Google Scholar 

  6. Okada, S., Soper, T.: A shortest path problem on a network with fuzzy are lengths. Fuzzy Sets Syst. 109, 129–140 (2000)

    Article  Google Scholar 

  7. Zadeh, L.A.: A note on Z-numbers. Inf. Sci. 181, 2923–2932 (2011)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  9. Zimmermann, H.J.: Fuzzy mathematical programming. Comput. Ops. Res. 10(4), 291–298 (1983)

    Article  MathSciNet  Google Scholar 

  10. De, P.K., Bhincher, A.: Dynamic programming and multi objective linear programming approaches. App. Math. Inf. Sci. 5(2), 253–263 (2011)

    Google Scholar 

  11. Aliev, R.A., Alizadeh, A.V., Huseynov, O.H.: The arithmetic of continuous Z-numbers. Inf. Sci. 373, 441–460 (2016)

    Article  Google Scholar 

  12. Aliev, R.A., Alizadeh, A.V., Huseynov, O.H.: The arithmetic of discrete Z-numbers. Inf. Sci. 290, 134–155 (2015)

    Article  MathSciNet  Google Scholar 

  13. Aliev, R.A., Huseynov, O.H., Aliyev, R.R., Alizadeh, A.V.: The Arithmetic of Z-Numbers: Theory and Applications. World Scientific, Singapore (2015)

    Book  Google Scholar 

  14. Aliev, R.A.: Uncertain Computation Based on Decision Theory. World Scientific Publishing, Singapore (2017)

    Google Scholar 

  15. Aliev, R.A., Perdycz, W., Huseynov, O.H.: Functions defined on a set of Z-numbers. Inf. Sci. 423, 353–375 (2018)

    Article  MathSciNet  Google Scholar 

  16. Aliev, R.A., Alizadeh, A.V., Huseynov, O.H., Jabbarova, K.I.: Z-number-based linear programming. Int. J. Intell. Syst. 30(5), 563–589 (2015)

    Article  Google Scholar 

  17. Aliev, R.A., Pedrycz, W.: Fundamentals of a fuzzy-logic-based generalized theory of stability. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 39(4), 971–988 (2009)

    Article  Google Scholar 

  18. Aliev, R., Tserkovny, A.: Systemic approach to fuzzy logic formalization for approximate reasoning. Inf. Sci. 181(6), 1045–1059 (2011)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rashad R. Aliyev .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Aliyev, R.R., Adilova, N.E. (2020). Solution of Zadeh’s “Fast Way” Problem Under Z-Information. In: Aliev, R., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F. (eds) 10th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions - ICSCCW-2019. ICSCCW 2019. Advances in Intelligent Systems and Computing, vol 1095. Springer, Cham. https://doi.org/10.1007/978-3-030-35249-3_10

Download citation

Publish with us

Policies and ethics