Skip to main content
SpringerLink
Log in
Book cover

International Fuzzy Systems Association World Congress

IFSA/NAFIPS 2019 2019: Fuzzy Techniques: Theory and Applications pp 318–329Cite as

A Ranking Method of Hexagonal Fuzzy Numbers Based on Their Possibilistic Mean Values

  • Conference paper
  • First Online:

  • 687 Accesses

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1000))

Abstract

A hexagonal fuzzy number (HFN) with its membership function as a nonlinear function, which is a generalization of triangular fuzzy numbers, trapezoidal fuzzy numbers, linear pentagonal fuzzy numbers and linear hexagonal fuzzy numbers, is defined in this paper. Cardinality of HFN is applied to achieve an algorithm for classifying types of HFNs. In addition, we present a ranking method for those fuzzy numbers based on their possibilistic mean values. Therefore, an explicit formula of the possibilistic mean value of HFN is proposed.

This is a preview of subscription content, 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 EPUB and 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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Bodjanova, S.: Median value and median interval of a fuzzy number. Inf. Sci. 172, 73–89 (2005)

    Article  MathSciNet  Google Scholar 

  2. Carlsson, C., Fullér, R.: On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets Syst. 122, 315–326 (2001)

    Article  MathSciNet  Google Scholar 

  3. Christi, A., Malini, D.: Solving transportation problems with hexagonal fuzzy numbers using best candidates method and different ranking techniques. Int. J. Eng. Res. Appl. 6, 76–81 (2016)

    Google Scholar 

  4. Dhanam, K., Kalaiselvi, T.: Multi-item inventory model using hexagonal fuzzy number. Int. J. Math. Soft Comput. 6, 93–105 (2016)

    Article  Google Scholar 

  5. Dhanam, K., Parimaladevi, M.: Cost analysis on a probabilistic multiitem inventory model with ranking of circumcenter of the centroid of pentagonal fuzzy number. Int. J. Pure Appl. Math. 113, 1–9 (2017)

    Google Scholar 

  6. Dinagar, D.S., Kannan, J.R.: On fuzzy inventory model with allowable shortage. Int. J. Pure Appl. Math. 99, 65–76 (2015)

    Article  Google Scholar 

  7. Dinagar, D.S., Narayanan, U.H.: On determinant of hexagonal fuzzy number matrices. Int. J. Math. Appl. 4, 357–363 (2016)

    Google Scholar 

  8. Dinagar, D.S., Narayanan, U.H.: On inverse of hexagonal fuzzy number matrices. Int. J. Pure Appl. Math. 115, 147–158 (2017)

    Google Scholar 

  9. Elumalai, P., Prabu, K., Santhoshkumar, S.: Fuzzy transportation problem using hexagonal fuzzy numbers by robust ranking method. Emperor Int. J. Financ. Manag. Res. UGC Jr. 45308, 52–58 (2017)

    Google Scholar 

  10. Fullér, R., Majlender, P.: On weighted possibilistic mean and variance of fuzzy numbers. Fuzzy Sets Syst. 136, 363–374 (2003)

    Article  MathSciNet  Google Scholar 

  11. Ghadle, K.P., Pathade, P.A.: Solving transportation problem with generalized hexagonal and generalized octagonal fuzzy numbers by ranking method. Glob. J. Pure Appl. Math. 13, 6367–6376 (2017)

    Google Scholar 

  12. Goetschel, R., Voxman, W.: Elementary fuzzy calculus. Fuzzy Sets Syst. 18, 31–43 (1986)

    Article  MathSciNet  Google Scholar 

  13. Hanss, M.: Applied Fuzzy Arithmetic. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  14. Hussain, R.J., Priya, A.: Solving fuzzy game problem using hexagonal fuzzy number. J. Comput. 1, 53–59 (2016)

    Google Scholar 

  15. Mondal, S.P., Mandal, M.: Pentagonal fuzzy number, its properties and application in fuzzy equation. Future Comput. Inform. J. 2, 110–117 (2017)

    Article  Google Scholar 

  16. Rajarajeswari, P., Sahaya, S.A.: Ranking of hexagonal fuzzy numbers for solving multi objective fuzzy linear programming problem. Int. J. Comput. Appl. 84, 14–19 (2013)

    Google Scholar 

  17. Sahaya, S.A., Revathy, M.: A new ranking on hexagonal fuzzy numbers. Int. J. Fuzzy Log. Syst. 6, 1–8 (2016)

    Google Scholar 

  18. Sahaya, S.A., Vijayalakshmi, K.R.: Fuzzy transportation problem using symmetric hexagonal fuzzy numbers. IOSR J. Math. 12, 76–81 (2016)

    Article  Google Scholar 

  19. Selvakumari, K., Sowmiya, G.: Fuzzy network problems using job sequencing technique in hexagonal fuzzy numbers. Int. J. Adv. Eng. Res. Dev. 4, 116–121 (2017)

    Google Scholar 

  20. Thamaraiselvi, A., Santhi, R.: Optimal solution of fuzzy transportation problem using hexagonal fuzzy numbers. Int. J. Sci. Eng. Res. 6, 40–45 (2015)

    Google Scholar 

  21. Vasanthi, L., Elakkiya, E.S.: Orthogonal fuzzy matrix using hexagonal fuzzy numbers. Int. J. Res. Appl. Sci. Eng. Technol. 6, 2349–2352 (2018)

    Article  Google Scholar 

  22. Venkatesan, A., Virginraj, A.: Algorithm for fully fuzzy linear system with hexegonal fuzzy number matrix by singular value decomposition. Int. J. Comput. Algorithms 3, 218–222 (2014)

    Article  Google Scholar 

  23. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank to the referees for valuable comments and suggestions.

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani, 12121, Thailand

    Worrawate Leela-apiradee

  2. Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok, 10330, Thailand

    Phantipa Thipwiwatpotjana

Authors
  1. Worrawate Leela-apiradee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Phantipa Thipwiwatpotjana
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Worrawate Leela-apiradee .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA

    Ralph Baker Kearfott

  2. Center for Computing Research (CIC), Instituto Politecnico Nacional, Ciudad de Mexico, Mexico

    Ildar Batyrshin

  3. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada

    Marek Reformat

  4. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Martine Ceberio

  5. Department of Computer Science, University of Texas at El Paso , El Paso, TX, USA

    Vladik Kreinovich

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Leela-apiradee, W., Thipwiwatpotjana, P. (2019). A Ranking Method of Hexagonal Fuzzy Numbers Based on Their Possibilistic Mean Values. In: Kearfott, R., Batyrshin, I., Reformat, M., Ceberio, M., Kreinovich, V. (eds) Fuzzy Techniques: Theory and Applications. IFSA/NAFIPS 2019 2019. Advances in Intelligent Systems and Computing, vol 1000. Springer, Cham. https://doi.org/10.1007/978-3-030-21920-8_29

Download citation

Publish with us

Policies and ethics

Search

Navigation