Skip to main content
SpringerLink
Log in

Positive and Negative Interval Type-2 Generalized Fuzzy Number as a Linguistic Variable in Interval Type-2 Fuzzy Entropy Weight for MCDM Problem

  • Conference paper
Forging Connections between Computational Mathematics and Computational Geometry

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 124))

  • 836 Accesses

Abstract

Generalized fuzzy number is an extended method of fuzzy number. Generalized fuzzy number has received significant attention from researchers in many areas. However, most of the generalized fuzzy number is defined only on one side which is in positive generalized fuzzy number. Therefore, the aim of this paper is to introduce a new generalized fuzzy number which considers positive and negative side in the concept of interval type-2 fuzzy set (IT2FS). Then, a new linguistic variable is established from the concept of new generalized fuzzy number. This new linguistic variable is applied into the interval type-2 entropy weight for multi-criteria decision-making (MCDM) method. Interval type-2 entropy weight is chosen as the weight in MCDM because the determination of this weight in the existing project delivery decision-making model relies on experts’ knowledge and experience excessively. An aggregation process in MCDM method is modified in line with the new linguistic variable. An illustrative example is used in order to check the efficiency of the new method. This approach offers a practical, effective, and simple way to produce a comprehensive judgment.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
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

References

  1. Giachetti, R.E., Young, R.E.: A parametric representation of fuzzy numbers and their arithmetic operators. Fuzzy Sets Syst. 91, 185–202 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cheng, C.-H.: A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets Syst. 95, 307–317 (1998)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. Beníteza, J.M., Martínb, J.C., Román, C.: Using fuzzy number for measuring quality of service in the hotel industry. Tour. Manag. 28, 544–555 (2007)

    Article  Google Scholar 

  5. Chen, S.H.: Operations on fuzzy numbers with function principal Tamkang. J. Manag. Sci. 6, 13–25 (1986)

    Google Scholar 

  6. Kaur, A., Kumar, A.: A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers. Appl. Soft Comput. 12, 1201–1213 (2012)

    Article  Google Scholar 

  7. Cho, S.-J., Lee, B.-S., Lee, G.-M., Kim, D.-S., Song, Y.-O.: Fubini theorem for generalized fuzzy number-valued integrals. Fuzzy Sets Syst. 105, 177–179 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chen, S.J., Chen, S.M.: Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers. Appl. Intell. 26(1), 1–11 (2007)

    Article  Google Scholar 

  9. Chen, S.M., Chen, J.H.: Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Syst. Appl. 36(3), 6833–6842 (2009)

    Article  Google Scholar 

  10. Farhadinia, B., Banb, A.I.: Developing new similarity measures of generalized intuitionistic fuzzy numbers and generalized interval-valued fuzzy numbers from similarity measures of generalized fuzzy numbers. Math. Comput. Model. 57, 812–825 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wei, G., Zhao, X., Lin, R., Wang, H.: Generalized triangular fuzzy correlated averaging operator and their application to multiple attribute decision making. Appl. Math. Model. 36(7), 2975–2982 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Su, Z.-X., Xia, G.-P., Chen, M.-Y., Wang, L.: Induced generalized intuitionistic fuzzy OWA operator for multi-attribute group decision making. Expert Syst. Appl. 39, 1902–1910 (2012)

    Article  Google Scholar 

  13. Yu, V.F., Chi, H.T.X., Dat, L.Q., Phuc, P.N.K., Shen, C.-W.: Ranking generalized fuzzy numbers in fuzzy decision making based on the left and right transfer coefficients and areas. Appl. Math. Model. 37, 8106–8117 (2013)

    Article  MathSciNet  Google Scholar 

  14. Imran, C.T., Syibrah, M.N., Mohd Lazim, A.: New condition for conflicting bifuzzy sets based on intuitionistic evaluation. World Acad. Sci. Eng. Technol. 19, 451–455 (2008)

    MathSciNet  Google Scholar 

  15. Chen, S.-M., Lee L-W, L.-W.: Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets. Expert Syst. Appl. 37, 824–833 (2010)

    Article  Google Scholar 

  16. Chen, S.-M., Lee, L.-W.: Fuzzy multiple attributes group decision-making based on the interval type-2 TOPSIS method. J. Expert Syst. Appl. 37, 2790–2798 (2010)

    Article  Google Scholar 

  17. Mendel, J.M., John, R.I., Liu, F.L.: Interval type-2 fuzzy logical systems made simple. IEEE Trans. Fuzzy Syst. 14(6), 808–821 (2006)

    Article  Google Scholar 

  18. Liu, H., Kong, F.: A new MADM algorithm based on fuzzy subjective and objective integrated weights. Int. J. Inf. Syst. Sci. 1, 420–427 (2005)

    MATH  Google Scholar 

  19. Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst. 118(3), 467–477 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  20. De Luca, A., Termini, S.: A definition of non-probabilistic entropy in the setting of fuzzy sets theory. J. Inf. Control 20, 301–312 (1972)

    Article  MATH  Google Scholar 

  21. Wang, Y.M., Luo, Y.: Area ranking of fuzzy numbers based on positive and negative ideal points. Comput. Math. Appl. 58(10), 1769–1779 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhang, S.F., Liu, S.Y.: A GRA-based intuitionistic fuzzy multi-criteria group decision making method for personnel selection. Experts Syst. Appl. 38, 11401–11405 (2011)

    Article  Google Scholar 

  23. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8, 199–249 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  24. Peng, D.-H., Gao, G.-Y., Gao, Z.-F.: Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision-making. Appl. Math. Model. 37(8), 5837–5850 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  25. Chen S.H.: Ranking generalized fuzzy number with graded mean integration. In: Proceedings of the 8th International Fuzzy Systems Association World Congress, Taipei, Taiwan, Republic of China, vol. 2, pp. 899–902, 1999

    Google Scholar 

  26. Wei, S.H., Chen, S.M.: Fuzzy risk analysis based on interval-valued fuzzy numbers. Expert Syst. Appl. 36(2), 2285–2299 (2009)

    Article  Google Scholar 

  27. Zamali, T., Abu Osman, M.T., Mohd Lazim, A.: Equilibrium linguistic computation method for fuzzy group decision-making. Malaysian J. Math. Sci. 6(2), 225–242 (2012)

    MathSciNet  Google Scholar 

  28. Zamali, T., Lazim, M.A., Abu Osman, M.T.: Sustainable decision-making model for municipal solid-waste management: bifuzzy approach. J. Sustain. Sci. Manag. 7(1), 56–68 (2012)

    Google Scholar 

Download references

Acknowledgment

This research is supported by Cluster Grant (Dana Penyelidikan Khas), Universiti Sultan Zainal Abidin. This support is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Faculty of Informatics and Computing, University Sultan Zainal Abidin, Besut Campus, 22200, Besut, Terengganu, Malaysia

    Nurnadiah Zamri

  2. Department of Mathematics, Faculty of Science and Technology, University Malaysia Terengganu, Kuala Terengganu, Terengganu, 21030, Malaysia

    Lazim Abdullah

Authors
  1. Nurnadiah Zamri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lazim Abdullah
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nurnadiah Zamri .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, The University of Liverpool, Liverpool, UK

    Ke Chen

  2. Global Science and Technology Forum, Singapore, Singapore

    Anton Ravindran (Managing Editor, President) (Managing Editor, President)

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Zamri, N., Abdullah, L. (2016). Positive and Negative Interval Type-2 Generalized Fuzzy Number as a Linguistic Variable in Interval Type-2 Fuzzy Entropy Weight for MCDM Problem. In: Chen, K., Ravindran, A. (eds) Forging Connections between Computational Mathematics and Computational Geometry. Springer Proceedings in Mathematics & Statistics, vol 124. Springer, Cham. https://doi.org/10.5176/2251-1911_CMCGS14.30_10

Download citation

Publish with us

Policies and ethics

Search

Navigation