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A New Sign Distance-Based Ranking Method for Fuzzy Numbers

  • Conference paper
Proceedings of the 18th Asia Pacific Symposium on Intelligent and Evolutionary Systems - Volume 2

Part of the book series: Proceedings in Adaptation, Learning and Optimization ((PALO,volume 2))

Abstract

In this paper, a new sign distance-based ranking method for fuzzy numbers is proposed. It is a synthesis of geometric centroid and sign distance. The use of centroid and sign distance in fuzzy ranking is not new. Most existing methods (e.g., distance-based method [9]) adopt the Euclidean distance from the origin to the centroid of a fuzzy number. In this paper, a fuzzy number is treated as a polygon, in which a new geometric centroid for the fuzzy number is proposed. Since a fuzzy number can be represented in different shapes with different spreads, a new dispersion coefficient pertaining to a fuzzy number is formulated. The dispersion coefficient is used to fine-tune the geometric centroid, and subsequently sign distance from the origin to the tuned geometric centroid is considered. As discussed in [5-9], an ideal fuzzy ranking method needs to satisfy seven reasonable fuzzy ordering properties. As a result, the capability of the proposed method in fulfilling these properties is analyzed and discussed. Positive experimental results are obtained.

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References

  1. Zhang, F., Ignatius, J., Lim, C.P., Zhao, Y.: A new method for ranking fuzzy num-bers and its application to group decision making. Appl. Math. Model. 38, 1563–1582 (2014)

    Article  MathSciNet  Google Scholar 

  2. Flaig, A., Barner, K.E., Arce, G.R.: Fuzzy ranking: theory and applications. Signal Proces. 80, 1017–1036 (2000)

    Article  MATH  Google Scholar 

  3. Wang, Y.M., Chin, K.S., Poon, G.K.K., Yang, J.B.: Risk evaluation in failure mode and effects analysis using fuzzy weighted geometric mean. Expert Syst. Appl. 36, 1195–1207 (2009)

    Article  Google Scholar 

  4. Lin, F.T.: Fuzzy job-shop scheduling based on ranking level ( ) interval-valued fuzzy numbers. IEEE Trans. Fuzzy Syst. 10, 510–522 (2002)

    Article  Google Scholar 

  5. Wang, Z.X., Liu, Y.J., Fan, Z.P., Feng, B.: Ranking LR fuzzy number based on deviation degree. Inform. Sciences 179, 2070–2077 (2009)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  7. Asady, B.: The revised method of ranking LR fuzzy number based on deviation degree. Expert Syst. Appl. 37, 5056–5060 (2010)

    Article  Google Scholar 

  8. Yu, V.F., Chi, H.T.X., Shen, C.: Ranking fuzzy numbers based on epsilon-deviation degree. Appl. Soft Comput. 13, 3621–3627 (2013)

    Article  Google Scholar 

  9. Abbasbandy, S., Asady, B.: Ranking of fuzzy numbers by sign distance. Inform. Sciences 176, 2405–2416 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  10. Wang, Z.X., Liu, Y.J., Fan, Z.P., Feng, B.: Ranking LR fuzzy number based on deviation degree. Inform. Sciences 179, 2070–2077 (2009)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  12. Dat, L.Q., Yu, V.F., Chou, S.Y.: An improved ranking method for fuzzy numbers based on the centroid-index. J. Intell. Fuzzy Syst. 14, 413–419 (2012)

    MathSciNet  Google Scholar 

  13. Deng, Y., Zhenfu, Z., Qi, L.: Ranking fuzzy numbers with an area method using radius of gyration. Comput. Math. Appl. 51, 1127–1136 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  14. Chai, K.C., Tay, K.M., Lim, C.P.: A new fuzzy ranking method using fuzzy prefer-ence relations. In: IEEE International Conference on Fuzzy Systems (FUZZ), pp. 1–5 (2014)

    Google Scholar 

  15. Bourke, P.: Calculating the area and centroid of a polygon (1988), http://www.seas.upenn.edu/~sys502/extra_materials/Polygon%20Area%20and%20Centroid.pdf

  16. Abbasbandy, S., Hajjari, T.: A new approach for ranking of trapezoidal fuzzy numbers. Comput. Math. Appl. 57, 413–419 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  17. Chen, S.M., Sanguansat, K.: Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers. Expert Syst. Appl. 38, 2163–2171 (2011)

    Article  Google Scholar 

  18. Chai, K.C., Tay, K.M.: A perceptual computing-based approach for peer assessment. In: IEEE International Conference on System of Systems Engineering (SoSE), pp. 1–6 (2014)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Universiti Malaysia Sarawak, Kota Samarahan, Sarawak, Malaysia

    Kok Chin Chai & Kai Meng Tay

  2. Centre for Intelligent Systems Research, Deakin University, Burwood, Australia

    Chee Peng Lim

Authors
  1. Kok Chin Chai
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  2. Kai Meng Tay
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  3. Chee Peng Lim
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Corresponding author

Correspondence to Kok Chin Chai .

Editor information

Editors and Affiliations

  1. Faculty of Science and Technology Department of Infomatics, Kindai University, Higashi-Osaka, Japan

    Hisashi Handa

  2. Department of Computer Science and Intelligent Systems, Osaka Prefecture University, Osaka, Japan

    Hisao Ishibuchi

  3. School of Computer Engineering, Nanyang Technological University, Singapore, Singapore

    Yew-Soon Ong

  4. Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore

    Kay-Chen Tan

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Chai, K.C., Tay, K.M., Lim, C.P. (2015). A New Sign Distance-Based Ranking Method for Fuzzy Numbers. In: Handa, H., Ishibuchi, H., Ong, YS., Tan, KC. (eds) Proceedings of the 18th Asia Pacific Symposium on Intelligent and Evolutionary Systems - Volume 2. Proceedings in Adaptation, Learning and Optimization, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-13356-0_5

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  • DOI: https://doi.org/10.1007/978-3-319-13356-0_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13355-3

  • Online ISBN: 978-3-319-13356-0

  • eBook Packages: EngineeringEngineering (R0)

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