Similarity Measure for Fuzzy Number Based on Distances and Geometric Shape Characteristics

  • Nur Amira Mat SaffieEmail author
  • Khairul A. Rasmani
  • Nor Hashimah Sulaiman
Conference paper


Fuzzy similarity measure is a very useful technique in the area of fuzzy decision making. Although various techniques have been developed to measure fuzzy similarity, it can be observed that several limitations still exist. In particular, there are methods that produce inconsistent degrees of similarity with regard to the compared fuzzy numbers which do not reflect the geometric characteristic of the fuzzy numbers. In this paper, a new fuzzy similarity measure for generalized trapezoidal fuzzy number (GTFN) is developed based on distance and geometric shape characteristics like height, area, centre, and perimeter to overcome the problems. Three existing fuzzy similarity measures were selected and compared with the proposed measure. The analysis on eight sets of GTFNs using the fuzzy similarity measures shows that the proposed measure produced a reasonable interpretation of similarity degree based on the graphical representation. Hence, this measure can serve as an alternative method in calculating the degree of similarity of compared GTFNs. The introduced concept in the proposed measure will enable a broader implementation of fuzzy similarity measures in real-world decision making.


Similarity measure Fuzzy similarity measure Generalized trapezoidal fuzzy number Geometric distance Geometric shape characteristics 



This research work is funded by the Ministry of Education, Malaysia under the Fundamental Research Grant Scheme (FRGS) with reference number 600-RMI/FRGS TD 5/3 (1/2015). The authors would also like to thank the Research Management Institute (RMI), Universiti Teknologi MARA, Malaysia.


  1. 1.
    Luo, L., Ren, H.: A new similarity measure-based MADM method under dynamic interval-valued intuitionistic fuzzy environment. AMSE J. 59(1), 84–92 (2016)Google Scholar
  2. 2.
    Beg, I., Ashraf, S.: Similarity measures for fuzzy sets. Appl. Comput. Math. 8(2), 192–202 (2009)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Khorshidi, H.A., Nikfalazar, S.: An improved similarity measure for generalized fuzzy numbers and its application to fuzzy risk analysis. Appl. Soft Comput. 52, 478–486 (2017). Scholar
  4. 4.
    Patra, K., Mondal, S.K.: Fuzzy risk analysis using area and height based similarity measure on generalized trapezoidal fuzzy numbers and its application. Appl. Soft Comput. 28, 276–284 (2015). Scholar
  5. 5.
    Chen, S.-J., Chen, S.-M.: A new method to measure the similarity between fuzzy numbers. In: 2001 The 10th IEEE International Conference on Fuzzy Systems, Melbourne, Australia, pp. 1123–1126. IEEE (2001)Google Scholar
  6. 6.
    Chen, S.-J.: A new similarity measure of generalized fuzzy numbers based on geometric-mean averaging operator. In: 2006 IEEE International Conference on Fuzzy Systems, Vancouver, Canada, pp. 1879–1886. IEEE (2006)Google Scholar
  7. 7.
    Xu, Z., Shang, S., Qian, W., Shu, W.: A method for fuzzy risk analysis based on the new similarity of trapezoidal fuzzy numbers. Expert Syst. Appl. 37(3), 1920–1927 (2010). Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Nur Amira Mat Saffie
    • 1
    Email author
  • Khairul A. Rasmani
    • 1
  • Nor Hashimah Sulaiman
    • 1
  1. 1.Faculty of Computer and Mathematical SciencesUniversiti Teknologi MARAShah AlamMalaysia

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