A Note on the Centroid, Yager Index and Sample Mean for Fuzzy Numbers

  • Juan Carlos Figueroa-GarcíaEmail author
  • Jairo Soriano-Mendez
  • Miguel Alberto Melgarejo-Rey
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1000)


This paper compares three well known defuzzifications methods with the sample mean for fuzzy numbers, namely: Yager index, centroid and possibilistic mean. Fuzzy random variable generation was performed to carry out the comparison over the necessity of statistical independence. Our experimental evidence suggests the four approaches exhibits interesting differences among them.


Yager index Centroid Fuzzy numbers Random variables 


  1. 1.
    Carlsson, C., Fullér, R.: On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets Syst. 122(1), 315–326 (2001)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Chaudhuri, B., RosenFeld, A.: A modified Hausdorff distance between fuzzy sets. Inf. Sci. 118, 159–171 (1999)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Figueroa-García, J.C., Chalco-Cano, Y., Román-Flores, H.: Yager index and ranking for interval type-2 fuzzy numbers. IEEE Trans. Fuzzy Syst. 81(1), 93–102 (2018)zbMATHGoogle Scholar
  4. 4.
    Hung, W.L., Yang, M.S.: Similarity measures between type-2 fuzzy sets. Int. J. Uncertainty, Fuzziness Knowl.-Based Syst. 12(6), 827–841 (2004)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Kolmogorov, A.N.: Foundations of the Theory of Probability. Chelsea Publishing, New York (1956)zbMATHGoogle Scholar
  6. 6.
    Kruse, R.: The strong law of large numbers for fuzzy random variables. Inf. Sci. 28(1), 233–241 (1982)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Kwarkernaak, H.: Fuzzy random variables I. Inf. Sci. 15(1), 1–29 (1978)CrossRefGoogle Scholar
  8. 8.
    Kwarkernaak, H.: Fuzzy random variables II. Inf. Sci. 17(1), 153–178 (1979)Google Scholar
  9. 9.
    Pulido-López, D.G., García, M., Figueroa-García, J.C.: Fuzzy uncertainty in random variable generation: a cumulative membership function approach. Communications in Computer and Information Science, vol. 742, no. 1, pp. 398–407 (2017). Scholar
  10. 10.
    Varón-Gaviria, C.A., Barbosa-Fontecha, J.L., Figueroa-García, J.C.: Fuzzy uncertainty in random variable generation: an \(\alpha \)-cut approach. Lecture Notes in Artificial Intelligence, vol. 10363, no. 1, pp. 1–10 (2017)Google Scholar
  11. 11.
    Wu, D., Mendel, J.M.: A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets. Inf. Sci. 179(1), 1169–1192 (2009)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Yager, R.: A procedure for ordering fuzzy subsets of the unit interval. Inf. Sci. 24(1), 143–161 (1981)MathSciNetCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Juan Carlos Figueroa-García
    • 1
    Email author
  • Jairo Soriano-Mendez
    • 2
  • Miguel Alberto Melgarejo-Rey
    • 2
  1. 1.Universidad Distrital Francisco José de CaldasBogotáColombia
  2. 2.Engineering DepartmentUniversidad Distrital Francisco José de CaldasBogotáColombia

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