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Submitted
December 9, 2022
Accepted
November 2, 2023
Published
November 30, 2023
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Abstract

Even though a large number of research studies have been presented in recent years for ranking and comparing fuzzy numbers, the majority of existing techniques suffer from plenty of shortcomings. These shortcomings include counterintuitiveness, the inability to distinguish the fuzzy number and its partnered image, and the inconsistent ability to distinguish symmetric fuzzy numbers and fuzzy numbers that represent the compensation of areas. To overcome the cited drawbacks, this paper suggests a unified distance that multiplies the centroid value (weighted mean value) of the fuzzy number on the horizontal axis and a linear sum of the
distances of the centroid points of the left and right fuzziness areas from the original
point through an indicator. The indicator reflects the attitude of the left and
right fuzziness of the fuzzy number, we can call it the indicator of fuzziness. To use
this technique, the membership functions of the fuzzy numbers need not be linear.
That is the proposed approach can also rank the fuzzy numbers with non-linear
membership functions. The suggested technique is highly convenient and reliable to
discriminate the symmetric fuzzy numbers and the fuzzy numbers having compensation
of areas. The advantages of the proposed approach are illustrated through
examples that are common for a wide range of numerical studies and comparisons
with several representative approaches, that existed in the literature.

Keywords

Fuzzy number Ranking Unified distance Centroid value Indicator of fuzziness

Article Details

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How to Cite
Prasad, S. P., & Shatabdi Sinha. (2023). A Unified Distance Approach for Ranking Fuzzy Numbers and Its Comparative Reviews. Journal of the Indonesian Mathematical Society, 29(3), 347–371. https://doi.org/10.22342/jims.29.3.1337.347-371
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References

  1. Abbasbandy, S. and Asady, B. “Ranking of fuzzy numbers by sign distance.” Information
  2. Sciences, 176(16), (2006), 2405–2416.
  3. Abbasbandy, S. and Hajjari, T. “A new approach for ranking of trapezoidal fuzzy numbers.”
  4. Computers Mathematics with Applications, 57(3), (2009), 413–419.
  5. Abbasi Shureshjani, R. and Darehmiraki, M. “A new parametric method for ranking fuzzy
  6. numbers.” Indagationes Mathematicae, 24(3), (2013), 518–529.
  7. Asady, B. “Revision of distance minimization method for ranking of fuzzy numbers.” Applied
  8. Mathematical Modelling, 35(3), (2011), 1306–1313.
  9. Asady, B. and Zendehnam, A. “Ranking fuzzy numbers by distance minimization.” Applied
  10. Mathematical Modelling, 31(11), (2007), 2589–2598.
  11. Barazandeh Hayati, Y. and Ghazanfari, B. “A novel method for ranking generalized fuzzy
  12. numbers with two different heights and its application in fuzzy risk analysis.” Iranian Journal
  13. of Fuzzy Systems, 18(2), (2021), 81–91.
  14. Bortolan, G. and Degani, R. “A review of some methods for ranking fuzzy subsets.” Fuzzy
  15. Sets and Systems, 15(1), (1985), 1–19.
  16. Chen, S.-H. “Ranking fuzzy numbers with maximizing set and minimizing set.” Fuzzy Sets
  17. and Systems, 17(2), (1985), 113–129.
  18. Cheng, C.-H. “A new approach for ranking fuzzy numbers by distance method.” Fuzzy Sets
  19. and Systems, 95(3), (1998), 307–317.
  20. Chi, H. T. X. and Yu, V. F. “Ranking generalized fuzzy numbers based on centroid and rank
  21. index.” Applied Soft Computing, 68, (2018), 283–292
  22. Choobineh, F. and Li, H. “An index for ordering fuzzy numbers.” Fuzzy Sets and Systems,
  23. (3), (1993), 287–294.
  24. Chu, T.-C. and Tsao, C.-T. “Ranking fuzzy numbers with an area between the centroid point
  25. and original point.” Computers Mathematics with Applications, 43(1), (2002), 111–117.
  26. Chutia, R. “Ranking of fuzzy numbers by using value and angle in the epsilon-deviation
  27. degree method.” Applied Soft Computing, 60, (2017), 706–721.
  28. Chutia, R. and Chutia, B. “A new method of ranking parametric form of fuzzy numbers
  29. using value and ambiguity.” Applied Soft Computing, 52, (2017), 1154–1168.
  30. Deng, Y., Zhenfu, Z. and Qi, L. “Ranking fuzzy numbers with an area method using radius
  31. of gyration.” Computers Mathematics with Applications, 51(6), (2006), 1127–1136.
  32. Dombi, J. and J´on´as, T. “Ranking trapezoidal fuzzy numbers using a parametric relation
  33. pair.” Fuzzy Sets and Systems, 399, (2020), 20–43. Fuzzy Intervals.
  34. Dubois, D. and Prade, H. “Operations on fuzzy numbers.” International Journal of Systems
  35. Science, 9(6), (1978), 613–626.
  36. Fortemps, P. and Roubens, M. “Ranking and defuzzification methods based on area compensation.” Fuzzy Sets and Systems, 82(3), (1996), 319–330.
  37. Hajjari, T. “Ranking fuzzy numbers by similarity measure index.” ICACS’20. Association for
  38. Computing Machinery, New York, NY, USA (2020). 12–16.
  39. Jain, R. “Decisionmaking in the presence of fuzzy variables.” IEEE Transactions on Systems,
  40. Man, and Cybernetics, 6(10), (1976), 698–703.
  41. Liou, T.-S. and Wang, M.-J. J. “Ranking fuzzy numbers with integral value.” Fuzzy Sets and
  42. Systems, 50(3), (1992), 247–255.
  43. Mao, Q. S. “Ranking fuzzy numbers based on weighted distance.” Journal of Physics: Conference Series, 1176, (2019), 032007.
  44. Nasseri, S., Zadeh, M., Kardoost, M. and Behmanesh, E. “Ranking fuzzy quantities based
  45. on the angle of the reference functions.” Applied Mathematical Modelling, 37(22), (2013),
  46. –9241.
  47. Nasseri, S. H., Taghi-Nezhad, N. and Ebrahimnejad, A. “A note on ranking fuzzy numbers
  48. with an area method using circumcenter of centroids.” Fuzzy Information and Engineering,
  49. (2), (2017), 259–268.
  50. Nguyen, T.-L. “Methods in ranking fuzzy numbers: A unified index and comparative reviews.” Fuzzy Calculus Theory and Its Applications, 1.
  51. Prasad, S. and Sinha, A. “Ranking fuzzy numbers with mean value of points and comparative
  52. reviews.” Journal of Scientific Research, 14(3), (2022), 755–771.
  53. Prasad, S. and Sinha, A. “Ranking fuzzy numbers with unified integral value and comparative
  54. reviews.” Journal of Scientific Research, 14(1), (2022), 131–151.
  55. Rao, P. B. “Defuzzification method for ranking fuzzy numbers based on centroids and maximizing and minimizing set.” Decision Science Letters, 8, (2019), 411–428.
  56. Rao, P. P. B. and Shankar, N. R. “Ranking fuzzy numbers with an area method using
  57. circumcenter of centroids.” Fuzzy Information and Engineering, 5(1), (2013), 3–18.
  58. Rezvani, S. “Ranking generalized exponential trapezoidal fuzzy numbers based on variance.”
  59. Applied Mathematics and Computation, 262, (2015), 191–198.
  60. Soccoro Garcia, M. and Teresa Lamata, M. “A modification of the index of liou and wang
  61. for ranking fuzzy number.” International Journal of Uncertainty, Fuzziness and KnowledgeBased Systems, 15(04), (2007), 411–424.
  62. Wang, Y.-J. and Lee, H.-S. “The revised method of ranking fuzzy numbers with an area
  63. between the centroid and original points.” Computers Mathematics with Applications, 55(9),
  64. (2008), 2033–2042.
  65. Yager, R. R. “Ranking fuzzy subsets over the unit interval.” “1978 IEEE Conference on
  66. Decision and Control including the 17th Symposium on Adaptive Processes,” (1978). 1435–
  67. Yager, R. R. “On choosing between fuzzy subsets.” 9(2), (1980), 151–154
  68. Yager, R. R. “A procedure for ordering fuzzy subsets of the unit interval.” Information
  69. Sciences, 24(2), (1981), 143–161.
  70. Yu, V. F., Chi, H. T. X., Dat, L. Q., Phuc, P. N. K. and wen Shen, C. “Ranking generalized
  71. fuzzy numbers in fuzzy decision making based on the left and right transfer coefficients and
  72. areas.” Applied Mathematical Modelling, 37(16), (2013), 8106–8117.
  73. Yu, V. F., Chi, H. T. X. and wen Shen, C. “Ranking fuzzy numbers based on epsilon-deviation
  74. degree.” Applied Soft Computing, 13(8), (2013), 3621–3627.
  75. Yua, V. F. and Dat, L. Q. “An improved ranking method for fuzzy numbers with integral
  76. values.” Applied Soft Computing, 14(1), (2014), 603–608.
  77. Zadeh, L. A. “Fuzzy sets.” Information and Control, 8(3), (1965), 338–353.
  78. Zhang, F., Ignatius, J., Lim, C. P. and Zhao, Y. “A new method for ranking fuzzy numbers and its application to group decision making.” Applied Mathematical Modelling, 38(4),
  79. (2014), 1563–1582