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A Straightforward Advanced Ranking Approach of Fuzzy Numbers

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Smart Intelligent Computing and Applications

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 159))

Abstract

Fuzzy set is commonly explored to deal with uncertainty generally involved in decision-making process. Moreover, ranking of fuzzy numbers plays efficient role in the process in order to adopt appropriate action by a decision-maker in any real-world problems under uncertain environment. A few numbers of ranking approaches have been encountered in last few decades. However, it is observed that the existing approaches are more often situation dependent and have lots of drawbacks. In this regard, this paper presents a straightforward general approach based on the concept of the exponential area of the input fuzzy numbers. The outputs produced by this present approach are more efficient in comparison to the other ranking approaches and successfully work in all situations. The efficiency of the approach has been showcased by comparing with existing recent approaches. Furthermore, the ranking approach has been successfully applied in medical investigation problem and observed that the results obtained by the approach corroborate the analytical result and human intuition as well.

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References

  1. Zadeh, L.A.: Fuzzy sets. Inf. Control. 8, 338–356 (1965)

    Article  Google Scholar 

  2. Fortemps, P., Roubens, M.: Ranking and defuzzification methods based on area compensation. Fuzzy Sets Syst. 82(3), 319–330 (1996)

    Article  MathSciNet  Google Scholar 

  3. Wang, Y.J., Lee, H.S.: The revised method of ranking fuzzy numbers with an area between the centroid and original points. Comput. Math. Appl. 55(9), 2033–2042 (2008)

    Article  MathSciNet  Google Scholar 

  4. Nejad, A.M., Mashinchi, M.: Ranking fuzzy numbers based on the areas on the left and the right sides of fuzzy number. Comput. Math. Appl. 61(2), 431–442 (2011)

    Article  MathSciNet  Google Scholar 

  5. 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. Modell. 37(16–17), 8106–8117 (2013)

    Article  MathSciNet  Google Scholar 

  6. Wang, Z.X., Liu, Y.J., Fan, Z.P., Feng, B.: Ranking L-R fuzzy number based on deviation degree. Inf. Sci. 179(13), 2070–2077 (2009)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  8. Hajjari, T., Abbasbandy, S.: A note on the revised method of ranking L-R fuzzy number based on deviation degree. Expert Syst. Appl. 38(10), 13491–13492 (2011)

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. Chu, T.C., Tsao, C.T.: Ranking fuzzy numbers with an area between the centroid point and original point. Comput. Math. Appl. 43(1–2), 111–117 (2002)

    Article  MathSciNet  Google Scholar 

  11. Wang, Y.M., Yang, J.B., Xu, D.L., Chin, K.S.: On the centroids of fuzzy numbers. Fuzzy Sets Syst. 157(7), 919–926 (2006)

    Article  MathSciNet  Google Scholar 

  12. Cheng, C.H.: A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets Syst. 95(3), 307–317 (1998)

    Article  MathSciNet  Google Scholar 

  13. Abbasbandy, S., Asady, B.: Ranking of fuzzy numbers by sign distance. Inf. Sci. 176(16), 2405–2416 (2006)

    Article  MathSciNet  Google Scholar 

  14. Asady, B., Zendehnam, A.: Ranking fuzzy numbers by distance minimization. Appl. Math. Modell. 31(11), 2589–2598 (2007)

    Article  Google Scholar 

  15. Liou, T.S., Wang, M.J.J.: Ranking fuzzy numbers with integral value. Fuzzy Sets Syst. 50(3), 247–255 (1992)

    Article  MathSciNet  Google Scholar 

  16. Chen, C.C., Tang, H.C.: Ranking nonnormal p-norm trapezoidal fuzzy numbers with integral value. Comput. Math. Appl. 56(9), 2340–2346 (2008)

    Article  MathSciNet  Google Scholar 

  17. Yu, V.F., Dat, L.Q.: An improved ranking method for fuzzy numbers with integral values. Appl. Soft Comput. 14(Part C), 603–608 (2014)

    Article  Google Scholar 

  18. Kim, K., Park, K.S.: Ranking fuzzy numbers with index of optimism. Fuzzy Sets Syst. 35(2), 143–150 (1990)

    Article  MathSciNet  Google Scholar 

  19. Choobineh, F., Li, H.: An index for ordering fuzzy numbers. Fuzzy Sets Syst. 54(3), 287–294 (1993)

    Article  MathSciNet  Google Scholar 

  20. Garcia, M.S., Lamata, M.T.: A modification of the index of liou and wang for ranking fuzzy numbers. Int. J. Uncert. Fuzziness Knowledge-Based Syst. 15(04), 411–424 (2007)

    Article  MathSciNet  Google Scholar 

  21. Kumar, A., Singh, P., Kaur, A., Kaur, P.: A new approach for ranking nonnormal p-norm trapezoidal fuzzy numbers. Comput. Math. Appl. 61(4), 881–887 (2011)

    Article  MathSciNet  Google Scholar 

  22. Chutia, R., Gogoi, R., Datta, D.: Ranking p-norm generalised fuzzy numbers with different left height and right height using integral values. Math. Sci. 9(1), 1–9 (2015)

    Article  MathSciNet  Google Scholar 

  23. 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 

  24. 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, Part 2), 6833–6842 (2009)

    Article  Google Scholar 

  25. Chen, S.M., Sanguansat, K.: Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers. Expert Syst. Appl. 38(3), 2163–2171 (2011)

    Article  Google Scholar 

  26. Abbasbandy, S., Hajjari, T.: A new approach for ranking of trapezoidal fuzzy numbers. Comput. Math. Appl. 57(3), 413–419 (2009)

    Article  MathSciNet  Google Scholar 

  27. Dutta, P., Dash S.R.: Medical decision making via the arithmetic of generalized triangular fuzzy numbers. Open Cybern. Syst. J. 12(1) (2018)

    Article  Google Scholar 

  28. Dutta, P., Boruah, H., Ali, T.: Fuzzy arithmetic with and without using \(\alpha \)-cut method: a comparative study. Int. J. Latest Trends Comput. 2(1), 99–107 (2011)

    Google Scholar 

  29. Yager, R.R.: Ranking fuzzy subsets over the unit interval. In: 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes, January, pp. 1435–1437 (1978)

    Google Scholar 

  30. Nasseri, S.H., Zadeh, M.M., Kardoost, M., Behmanesh, E.: Ranking fuzzy quantities based on the angle of the reference functions. Appl. Math. Modell. 37(22), 9230–9241 (2013)

    Article  MathSciNet  Google Scholar 

  31. Rezvani, S.: Ranking generalized exponential trapezoidal fuzzy numbers based on variance. Appl. Math. Computat. 262, 191–198 (2015)

    Article  MathSciNet  Google Scholar 

  32. Chutia, R., Chutia, B.: A new method of ranking parametric form of fuzzy numbers using value and ambiguity. Appl. Soft Comput. 52, 1154–1168 (2017)

    Article  Google Scholar 

  33. Chen, S.M., Munif, A., Chen, G.S., Liu, V., Kuo, B.C.: Fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights. Expert Syst. Appl. 39(7), 6320–6334 (2012)

    Article  Google Scholar 

  34. Zadeh, L.A.: Biological application of the theory of fuzzy sets and systems. In: Proctor, L.D. (ed.) Biocybernetics of the Central Nervous System, pp. 199–212. Little Brown, Boston, MA (1969)

    Google Scholar 

  35. Sanchez, E.: Resolution of composite fuzzy relation equations. Inf. Control. 30, 38–48 (1976)

    Article  MathSciNet  Google Scholar 

  36. Sanchez, E.: Medical diagnosis and composite fuzzy relations. In: Gupta, M.M., Ragade, R.K., Yager, R.R. (eds.) Advances in Fuzzy Set Theory and Applications, pp. 437–444. North-Holland, Amsterdam (1979)

    Google Scholar 

  37. Çelik, Y., Yamak, S.: Fuzzy soft set theory applied to medical diagnosis using fuzzy arithmetic operations. J. Inequalities Appl. pp. 1–9 (2013)

    Google Scholar 

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Correspondence to Palash Dutta .

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Dutta, P. (2020). A Straightforward Advanced Ranking Approach of Fuzzy Numbers. In: Satapathy, S., Bhateja, V., Mohanty, J., Udgata, S. (eds) Smart Intelligent Computing and Applications . Smart Innovation, Systems and Technologies, vol 159. Springer, Singapore. https://doi.org/10.1007/978-981-13-9282-5_45

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