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A Novel Fuzzy Decision-Making Method Using Entropy Weights-Based Correlation Coefficients Under Intuitionistic Fuzzy Environment

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Abstract

In this communication, a new two parametric intuitionistic fuzzy entropy has been introduced and validated. Some of the properties of the proposed measure are also discussed. In addition to this, a new multiple attribute decision-making (MADM) method based on weighted correlation coefficients and the proposed IF entropy is introduced. The necessity of proposed MADM method has been reasonably established. The method is effectively explained with the help of two numerical examples, and the performance is genuinely compared with some existing MADM methods in the literature. Attribute weights play an important role in the solution of MADM problem. In this paper, two methods of obtaining attributes weights are discussed.

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References

  1. Atanassov, K.T.: Intutionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)

    Article  MATH  Google Scholar 

  2. Atanassov, K.T.: Intutionistic Fuzzy Sets. Springer, New York (1999)

    Book  MATH  Google Scholar 

  3. Burillo, P., Bustince, H.: Entropy on intutionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst. 118, 305–316 (2001)

    MathSciNet  MATH  Google Scholar 

  4. Chen, T., Li, C.: Determining objective weights with intutionistic fuzzy entropy measures: a comparative analysis. Inf. Sci. 180, 4207–4222 (2010)

    Article  Google Scholar 

  5. Chen, T.Y., Tsao, C.Y.: The interval-valued fuzzy TOPSIS method and experimental analysis. Fuzzy Sets Syst. 159(11), 1410–1428 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chu, A.T.W., Kalaba, R.E., Spingarn, K.: A comparison of two methods for determining the weights of belonging to fuzzy sets. J. Optim. Theor. Appl. 27, 531–538 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  7. Choo, E.U., Wedley, W.C.: Optimal criterion weights in repetitive multi-criteria decision making. J. Oper. Res. Soc. 36, 983–992 (1985)

    Article  MATH  Google Scholar 

  8. Ejegwa, P.A., Akowe, S.O., Otene, P.M., Ikyule, J.M.: An overview on intuitionistic fuzzy sets. Int. J. Sci. Technol. Res. 3(3), 142–145 (2014)

    Google Scholar 

  9. Fan, Z.P.: Complicated multiple attribute decision making: theory and applications. Ph.D. Dissertation. Northeastern University, Shenyang, China (1996)

  10. Gerstenkorn, T., Manko, J.: Correlation of intuitionistic fuzzy sets. Fuzzy Sets Syst. 44, 39–43 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hung, W.L., Yang, M.S.: Fuzzy entropy on intutionistic fuzzy sets. Int. J. Intell. Syst. 21, 443–451 (2006)

    Article  MATH  Google Scholar 

  12. Hwang, C.L., Lin, M.J.: Group Decision Making Under Multiple Criteria: Methods and Applications. Springer, Berlin (1987)

    Book  MATH  Google Scholar 

  13. Havdra, M.E., Charavat, F.: Quantification method of classification processes: concept of structural \(\alpha \) entropy. Kybernetica 3, 30–35 (1967)

    MathSciNet  Google Scholar 

  14. Joshi, R., Kumar, S.: A new approach in multiple attribute decision making using \(R\)-norm entropy and Hamming distance measure. Int. J. Inf. Manag. Sci. 27(3), 253–268 (2016)

    Google Scholar 

  15. Joshi, R., Kumar, S.: An \((R, S)\)-norm fuzzy information measure with its application in multiple attribute decision making. Comput. Appl. Math. (2017). https://doi.org/10.1007/s40314-017-0491-4

    MATH  Google Scholar 

  16. Joshi, R., Kumar, S.: A new exponential fuzzy entropy of order \((\alpha, \beta )\) and its applications in multiple attribute decision making problems. Commun. Math. Stat. 5(2), 213–229 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  17. Joshi, R., Kumar, S.: Parametric \((R; S)\)-norm entropy on intuitionistic fuzzy sets with a new approach in multiple attribute decision making. Fuzzy Inf. Eng. 9, 181–203 (2017)

    Article  MathSciNet  Google Scholar 

  18. Joshi, R., Kumar, S.: A new intuitionistic fuzzy entropy of order-\(\alpha \) with applications in multiple attribute decision-making. Adv. Intell. Syst. Comput. 546, 212–219 (2017)

    Google Scholar 

  19. Joshi, R., Kumar, S.: An \((R^{\prime }, S^{\prime })\)-norm fuzzy relative information measure and its applications in strategic decision-making. Comput. Appl. Math. (2018). https://doi.org/10.1007/s40314-018-0582-x

    MathSciNet  MATH  Google Scholar 

  20. Joshi, R., Kumar, S.: An intuitionistic fuzzy information measure of order \((\alpha, \beta )\) with a new approach in supplier selection problems using an extended VIKOR method. J. Appl. Math. Comput. (2018). https://doi.org/10.1007/s12190-018-1202-z

    Google Scholar 

  21. Joshi, R., Kumar, S.: An intuitionistic fuzzy \((\delta, \gamma )\)-norm entropy with its application in supplier selection problem. Comput. Appl. Math. (2018). https://doi.org/10.1007/s40314-018-0656-9

    MathSciNet  MATH  Google Scholar 

  22. Joshi, R., Kumar, S.: A new parametric intuitionistic fuzzy entropy and its applications in multiple attribute decision making. Int. J. Appl. Comput. Math. (2018). https://doi.org/10.1007/s40819-018-0486-x

    MathSciNet  MATH  Google Scholar 

  23. Joshi, R., Kumar, S.: Application of interval-valued intuitionistic fuzzy \(R\)-norm entropy in multiple attribute decision making. Int. J. Inf. Manag. Sci. 28(3), 233–251 (2017)

    MathSciNet  Google Scholar 

  24. Joshi, R., Kumar, S., Gupta, D., Kaur, H.: A Jensen-\(\alpha \)-norm dissimilarity measure for intuitionistic fuzzy sets and its applications in multiple attribute decision making. Int. J. Fuzzy Syst. 20(4), 1188–1202 (2018)

    Article  MathSciNet  Google Scholar 

  25. Joshi, R., Kumar, S.: A dissimilarity Jensen-Shannon divergence measure for intuitionistic fuzzy sets. Int. J. Intell. Syst. (2018). https://doi.org/10.1002/int.22026

    Google Scholar 

  26. Joshi, R., Kumar, S.: An exponential Jensen fuzzy divergence measure with applications in multiple attribute decision making. Math. Probl. Eng. (2018). https://doi.org/10.1155/2018/4342098

  27. Li, D.F.: Multiattribute decision-making models and methods using intutionistic fuzzy sets. J. Comput. Syst. Sci. 70, 73–85 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  28. Liu, H., Wang, G.: Multi-criteria decision-making methods based on intutionistic fuzzy sets. Eur. J. Oper. Res. 179, 220–233 (2007)

    Article  MATH  Google Scholar 

  29. Szmidt, E., Kacprzyk, J.: Using intutionistic fuzzy sets in group decision-making. Control Cybern. 31, 1037–1054 (2002)

    MATH  Google Scholar 

  30. Saaty, T.L.: The Analytical Hierarchy Process. McGraw-Hill, New York (1980)

    MATH  Google Scholar 

  31. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  32. Sharma, B.D., Mittal, D.P.: New non-additive measures of entropy of discrete probability distribution. J. Math. Sci. 10, 28–40 (1975)

    MathSciNet  Google Scholar 

  33. Tsallis, C.: Possible generalization of Boltzman–Gibbs ststistics. J. Stat. Phys. 52, 480–487 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  34. Vlachos, I.K., Sergiadis, G.D.: Intuitionistic fuzzy information—applications to pattern recognition. Pattern Recognit. Lett. 28, 197–206 (2007)

    Article  Google Scholar 

  35. Wang, J., Wang, P.: Intuitionistic linguistic fuzzy multi-criteria decision-making method based on intuitionistic fuzzy entropy. Control Decis. 27, 1694–1698 (2012)

    MathSciNet  Google Scholar 

  36. Wang, W., Xin, X.: Distance measure between intuitionistic fuzzy sets. Pattern Recognit. Lett. 26, 2063–2069 (2005)

    Article  Google Scholar 

  37. Ye, J.: Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment. Eur. J. Oper. Res. 205, 202–204 (2010)

    Article  MATH  Google Scholar 

  38. Zadeh, L.A.: Probability measures of fuzzy events. J. Math. Anal. Appl. 23, 421–427 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  39. Zhang, Q., Jiang, S.: A note on information entropy measure for vague sets. Inf. Sci. 178, 4184–4191 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors are thankful to the anonymous referees for their precious and constructive suggestions which enhanced our knowledge and improved this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Maharishi Markandeshwar University, Mullana-Ambala, 133207, India

    Rajesh Joshi & Satish Kumar

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  1. Rajesh Joshi
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  2. Satish Kumar
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Correspondence to Rajesh Joshi.

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Joshi, R., Kumar, S. A Novel Fuzzy Decision-Making Method Using Entropy Weights-Based Correlation Coefficients Under Intuitionistic Fuzzy Environment. Int. J. Fuzzy Syst. 21, 232–242 (2019). https://doi.org/10.1007/s40815-018-0538-8

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  • DOI: https://doi.org/10.1007/s40815-018-0538-8

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