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An Advanced Distance Measure for Intuitionistic Fuzzy Sets and Its Application in Decision Making

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Recent Advances in Intelligent Information Systems and Applied Mathematics (ICITAM 2019)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 863))

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Abstract

The intuitionistic fuzzy set (IFS), which is the generalization of fuzzy set, is a very useful tool to deal with vagueness and ambiguity. In the application of IFSs, distance measure is an imperative device in decision sciences. Though a lot of distance measures have been defined in literature, many of them fail to satisfy some axioms of distance measure or encounter some counterintuitive cases. In this paper, a novel distance measure for IFSs is developed which is based on matrix norm and an increasing function; and accordingly, a comparative study is also carried out to demonstrate the efficiency and validity of the proposed novel distance measure. Furthermore, some numerical examples of pattern recognition and medical decision making are performed under this setting.

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References

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

    Article  Google Scholar 

  2. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

  3. Burillo, P., Bustince, H.: Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst. 78, 305–316 (1996)

    Article  MathSciNet  Google Scholar 

  4. Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst. 114(3), 505–518 (2000)

    Article  MathSciNet  Google Scholar 

  5. Grzegorzewski, P.: Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets Syst. 148(2), 319–328 (2004)

    Article  MathSciNet  Google Scholar 

  6. Chen, T.Y.: A note on distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets Syst. 158, 2523–2525 (2007)

    Article  MathSciNet  Google Scholar 

  7. Xu, Z.S.: Some similarity of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optim. Decis. Making 6, 109–121 (2007)

    Article  MathSciNet  Google Scholar 

  8. Zhang, H., Yu, L.: New distance measures between intuitionistic fuzzy sets and interval-valued fuzzy sets. Inf. Sci. 245, 181–196 (2013)

    Article  MathSciNet  Google Scholar 

  9. Boran, F.E., Akay, D.: A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition. Inf. Sci. 255, 45–57 (2014)

    Article  MathSciNet  Google Scholar 

  10. Wang, W., Xin, X.: Distance measure between intuitionistic fuzzy sets. Pattern Recogn. Lett. 26(13), 2063–2069 (2005)

    Article  Google Scholar 

  11. Park, J.H., Lim, K.M., Kwun, Y.C.: Distance measure between intuitionistic fuzzy sets and its application to pattern recognition. Korean Inst. Intell. Syst. 19(4), 556–561 (2009)

    Article  Google Scholar 

  12. Yang, Y., Chiclana, F.: Consistency of 2D and 3D distances of intuitionistic fuzzy sets. Expert Syst. Appl. 39(10), 8665–8670 (2012)

    Article  Google Scholar 

  13. Song, Y.F., Wang, X.D., Quan, W., Huang, W.: A new approach to construct similarity measure for intuitionistic fuzzy sets. Soft Comput. 1, 1–14 (2017)

    Google Scholar 

  14. Hatzimichailidis, A.G., Papakostas, G.A., Kaburlasos, V.G.: A novel distance measure of intuitionistic fuzzy sets and its application to pattern recognition problems. Int. J. Intell. Syst. 27, 396–409 (2012)

    Article  Google Scholar 

  15. Luo, M., Zhao, R.: A distance measure between intuitionistic fuzzy sets and its application in medical diagnosis. Artif. Intell. Med. 89, 34–39 (2018)

    Article  Google Scholar 

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

    Google Scholar 

  17. Kumar, K., Garge, H.: Connection number of set pair analysis based TOPSIS method on intuitionistic fuzzy sets and their application to decision making. Appl. Intell. 48, 2112–2119 (2017)

    Article  Google Scholar 

  18. Szmidt, E., Kacprzyk, J.: A similarity measure for intuitionistic fuzzy sets and its application in sup-porting medical diagnostic reasoning. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) Artificial Intelligence and Soft Computing - ICAISC 2004. LNCS, vol. 3070, pp. 388–393. Springer, Berlin (2004)

    MATH  Google Scholar 

  19. Xu, C.: Improvement of the distance between intuitionistic fuzzy sets and its applications. J. Intell. Fuzzy Syst. 33, 1563–1575 (2017)

    Article  Google Scholar 

  20. Luo, X., Li, W., Zhao, W.: Intuitive distance for intuitionistic fuzzy sets with applications in pattern recognition. Appl. Intell. 48, 2792–2808 (2017)

    Article  Google Scholar 

  21. Own, C.M.: Switching between type-2 fuzzy sets and intuitionistic fuzzy sets an application in medical diagnosis. Appl. Intell. 31, 283–291 (2009)

    Article  Google Scholar 

  22. De Kumar, S., Biswas, R., Roy, A.R.: An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets Syst. 117, 209–213 (2001)

    Article  Google Scholar 

  23. Pramanik, S., Mondal, K.: Intuitionistic fuzzy similarity measure based on tangent function and its application to multi-attribute decision making. Glob. J. Adv. Res. 2, 464–471 (2015)

    Google Scholar 

  24. Wei, C.P., Wang, P., Zhang, Y.Z.: Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications. Inf. Sci. 181, 4273–4286 (2011)

    Article  MathSciNet  Google Scholar 

  25. Szmidt, E., Kacprzyk, J.: Intuitionistic fuzzy sets in intelligent data analysis for medical diagnosis. In: International Conference on Computational Science, pp. 263–271. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  26. Talukdar, P., Dutta, P.: Disease diagnosis using an advanced distance measure for intuitionistic fuzzy sets. Int. Res. J. Microbiol. 7, 29–42 (2018)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Dibrugarh University, Dibrugarh, 786004, Assam, India

    Pranjal Talukdar & Palash Dutta

Authors
  1. Pranjal Talukdar
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  2. Palash Dutta
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Corresponding author

Correspondence to Pranjal Talukdar .

Editor information

Editors and Affiliations

  1. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Mexico

    Oscar Castillo

  2. Haldia Institute of Technology, Haldia, West Bengal, India

    Dipak Kumar Jana

  3. Maulana Abul Kalam Azad University of Technology, Haringhata, India

    Debasis Giri

  4. Haldia Institute of Technology, Haldia, India

    Arif Ahmed

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Talukdar, P., Dutta, P. (2020). An Advanced Distance Measure for Intuitionistic Fuzzy Sets and Its Application in Decision Making. In: Castillo, O., Jana, D., Giri, D., Ahmed, A. (eds) Recent Advances in Intelligent Information Systems and Applied Mathematics. ICITAM 2019. Studies in Computational Intelligence, vol 863. Springer, Cham. https://doi.org/10.1007/978-3-030-34152-7_24

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