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On some pseudometrics in the intuitionistic fuzzy environment

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Abstract

Three novel pseudometrics on the set of intuitionistic fuzzy numbers, called intuitionistic fuzzy cumulative pseudometrics, are first proposed. Then, the unified method to calculate the distances between intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and high-dimensional intuitionistic fuzzy sets based on such pseudometric is presented, and corresponding proofs are given.

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References

  • Atanassov KT (1983) Intuitionistic fuzzy sets. Central Technical Library, Bulgarian Academy Science, Sofia, Bulgaria, Report No. 1697/84

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

    Article  Google Scholar 

  • Atanassov KT (2012) On intuitionistic fuzzy sets theory. Springer, Heidelberg

    Book  Google Scholar 

  • Atanassov KT, Gargov G (1989) Interval valued intuitionistic fuzzy sets”. Fuzzy Sets Syst 31:343–349

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Cheng C, Xiao F, Cao Z (2019) A new distance for intuitionistic fuzzy sets based on similarity matrix. IEEE Access 7:70436–70446

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • Jiang Q, Jin X, Lee S-J, Yao S (2018) A new similarity/distance measure between intuitionistic fuzzy sets based on the transformed isosceles triangles and its applications to pattern recognition. Expert Syst Appl 116:439–453

    Article  Google Scholar 

  • Ke D, Song Y, Quan W (2018) New distance measure for Atanassov’s intuitionistic fuzzy sets and its application in decision making. Symmetry 10:429

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ngan RT, Son LH, Cuong BC, Ali M (2018) H-max distance measure of intuitionistic fuzzy sets in decision making. Appl Soft Comput 69:393–425

    Article  Google Scholar 

  • Shen F et al (2017) An extended intuitionistic fuzzy TOPSIS method based on a new distance measure with an application to credit risk evaluation. Inf Sci 428:105–119

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Wang WQ, Xin XL (2005) Distance measure between intuitionistic fuzzy sets. Pattern Recognit Lett 26:2063–2069. Lecture notes in artificial intelligence, vol 3885, pp 150–160 (2006)

  • Xu ZS (2007a) Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control Decis 22:215–219

    Google Scholar 

  • Xu ZS (2007b) Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optim Decis Mak 6:109–121

    Article  MathSciNet  Google Scholar 

  • Xu ZS (2007c) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Xu ZS, Chen J (2008) An overview of distance and similarity measures of intuitionistic fuzzy sets. Int J Uncertain Fuzziness Knowl Based Syst 16:529–555

    Article  MathSciNet  Google Scholar 

  • Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433

    Article  MathSciNet  Google Scholar 

  • Yang Y, Chiclana F (2009) Intuitionistic fuzzy sets: spherical representation and distances. Int J Intell Syst 24:399–420

    Article  Google Scholar 

  • Zhou L (2016) On Atanassov’s intuitionistic fuzzy sets in the complex plane and the field of intuitionistic fuzzy numbers. IEEE Trans Fuzzy Syst 2:253–259

    Article  Google Scholar 

Download references

Acknowledgements

We thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions.

Funding

This study was funded by the Doctoral Research Grant of the Southwest University of Science and Technology (Grant No. 16zx7112), and the “Thousand Talents Program” of Sichuan Province, P.R. China (Grant No. 17QR003).

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Authors and Affiliations

  1. School of Science, Southwest University of Science and Technology, Mianyang, 621010, Sichuan, China

    Lei Zhou & Kun Gao

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  1. Lei Zhou
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  2. Kun Gao
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Correspondence to Lei Zhou.

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Authors L. Zhou and K. Gao declare that they have no conflict of interest.

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Zhou, L., Gao, K. On some pseudometrics in the intuitionistic fuzzy environment. Soft Comput 25, 13797–13804 (2021). https://doi.org/10.1007/s00500-020-04705-1

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