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Similarity measure on incomplete imprecise interval information and its applications

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Abstract

The concept of fuzzy numbers has been generalized to intuitionistic fuzzy interval numbers (IFINs) to solve problems with imprecision in the information modeling. Similarity measure is an important tool to measure the degree of resemblance between any two objects in real-life situations and is applied in many areas such as decision making, image processing, pattern recognition, etc. In this paper, a new distance-based similarity measure between IFINs is proposed using which a similarity measure on incomplete imprecise interval information is attempted. Some properties of the proposed distance measure and similarity measure are studied using illustrative examples. The nominal decreasing and increasing properties based on the proposed distance measure and similarity measure are proved. Further, the superiority of the proposed similarity measure over familiar existing methods is shown by different numerical examples and the proposed measure is applied to technique for order preference by similarity to ideal solution method under interval-valued intuitionistic fuzzy environment. Finally, the applicability of the proposed method in pattern recognition problems is illustrated.

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References

  1. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–356

    Article  Google Scholar 

  2. Atanassov K, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31(3):343–349

    Article  MathSciNet  Google Scholar 

  3. Nayagam VLG, Muralikrishnan S, Sivaraman G (2011) Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets. Expert Syst Appl 38:1464–1467

    Article  Google Scholar 

  4. Xu ZS, Chen J (2007) An approach to group decision making based on interval-valued intuitionistic judgement matrices. Syst Eng Theory Pract 27:126–133

    Article  Google Scholar 

  5. Xu ZS (2007) 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 

  6. Ye J (2013) Interval-valued intuitionistic fuzzy cosine similarity measures for multiple attribute decision-making. Int J Gen Syst 42(8):883–891

    Article  MathSciNet  Google Scholar 

  7. Chen SM, Cheng SH, Lan TC (2016) A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Inf Sci 343–344:15–40

    Article  MathSciNet  Google Scholar 

  8. Li DF, Cheng CT (2002) New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognit Lett 23:221–225

    Article  Google Scholar 

  9. Mitchell HB (2003) On the Dengfeng–Chuntian similarity measure and its application to pattern recognition. Pattern Recognit Lett 24:3101–3104

    Article  Google Scholar 

  10. Xu ZS (2007) On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognitions. J Southeast Univ (Engl Ed) 23(1):139–143

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  12. Chen SM (1995) Measures of similarity between vague sets. Fuzzy Sets Syst 74(2):217–223

    Article  MathSciNet  Google Scholar 

  13. Chen SM (1997) Similarity measures between vague sets and between elements. IEEE Trans Syst Man Cybern 27(1):153–158

    Article  MathSciNet  Google Scholar 

  14. Egghe L (2010) Good properties of similarity measures and their complementarity. J Am Soc Inf Sci Technol 61(10):2151–2160

    Article  Google Scholar 

  15. Hong DH, Kim C (1999) A note on similarity measures between vague sets and between elements. Inf Sci 115:83–96

    Article  MathSciNet  Google Scholar 

  16. Hung WL, Yang MS (2004) Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recognit Lett 25:1603–1611

    Article  Google Scholar 

  17. Hung WL, Yang MS (2007) Similarity measures of intuitionistic fuzzy sets based on Lp metric. Int J Approx Reason 46:120–136

    Article  Google Scholar 

  18. Liang Z, Shi P (2003) Similarity measures on intuitionistic fuzzy sets. Pattern Recognit Lett 24:2687–2693

    Article  Google Scholar 

  19. Liu W (2005) New similarity measures between intuitionistic fuzzy sets and between elements. Math Comput Model 42:61–70

    Article  MathSciNet  Google Scholar 

  20. Song Y, Wang X (2015) A new similarity measure between intuitionistic fuzzy sets and the positive definiteness of the similarity matrix. Pattern Anal Appl. https://doi.org/10.1007/s10044-015-0490-2

  21. Ye J (2011) Cosine similarity measures for intuitionistic fuzzy sets and their applications. Math Comput Model 53(1–2):91–97

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  24. Wang WQ, Xin XL (2005) Distance measure between intuitionistic fuzzy sets. Pattern Recognit Lett 26(13):2063–2069

    Article  Google Scholar 

  25. Xu ZS, Chen J (2008) An overview of distance and similarity measures of intuitionistic sets. Int J Uncertain Fuzziness Knowl Based Syst 16(4):529–555

    Article  MathSciNet  Google Scholar 

  26. Lee W, Shen HW, Zhang G (2009) Research on fault diagnosis of turbine based on similarity measures between interval-valued intuitionistic fuzzy sets. In: IEEE international conference on measuring technology and mechatronics automation, pp 700–703

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

    Article  Google Scholar 

  28. Atanassov K (1994) Operators over interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 64:159–174

    Article  MathSciNet  Google Scholar 

  29. Xu ZS, Chen J (2007) On geometric aggregation over interval-valued intuitionistic fuzzy information. In: Proceedings of fourth international conference on fuzzy systems and knowledge discovery (FSKD 2007), vol 2, pp 466–471

  30. Sivaraman G, Nayagam VLG, Ponalagusamy R (2014) A complete ranking of incomplete interval information. Expert Syst Appl 41:1947–1954

    Article  Google Scholar 

  31. Hwang CL, Yoon K (1981) Multiple attributes decision making methods and applications. Springer, Berlin

    Book  Google Scholar 

  32. Dhanasekaran P, Jeevaraj S, Nayagam VLG (2018) A complete ranking of trapezoidal fuzzy numbers and its applications to multi-criteria decision making. Neural Comput Appl 30(11):3303–3315

    Article  Google Scholar 

  33. Nayagam VLG, Sivaraman G (2011) Ranking of interval-valued intuitionistic fuzzy sets. Appl Soft Comput 11:3368–3372

    Article  Google Scholar 

  34. Nayagam VLG, Jeevaraj S, Dhanasekaran P (2017) An intuitionistic fuzzy multi criteria decision making method based on non-hesitance score for interval-valued intuitionistic fuzzy sets. Soft Comput 21(23):7077–7082

    Article  Google Scholar 

  35. Nayagam VLG, Dhanasekaran P, Jeevaraj S (2016) A complete ranking of incomplete trapezoidal information. J Intell Fuzzy Syst 30(6):3209–3225

    Article  Google Scholar 

  36. Nayagam VLG, Jeevaraj S, Dhanasekaran P (2016) A linear ordering on the class of trapezoidal intuitionistic fuzzy numbers. Expert Syst Appl 60:269–279

    Article  Google Scholar 

  37. Nayagam VLG, Jeevaraj S, Dhanasekaran P (2017) A new ranking principle for ordering trapezoidal intuitionistic fuzzy numbers. Complexity, Article ID 3049041, 1–24

  38. Nayagam VLG, Jeevaraj S, Dhanasekaran P (2018) An improved ranking method for comparing trapezoidal intuitionistic fuzzy numbers and its applications to multicriteria decision making. Neural Comput Appl 30(2):671–682

    Article  Google Scholar 

  39. Nayagam VLG, Jeevaraj S, Geetha S (2016) Total ordering for intuitionistic fuzzy numbers. Complexity 21(S2):54–66

    Article  MathSciNet  Google Scholar 

  40. Nayagam VLG, Jeevaraj S, Sivaraman G (2016) Complete ranking of intuitionistic fuzzy numbers. Fuzzy Inf Eng 8:237–254

    Article  MathSciNet  Google Scholar 

  41. Nayagam VLG, Jeevaraj S, Sivaraman G (2016) Total ordering defined on the set of all intuitionistic fuzzy numbers. J Intell Fuzzy Syst 30(4):2015–2028

    Article  Google Scholar 

  42. Nayagam VLG, Jeevaraj S, Sivaraman G (2017) Rank Incomplete trapezoidal information. Soft Comput 21:7125–7140

    Article  Google Scholar 

  43. Nayagam VLG, Venkateshwari G, Sivaraman G (2008) Ranking of intuitionistic fuzzy numbers. In: IEEE International conference on fuzzy systems (IEEE World Congress on Computational Intelligence 2008), pp 1971–1974

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Tiruchirappalli, 620 015, India

    V. Lakshmana Gomathi Nayagam

  2. Department of Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur, Andhra Pradesh, 522 502, India

    Dhanasekaran Ponnialagan

  3. ABV-Indian Institute of Information Technology and Management, Gwalior, 474 015, India

    S. Jeevaraj

Authors
  1. V. Lakshmana Gomathi Nayagam
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  2. Dhanasekaran Ponnialagan
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  3. S. Jeevaraj
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Correspondence to Dhanasekaran Ponnialagan.

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Nayagam, V.L.G., Ponnialagan, D. & Jeevaraj, S. Similarity measure on incomplete imprecise interval information and its applications. Neural Comput & Applic 32, 3749–3761 (2020). https://doi.org/10.1007/s00521-019-04277-8

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  • DOI: https://doi.org/10.1007/s00521-019-04277-8

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