Skip to main content

A novel projection-based distance measure for interval-valued intuitionistic multiplicative clustering algorithm

Soft Computing volume 27, pages 2369–2383 (2023)Cite this article

Abstract

Distance measure is an effective tool for describing the difference between two vectors. Many scholars have proposed a lot of distance measures between the intuitionistic fuzzy sets. However, there are few works about the interval-valued intuitionistic multiplicative (IVIM) distance measure. The few research achievements are not sufficient to deal with the problems involving the distance between two interval-valued intuitionistic multiplicative sets (IVIMSs). Thus, there still exist some shortages in fully describing the difference between two IVIMSs. In this paper, we first propose an improved distance measure, the projection-based distance measure, which can reflect the difference between two objects more accurately with IVIM information. After that, a new method is introduced to determine the experts’ weights based on the projection-based distance measure. Then, to handle the group decision making problem in which the weights of experts are unknown, we use the proposed projection-based distance measure to construct the similarity matrix in Boole clustering method. Finally, the clustering method is applied to the customer classification problem to test the reliability of the method.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1

Data availability

Due to the nature of this research, participants of this study did not agree for their data to be shared publicly, so supporting data is not available.

References

  • Danish Lohani QM, Rinki S, Pranab KM (2018) Novel adaptive clustering algorithms based on a probabilistic similarity measure over Atanassov intuitionistic fuzzy set. IEEE Trans Fuzzy Syst 26:3715–3729

    Article  Google Scholar 

  • He LH, Wang LQ, Zhang LY (2014) A method for determining the experts’ weights of multi-attribute group decision-making based on clustering analysis. Oper Res Manag Sci 6:65–72

    Google Scholar 

  • Jiang Y, Xu ZS, Xu JP (2014) Interval-valued intuitionistic multiplicative set. Int J Uncertain Fuzziness Knowl Based Syst 22:385–406

    Article  MathSciNet  MATH  Google Scholar 

  • Le HS (2017) Measuring analogousness in picture fuzzy sets: from picture distance measures to picture association measures. Fuzzy Optim Decis Making 16:359–378

    Article  MathSciNet  MATH  Google Scholar 

  • Li YL, Zhu YH, Wu JW (2017) Research on expert weighting method based on D-S evidence theory. Adv Inf Technol 13:3043–3047

    Google Scholar 

  • Liao HC, Zhang C, Luo L (2018) A multiple attribute group decision making method based on two novel intuitionistic multiplicative distance measures. Inf Sci 467:766–783

    Article  MathSciNet  MATH  Google Scholar 

  • Sahu M, Gupta A, Mehra A (2017) Hierarchical clustering of interval-valued intuitionistic fuzzy relations and its application to elicit criteria weights in MCDM problems. Opsearch 6:388–416

    Article  MathSciNet  MATH  Google Scholar 

  • She R, Liu SY, Fan PY (2017) Amplifying inter-message distance: on information divergence measures in big data. IEEE Access 5:24105–24119

    Article  Google Scholar 

  • Tian ZP, Nie RX, Wang JQ, Li L (2019) Group multigranular linguistic QFD for prioritizing service designs with combined weighting method. Expert Syst 36:101–105

    Article  Google Scholar 

  • Valderrama JFB, Valderrama DLB (2018) On LAMDA clustering method based on typicality degree and intuitionistic fuzzy sets. Expert Syst Appl 107:196–221

    Article  Google Scholar 

  • Wang WQ, Xin XL (2011) Distance measure between intuitionistic fuzzy sets. Math Pract Theory 17:38–42

    MathSciNet  Google Scholar 

  • Wang Y, Zang QB (2006) The application of Boole matrix fuzzy clustering used in topographic diagrams data mining. J Sci Teachers’ Coll Univ 26:71–75

    Google Scholar 

  • Wang Z, Xu ZS, Liu SS (2011) A netting clustering analysis method under intuitionistic fuzzy environment. Appl Soft Comput 11:5558–5564

    Article  Google Scholar 

  • Wu HY, Xu ZS, Ren PJ, Liao HC (2018) Hesitant fuzzy linguistic projection model to multi-criteria decision making for hospital decision support systems. Comput Ind Eng 115:449–458

    Article  Google Scholar 

  • Xia MM, Xu ZS, Liao HC (2013) Preference relations based on intuitionistic multiplicative information. IEEE Trans Fuzzy Syst 21:113–133

    Article  Google Scholar 

  • Xu ZS (2007) Multiple-attribute group decision making with different formats of preference information on attributes. IEEE Trans Syst Man Cybernet Part B 37:1500–1511

    Article  Google Scholar 

  • Xu GL, Liu F (2013) An approach to group decision making based on interval multiplicative and fuzzy preference relations by using projection. Appl Math Model 37:3929–3943

    Article  MathSciNet  MATH  Google Scholar 

  • Xu ZS, Wu JJ (2010) Intuitionistic fuzzy C-means clustering algorithms. J Syst Eng Electron 4:580–590

    Article  Google Scholar 

  • Xu ZS, Chen J, Wu JJ (2008) Clustering algorithm for intuitionistic fuzzy sets. Inf Sci 19:3775–3790

    Article  MathSciNet  MATH  Google Scholar 

  • Xu ZS, Tang J, Liu SS (2011) An orthogonal algorithm for clustering intuitionistic fuzzy information. Inf Int Interdiscipl J 14:65–78

    Google Scholar 

  • Xu DW, Xu ZS, Liu SS, Zhao H (2013) A spectral clustering algorithm based on intuitionistic fuzzy information. Knowl-Based Syst 53:20–26

    Article  Google Scholar 

  • Ye J (2017) Simplified neutrosophic harmonic averaging projection-based method for multiple attribute decision-making problems. Int J Mach Learn Cybern 8:981–987

    Article  Google Scholar 

  • Yu DJ, Merigó JM, Zhou LG (2013) Interval-valued multiplicative intuitionistic fuzzy preference relations. Int J Fuzzy Syst 15:412–422

    MathSciNet  Google Scholar 

  • Yue ZL (2011) An extended TOPSIS for determining weights of decision makers with interval numbers. Knowl-Based Syst 24:146–153

    Article  Google Scholar 

  • Yue ZL (2012) An Application of the projection method to determine weights of decision makers for group decision making. Scientia Iranica 19(3):872–878

    Article  Google Scholar 

  • Yue ZL, Jia YY (2015) A direct projection-based group decision-making methodology with crisp values and interval data. Soft Comput 21:2395–2405

    Article  MATH  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  • Zhao H, Xu ZS, Liu SS, Wang Z (2012) Intuitionistic fuzzy MST clustering algorithms. Comput Ind Eng 4:1130–1140

    Article  Google Scholar 

  • Zhao H, Xu ZS, Wang Z (2013) Intuitionistic fuzzy clustering algorithm based on Boole matrix and association measure. Int J Inf Technol Decis Mak 12:95–118

    Article  Google Scholar 

  • Zhou W, He JM, Yu DJ (2013) Accurate method of obtaining decision expert weights in intuitionistic fuzzy group decision making. Control Decis 28:716–720

    Google Scholar 

Download references

Funding

The work was supported in part by the China National Natural Science Foundation (No. 71771155).

Author information

Authors and Affiliations

  1. The 63rd Research Institute, National University of Defense Technology, Nanjing, 210007, China

    Ming Liu

  2. Department of General Education, Army Engineering University of PLA, Nanjing, 210007, China

    Hua Zhao

  3. Business School, State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, 610064, China

    Zeshui Xu

  4. College of Humanities and Social Sciences, Nanjing Agricultural University, Nanjing, 210095, China

    Feng Cui

Authors
  1. Ming Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hua Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zeshui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Feng Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Hua Zhao or Zeshui Xu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Liu, M., Zhao, H., Xu, Z. et al. A novel projection-based distance measure for interval-valued intuitionistic multiplicative clustering algorithm. Soft Comput 27, 2369–2383 (2023). https://doi.org/10.1007/s00500-022-07765-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-022-07765-7

Keywords

  • Interval-valued intuitionistic multiplicative set
  • Projection-based distance measure
  • Expert weights determination
  • Clustering algorithm
  • Group of experts’ opinions