Skip to main content
SpringerLink
Log in

On a new distance measure of three-parameter interval numbers and its application to pattern recognition

  • Fuzzy systems and their mathematics
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

In this paper, a new distance measure of three-parameter interval numbers is proposed, which considers not only the particularity of the center of gravity in a three-parameter interval number but also the influence of risk attitudes of decision makers. Some properties of the proposed distance measure are also proved from the perspective of metric spaces. Based on the proposed distance measure of three-parameter interval numbers, a new type of distance measure of LR-type fuzzy numbers is introduced. By considering different left and right shape functions in the proposed distance measure of LR-type fuzzy numbers, some new distance measures of triangular fuzzy numbers and normal fuzzy numbers are obtained. It is shown from some examples that the proposed distance measures of triangular fuzzy numbers and normal fuzzy numbers may overcome drawbacks of some existing similarity measures of triangular fuzzy numbers and normal fuzzy numbers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Chen SM (1996) New methods for subjective mental workload assessment and fuzzy risk analysis. J Cybern 27(5):449–472

    MATH  Google Scholar 

  • Chen SJ, Chen SM (2003) Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. IEEE Trans Fuzzy Syst 11(1):45–56

    Article  Google Scholar 

  • Cao LY, Li MZ, Sadiq RH et al (2015) Developing environmental indices using fuzzy numbers power average (FN-PA) operator. Int J Syst Assur Eng Manage 6(2):139–149

    Article  Google Scholar 

  • Diamond P, Körner R (1997) Extended fuzzy linear models and least-squares estimates. Comput Math Appl 33:15–32

    Article  MathSciNet  Google Scholar 

  • Dubois D, Prade H (1978) Operations on fuzzy numbers. Int J Syst Sci 9(6):613–626

    Article  MathSciNet  Google Scholar 

  • Dubois D, Prade H (1988) Possibility Theory. Plenum Press, New York

    Book  Google Scholar 

  • Fu S (2016) Three-parameter interval grey number multi-attribute decision making method based on information entropy. Math Comput Appl 21(2):1–8

    MathSciNet  Google Scholar 

  • Gong YB, Jiang YD, Liang XC (2015) Similarity measurement for normal cloud models based on fuzzy similarity measure. Syst Eng 33(9):133–137

    Google Scholar 

  • Hsieh CH, Chen SH (1999) Similarity of generalized fuzzy numbers with graded mean integration representation, In: Proceedings of 8th international fuzzy systems association world congress vol 2, pp 551–555

  • Hu BQ (2010) The basis of fuzzy theory. Wuhan University Press, Wuhan

    Google Scholar 

  • Kaleva O (1987) Fuzzy differential equations. Fuzzy Sets Syst 24(3):301–317

    Article  MathSciNet  Google Scholar 

  • Li DY (1997) Knowledge representation in KDD based on linguistic atoms. J Comput Sci Technol 12(6):481–496

    Article  Google Scholar 

  • Li HL, Guo CH, Qiu WR (2011) Similarity measurement between normal cloud models. Acta Electr Sin 39(11):2561–2567

  • Luo D, Wang X (2012) The multi-attribute grey target decision method for attribute value within three-parameter interval grey number. Appl Math Model 36(5):1957–1963

    Article  MathSciNet  Google Scholar 

  • Nozari H, Jafari-Eskandari M, Kamfirozi MH, Mozafari A (2014) Using numerical taxonomy and combined bulls-eye-shapley weighting method in order to ranking websites of Iranian universities by three-parameter interval gray numbers. Arab J Sci Eng 39(4):3299–3305

    Article  Google Scholar 

  • Seetha H, Saravanan R (2007) Short term electric load prediction using Fuzzy BP. J Comput Inf Technol 15(3):267–282

    Article  Google Scholar 

  • Sengupta A, Pal TK (2000) On comparing interval numbers. Eur J Oper Res 127(1):28–43

    Article  MathSciNet  Google Scholar 

  • Wang X, Dang YG (2015) Dynamic multi-attribute decision making methods with three-parameter interval grey number. Control Decis 30(9):1623–1629

    MATH  Google Scholar 

  • Wang JF, Liu SF (2011) Method of ranking three parameters interval grey numbers and its application in interval DEA model. Syst Eng Electr 33(1):106–109

    Google Scholar 

  • Xie JJ, Liu CP (2006) Fuzzy mathematics method and its application. Huazhong University of Science and Technology Press, Wuhan

    Google Scholar 

  • Yan SL, Liu SF, Wu LF (2015) A group grey target decision making method with three parameter interval grey number based on prospect theory. Control Decis 30(1):105–109

    MATH  Google Scholar 

  • Yang MS, Ko CH (1996) On a class of fuzzy \(c\)-numbers clustering procedures for fuzzy data. Fuzzy Sets Syst 84(1):49–60

    Article  MathSciNet  Google Scholar 

  • Yang MS, Hung WL, Chang-Chien SJ (2005) On a similarity measure between \(LR\)-type fuzzy numbers and its application to database acquisition. Int J Intell Syst 20:1001–1016

    Article  Google Scholar 

  • Yang NG, Han WW (2010) The approach degree of a modified normal fuzzy set. J Shantou Univ Nat Sci Ed 25(1):7–11

    Google Scholar 

  • Yang BH, Fang ZG, Zhou W, Liu J (2012) Incidence decision model of multi-attribute interval grey number based on information reduction operator. Control Decis 27(2):182–186

    MATH  Google Scholar 

  • Zhang Y, Zhao DN, Li DY (2004) The similar cloud and the measurement method. Inf Control 33(2):129–132

    Google Scholar 

Download references

Acknowledgements

This research is supported by the National Natural Science Foundation of China (Grant Nos. 61603307 and 62006154), the Fundamental Research Funds for the Central Universities (Grant No. 2682020ZT107, JBK2102037) and the Grant from MOE (Ministry of Education in China) Project of Humanities and Social Sciences (Grant No. 19YJCZH048, 20XJCZH016).

Author information

Authors and Affiliations

  1. School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, Sichuan, China

    Xingxing He & Keyun Qin

  2. School of Economics Information Engineering, Southwestern University of Finance and Economics, Chengdu, 611130, Sichuan, China

    Yingfang Li

Authors
  1. Xingxing He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yingfang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Keyun Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yingfang Li.

Ethics declarations

Conflict of interest

The author declares that he/she has no conflicts of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, X., Li, Y. & Qin, K. On a new distance measure of three-parameter interval numbers and its application to pattern recognition. Soft Comput 25, 8595–8607 (2021). https://doi.org/10.1007/s00500-021-05741-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-021-05741-1

Keywords

Search

Navigation