Skip to main content
SpringerLink
Log in

Some novel q-rung orthopair fuzzy correlation coefficients based on the statistical viewpoint with their applications

  • Original Research
  • Published:
Journal of Ambient Intelligence and Humanized Computing Aims and scope Submit manuscript

Abstract

The q-rung orthopair fuzzy set is a recent development to study the ambiguous information present in a system. This is more powerful and comprehensive than the notion of fuzzy set, intuitionistic fuzzy set, and Pythagorean fuzzy set. The space of uncertain information described by q-rung orthopair fuzzy set is found to be more extensive and flexible due to the inclusion of the parameter q. The aim of the present study is to propose some new correlation coefficients for q-rung orthopair fuzzy sets. The existing correlation coefficients concerning q-rung orthopair fuzzy sets describe the extent of linear association between two q-rung orthopair fuzzy sets not the nature or direction. The proposed correlation coefficients determine degree as well as the nature of correlation (positive or negative) between two q-rung orthopair fuzzy sets. The proposed correlation coefficients receive their values in [− 1, 1]. We obtain the new correlation coefficients for q-rung orthopair fuzzy sets analogous to the crisp correlation coefficients. We expound the advantages of the proposed correlation coefficients using the notions of structured linguistic variables and degree of confidence. The comparative analysis of the proposed correlation coefficients with the existing non-standard fuzzy correlation/compatibility measures appropriately justifies the advantages. For the comparative analysis, we use synthetic as well as real data. The newly proposed measures show the greater degree of confidence in pattern classification and capture the linguistic variables more effectively. We also investigate the reasonability of the proposed correlation coefficients on the real data of the Iris plant. Moreover, we observe that the results of the proposed correlation coefficients in medical diagnosis are consistent with the existing compatibility measures. At last, we introduce a novel correlation-based closeness coefficient for solving a multi-attribute decision-making problem in q-rung orthopair fuzzy environment.

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

Similar content being viewed by others

References

  • Akram M, Alsulami S, Karaaslan F, Khan A (2021) q-Rung orthopair fuzzy graphs under Hamacher operators. J Intell Fuzzy Syst 40(1):1367–1390

    Google Scholar 

  • Akram M, Shahzadi G (2020) A hybrid decision-making model under q-rung orthopair fuzzy Yager aggregation operators. Granul Comp. https://doi.org/10.1007/s41066-020-00229-z

    Article  Google Scholar 

  • Akram M, Shahzadi G, Peng X (2020) Extension of Einstein geometric operators to multi-attribute decision-making under q-rung orthopair fuzzy information. Granul Comp. https://doi.org/10.1007/s41066-020-00233-3

    Article  Google Scholar 

  • Ali MI (2018) Another view on q-rung orthopair fuzzy sets. Int J Intell Syst 33(11):2139–2153

    Google Scholar 

  • Atanassov K (1986) Intuitionistic fuzzy sets: theory and applications. Springer Pyhsica-Verlag, New York

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Bustince H, Burillo P (1995) Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 74(2):237–244

    MathSciNet  MATH  Google Scholar 

  • Chaudhuri BB, Bhattacharya A (2001) On correlation between two fuzzy sets. Fuzzy Sets Syst 118(3):447–456

    MathSciNet  MATH  Google Scholar 

  • Chiang DA, Lin NP (1999) Correlation of fuzzy sets. Fuzzy Sets Syst 102(2):221–226

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Chen SM, Chang CH (2015) A novel similarity measure between Atanssovas intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition. Inf Sci 291:96–114

    Google Scholar 

  • Cuong BC, Kreinovich V (2013) Picture Fuzzy Sets-a new concept for computational intelligence problems. In Proceedings of Third World Congress on Information and Communication Technologies (WICT) Hanoi, Vietnam, December 15–18, pp. 1–6

  • Das S, Malakar D, Kar S, Pal T (2019) Correlation measure of hesitant fuzzy soft sets and their application in decision making. Neural Comput Appl 31(4):1023–1039

    Google Scholar 

  • Du WS (2018) Minkowski-type distance measures for generalized orthopair fuzzy sets. Int J Intell Syst 33(4):802–817

    Google Scholar 

  • Du WS (2019) Correlation and correlation coefficient of generalized orthopair fuzzy sets. Int J Intell Syst 34(4):564–583

    Google Scholar 

  • Ganie AH, Singh S, Bhatia PK (2020) Some new correlation coefficients of picture fuzzy sets with applications. Neural Comput Appl 32:12609–12625

    Google Scholar 

  • Gao J, Liang ZL, Shang J, Xu ZS (2018) Continuities, derivatives and differentials of q-rung orthopair fuzzy functions. IEEE Trans Fuzzy Syst 27(8):1687–1699

    Google Scholar 

  • Gao J, Xu Z (2019) Differential calculus of interval-valued q-rung orthopair fuzzy functions and their applications. Int J Intell Syst 34(12):3190–3219

    Google Scholar 

  • Garg H (2016) A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making processes. Int J Intell Syst 31(12):1234–1252

    Google Scholar 

  • Garg H (2020) A new possibility degree measure for interval-valued q-rung orthopair fuzzy sets in decision making. Int J Intell Syst. https://doi.org/10.1002/int.22308

    Article  Google Scholar 

  • Garg H, Chen SM (2020) Multi attribute group decision-making based on neutrality aggregation operators of q-rung orthopair fuzzy sets. Inform Sci 517:427–447

    MathSciNet  MATH  Google Scholar 

  • Gerstenkorn T, Mańko J (1991) Correlation of intuitionistic fuzzy sets. Fuzzy Sets Syst 44(1):39–43

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Gundogdu FK, Kahraman C (2019) A novel fuzzy TOPSIS method using emerging interval-valued spherical fuzzy sets. Eng Appl Artif Intell 85:307–323

    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(4):396–409

    Google Scholar 

  • Hinde CJ, Patching RS, McCoy SA (2007) Inconsistent intuitionistic fuzzy sets and mass assignment. Developments in fuzzy sets, intuitionistic fuzzy sets, generalized nets and related topics, Foundations, 133–153

  • Hong DH, Hwang SY (1995) Correlation of intuitionistic fuzzy sets in probability spaces. Fuzzy Sets Syst 75(1):77–81

    MathSciNet  MATH  Google Scholar 

  • Hong DH, Kim C (1999) A note on similarity measures between vague sets and between elements. Inf Sci 115(1–4):83–96

    MathSciNet  MATH  Google Scholar 

  • Hung WL, Yang MS (2004) Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recognit Lett 25(14):1603–1611

    Google Scholar 

  • Hung WL, Wu JW (2002) Correlation of intuitionistic fuzzy sets by centroid method. Inform Sci 144(1–4):219–225

    MathSciNet  MATH  Google Scholar 

  • Jan N, Zedam L, Mahmood T, Rak E, Ali Z (2020) Generalized dice similarity measures for q-rung orthopair fuzzy sets with applications. Complex Intelligent Syst 6:545–558

    Google Scholar 

  • Jiang Q, Jin X, Lee SJ, Yao S (2019) 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

    Google Scholar 

  • Joshi BP, Singh A, Bhatt PK, Vaisla KS (2018) Interval valued q-rung orthopair fuzzy sets and their properties J. Intell Fuzzy Syst 35(3):5225–5230

    Google Scholar 

  • Khan MJ, Kumam P, Shutaywi M (2020a) Knowledge measure for q-rung orthopair fuzzy sets. Int J Intell Syst. https://doi.org/10.1002/int.22313

    Article  Google Scholar 

  • Khan MJ, Ali MI, Kumam P (2020b) A new ranking technique for q-rung orthopair fuzzy values. Int J Intell Syst. https://doi.org/10.1002/int.22311

    Article  Google Scholar 

  • Li Y, Olson DL, Qin Z (2007) Similarity measures between intuitionistic fuzzy (vague) sets: a comparative analysis. Pattern Recognit Lett 28(2):278–285

    Google Scholar 

  • Li Z, Wei G, Wang R, Wu J, Wei C, Wei Y (2020) EDAS method for multiple attribute group decision-making under q-rung orthopair fuzzy environment. Technol Econ Dev Eco 26(1):86–102

    Google Scholar 

  • Li H, Yin S, Yang Y (2019) Some preference relations based on q-rung orthopair fuzzy sets. Int J Intell Sys 34(11):2920–2936

    Google Scholar 

  • Liu D, Peng D, Liu Z (2019) The distance measures between q-rung orthopair hesitant fuzzy sets and their application in multiple criteria decision making. Int J Intell Syst 34(9):2104–2121

    Google Scholar 

  • Liu PD, Wang P (2018) Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. Int J Intell Syst 33(2):259–280

    Google Scholar 

  • Liu PD, Liu JL (2018) Some q-rung orthopai fuzzy Bonferroni mean operators and their application to multi-attribute group decision making. Int J Intell Syst 33(2):315–347

    Google Scholar 

  • Liu PD, Wang P (2019) Multiple-attribute decision making based on Bonferroni operators of q-rung orthopair fuzzy numbers. IEEE Trans Fuzzy Syst 27(5):834–848

    Google Scholar 

  • Liu PD, Chen SM, Wang P (2018a) Multiple-attribute group decision-making based on q-rung orthopair fuzzy power Maclaurin symmetric mean operators. IEEE Trans Syst Man Cybern Syst 99:1–16

    Google Scholar 

  • Liu P, Shahzadi G, Akram M (2020a) Specific types of q-rung picture fuzzy Yager aggregation operators for decision-making. Int J Comput Int Sys 13(1):1072–1091

    Google Scholar 

  • Liu P, Akram M, Sattar A (2020b) Extensions of prioritized weighted aggregation operators for decision-making under complex q-rung orthopair fuzzy information. J Intell Fuzzy Syst 39(5):7469–7493

    Google Scholar 

  • Liu Z, Wang X, Li L, Zhao X, Liu P (2020c) q-rung orthopair fuzzy multi-attribute group decision-making method based on normalized bidirectional projection method and generalized knowledge-based entropy measure. J Amb Intel Hum Comp. https://doi.org/10.1007/s12652-020-02433-w

    Article  Google Scholar 

  • Liu ZM, Liu PD, Liang X (2018b) Multiple attribute decision-making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q-rung orthopair fuzzy environment. Int J Intell Syst 33(9):1900–1928

    Google Scholar 

  • Luqman A, Akram M, Koam AN (2019) Granulation of hyper network models under the q-rung picture fuzzy environment. Mathematics 7(6):496

    Google Scholar 

  • Mahmood T, Ullah K, Khan Q, Jan N (2018) An approach towards decision making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Comput Appl 31(11):7041–7053

    Google Scholar 

  • Mendel JM, John RI (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2):117–127

    Google Scholar 

  • Mitchell HB (2004) A correlation coefficient for intuitionistic fuzzy sets. Int J Intell Syst 19(5):483–490

    MATH  Google Scholar 

  • Miyamoto S (2005) Remarks on basics of fuzzy sets and fuzzy multisets. Fuzzy Set Syst 156(3):427–431

    MathSciNet  MATH  Google Scholar 

  • Park DG, Kwun YC, Park JH, Park IY (2009) Correlation coefficient of interval-valued intuitionistic fuzzy sets and its application to multiple attribute group decision making problems. Math Comput Model 50(9–10):1279–1293

    MathSciNet  MATH  Google Scholar 

  • Peng X, Dai J, Garg H (2018) Exponential operation and aggregation operator for q-rung orthopair fuzzy set and their decision-making method with a new score function. Int J Intell Syst 33(11):2255–2282

    Google Scholar 

  • Peng X, Liu L (2019) Information measures for q-rung orthopair fuzzy sets. Int J Intell Syst 34(8):1795–1834

    Google Scholar 

  • Peng X, Yuan H, Yang Y (2017) Pythagorean fuzzy information measures and their applications. Int J Intell Syst 32(10):991–1029

    Google Scholar 

  • Qin Y, Cui X, Huang M, Zhong Y, Tang Z, Shi P (2019a) Archimedean Muirhead aggregation operators of q-rung orthopair fuzzy numbers for multicriteria group decision-making. Complexity. https://doi.org/10.1155/2019/3103741

    Article  MATH  Google Scholar 

  • Qin Y, Qi Q, Scott PJ, Jiang X (2019b) Multiple criteria group decision making based onArchimedean power partitioned Muirhead mean operators of q-rung orthopair fuzzy numbers. PLoS ONE 14(9):e0221759. https://doi.org/10.1371/journal.pone.0221759

    Article  Google Scholar 

  • Qin Y, Qi Q, Scott PJ, Jiang X (2020) Multiple criteria decision making based on weighted Archimedean power partitioned Bonferroni aggregation operators of generalized orthopair membership grades. Soft Comput 24:12329–12355

    Google Scholar 

  • Ren PJ, Xu ZS, Gou XJ (2016) Pythagorean fuzzy TODIM approach to multi-criteria decision making. Appl Soft Comput 42:246–259

    Google Scholar 

  • Saha A, Majumder P, Dutta D, Debnath BK (2020) Multi-attribute decision making using q-rung orthopair fuzzy weighted fairly aggregation operators. J Amb Intel Hum Comp. https://doi.org/10.1007/s12652-020-02551-5

    Article  Google Scholar 

  • Singh S, Lalotra S (2018) Generalized correlation coefficients of the hesitant fuzzy sets and the hesitant fuzzy soft sets with application in group decision-making. J Intell Fuzzy Syst 35(3):3821–3833

    Google Scholar 

  • Singh S, Lalotra S (2019) On generalized correlation coefficients of the hesitant fuzzy sets with their application to clustering analysis. Comput Appl Math 38(1):11

    MathSciNet  MATH  Google Scholar 

  • Singh S, Ganie AH (2020a) On some correlation coefficients in Pythagorean fuzzy environment with applications. Int J Intell Syst 35(4):682–717

    Google Scholar 

  • Singh S, Ganie AH (2020b) Applications of picture fuzzy similarity measures in pattern recognition, clustering and MADM. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2020.114264

    Article  Google Scholar 

  • Sharma S, Singh S (2019) On some generalized correlation coefficients of the fuzzy sets and fuzzy soft sets with application in cleanliness ranking of public health centres. J Intell Fuzzy Syst 36(4):3671–3683

    Google Scholar 

  • Szmidt E, Kacprzyk J (2004) A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. In: Rutkowski L, Siekmann JH, Tadeusiewicz R, Zadeh LA (eds) ICAISC. Springer, Zakopane, Poland, pp 388–393

    Google Scholar 

  • Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539

    MATH  Google Scholar 

  • Ullah K, Hassan N, Mahmood T, Jan N, Mazlan H (2019) Evaluation of investment policy based on multi-attribute decision-making using interval-valued T-spherical fuzzy aggregation operators. Symmetry 11:357. https://doi.org/10.3390/sym11030357

    Article  Google Scholar 

  • Wei G, Wei C, Wang J, Gao H, Wei Y (2018) Some q-rung orthopair fuzzy Maclaurin symmetric mean operators and their applications to potential evaluation of emerging technology commercialisation. Int J Intell Syst 34(1):50–81

    Google Scholar 

  • Wei G, Wei Y (2018) Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications. Int J Intell Syst 33(3):634–652

    Google Scholar 

  • Xu Z, Xia M (2011) On distance and correlation measures of hesitant fuzzy information. Int J Intell Syst 26(5):410–425

    MATH  Google Scholar 

  • Yager RR (2017) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25(5):1222–1230

    Google Scholar 

  • Yager RR (2014) Pythagorean membership grades in multi criteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965

    Google Scholar 

  • Yager RR, Alajlan N, Bazi Y (2018) Aspects of generalized orthopair fuzzy sets. Int J Intell Syst 33(11):2154–2174

    Google Scholar 

  • Yager RR (1986) On the theory of bags. Int J Gen Syst 13(1):23–37

    MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Comput 8(3):338–353

    MATH  Google Scholar 

  • Zhang X (2016) A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. Int J Intell Syst 31(6):593–611

    Google Scholar 

  • Zhang XL, Xu ZS (2014) Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29(12):1061–1078

    MathSciNet  Google Scholar 

Download references

Acknowledgements

Authors are highly thankful to the Editor and anonymous reviewers for their valuable suggestions to bring this paper in the present form.

Author information

Authors and Affiliations

  1. School of Mathematics, Faculty of Sciences, Shri Mata Vaishno Devi University, Katra, 182320, Jammu and Kashmir, India

    Surender Singh & Abdul Haseeb Ganie

Authors
  1. Surender Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abdul Haseeb Ganie
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Surender Singh.

Ethics declarations

Conflict of interest

Authors declare that there is no conflict of interest.

Ethical approval

The present article does not contain any studies with human participants or animals performed by any of the authors.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singh, S., Ganie, A.H. Some novel q-rung orthopair fuzzy correlation coefficients based on the statistical viewpoint with their applications. J Ambient Intell Human Comput 13, 2227–2252 (2022). https://doi.org/10.1007/s12652-021-02983-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12652-021-02983-7

Keywords

Search

Navigation