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Multicriteria decision-making based on the confidence level Q-rung orthopair normal fuzzy aggregation operator

Granular Computing volume 8, pages 77–96 (2023)Cite this article

Abstract

Q-rung orthopair fuzzy sets have been widely utilized in recent years to encounter uncertainties. At the same time, the idea of normal fuzzy numbers seems closer to human thinking. The notion of the Q-rung orthopair normal fuzzy set is a more flexible tool to capture the uncertainties because of the combined concept of Q-rung orthopair fuzzy sets and normal fuzzy numbers. This paper proposes some new weighted averaging, weighted geometric, ordered weighted averaging, and ordered weighted geometric aggregation operators for Q-rung orthopair normal fuzzy numbers, which also comprise the confidence level for the alternatives given by the decision-maker. We then introduce a multicriteria decision-making approach based on these operators to get more rational results than the existing approaches. Furthermore, to prove the superiority of the proposed approach, a comparative analysis with the different existing methods has also been done. Finally, sensitivity analyses on the parameter Q and the confidence level of Q-rung orthopair normal fuzzy numbers have been demonstrated to highlight the importance of these parameters and to show the stability of the proposed method.

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Data Availability Statement

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

References

  • Akram M, Shahzadi G, Peng X (2021) Extension of Einstein geometric operators to multi-attribute decision making under q-rung orthopair fuzzy information. Granul Comput 6(4):779–795. https://doi.org/10.1007/s41066-020-00233-3

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Chen SM (1997) Interval-valued fuzzy hypergraph and fuzzy partition. IEEE Trans Syst Man Cybern Part B Cybern 27(4):725–733

    Article  Google Scholar 

  • Chen SM, Hsiao WH (2000) Bidirectional approximate reasoning for rule-based systems using interval-valued fuzzy sets. Fuzzy Sets Syst 113(2):185–203. https://doi.org/10.1016/S0165-0114(98)00351-0

    Article  MathSciNet  MATH  Google Scholar 

  • Chen SM, Randyanto Y (2013) A novel similarity measure between intuitionistic fuzzy sets and its applications. Intern J Pattern Recognit Artif Intell 27(7):1350021

    Article  Google Scholar 

  • Chen SM, Tan JM (1994) Handling multi criteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 67:163–172

    Article  MATH  Google Scholar 

  • Chen SM, Hsiao WH, Jong WT (1997) Bidirectional approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 91(3):339–353. https://doi.org/10.1016/S0165-0114(97)86594-3

    Article  MathSciNet  MATH  Google Scholar 

  • Ejegwa PA (2020) Distance and similarity measures for Pythagorean fuzzy sets. Granul Comput 5:225–238

    Article  Google Scholar 

  • Ejegwa PA (2020) Modified Zhang and Xu’s distance measure for Pythagorean fuzzy sets and its application to pattern recognition problems. Neural Comput Appl 32:10199–10208

    Article  Google Scholar 

  • Feng F, Zheng Y, Sun B et al (2022) Novel score functions of generalized orthopair fuzzy membership grades with application to multiple attribute decision making. Granul Comput 7(1):95–111. https://doi.org/10.1007/s41066-021-00253-7

    Article  Google Scholar 

  • Gao H, Ran L, Wei G, Wei C, Wu J (2020) VIKOR method for MAGDM based on q-rung interval-valued orthopair fuzzy information and its application to supplier selection of medical consumption products. Int J Environ Res Public Health 17(2):525

    Article  Google Scholar 

  • Garg H (2016) A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems. Appl Soft Comput 38:988–999

    Article  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 36:526–557

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Garg H, Kumar K (2012) Linguistic interval-valued Atanassov intuitionistic fuzzy sets and their applications to group decision-making problems. IEEE Trans Fuzzy Syst 27:2302–2311

    Article  Google Scholar 

  • Garg H, Kumar K (2019) Improved possibility degree method for ranking intuitionistic fuzzy numbers and their application in multi-attribute decision-making. Granul Comput 4:237–247

    Article  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. Soft Comput 6(1):545–558

    Google Scholar 

  • Joshi BP, Gegov A (2020) Confidence levels q-rung orthopair fuzzy aggregation operators and its applications to MCDM problems. Int J Intell Syst 35(1):125–149

    Article  Google Scholar 

  • Lakshmana V, Nayagam G, Sivaraman G (2011) Ranking of interval-valued intuitionistic fuzzy sets. Appl Soft Comput 11(4):3368–3372

    Article  MATH  Google Scholar 

  • Li DF (2005) Multi-attribute decision making models and methods using intuitionistic fuzzy sets. J Comput Syst Sci 70:73–85

    Article  MATH  Google Scholar 

  • Li DY, Liu CY (2004) Study on the universality of the normal cloud model. Eng Sci 6:28–34

    Google Scholar 

  • Lin L, Yuan XH, Xia ZQ (2007) Multi-criteria fuzzy decision-making methods based on intuitionistic fuzzy sets. J Comput Syst Sci 73(1):84–88

    Article  MATH  Google Scholar 

  • Liu HW, Wang GJ (2007) Multi-criteria decision-making methods based on intuitionistic fuzzy sets. Eur J Oper Res 179:220–233

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Peng X, Yang Y (2015) Some Results for Pythagorean Fuzzy Sets. Int J Intell Syst 30:1133–1160

    Article  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

    Article  Google Scholar 

  • Seikh MR, Mandal U (2021) Q-rung orthopair fuzzy Frank aggregation operators and its application in multiple attribute decision-making with unknown attribute weights. Granul Comput. https://doi.org/10.1007/s41066-021-00290-2

    Article  Google Scholar 

  • Turksen IB (1986) Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst 20(2):191–210. https://doi.org/10.1016/0165-0114(86)90077-1

    Article  MathSciNet  MATH  Google Scholar 

  • Ullah K, Mahmood T, Ali Z et al (2012) On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition. Complex Intell Syst 6:15–27

    Article  Google Scholar 

  • Wang W, Liu X (2012) Intuitionistic fuzzy Information aggregation using Einstein operations. IEEE Trans Fuzzy Syst 20(5):923–938

    Article  Google Scholar 

  • Wang JQ, Li KJ, Zhang H (2012) Multi-criteria decision-making method based on induced intutionistic normal fuzzy related aggregation operators. Int J Uncertain Fuzz 20(4):559–578

    Article  MATH  Google Scholar 

  • Wang P, Wang J, Wei G, Wei C (2019) Similarity measures of q-rung orthopair fuzzy sets based on cosine function and their applications. Mathematics 7(4):340

    Article  Google Scholar 

  • Wang L, Garg H, Li N (2021) Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weight. Soft Comput 25:9730–993

    MATH  Google Scholar 

  • Wei GW, Wei C, Wang J, Gao H, Wei Y (2019) Some q-rung orthopair fuzzy maclaurin symmetric mean operators and their applications to potential evaluation of emerging technology commercialization. Int J Intell Syst 34:50–81

    Article  Google Scholar 

  • Xiao F, Weiping D (2019) Divergence measure of Pythagorean fuzzy sets and its application in medical diagnosis. Appl Soft Comput 79:254–267

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Xu Z (2007b) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6):1179–1187

    Article  Google Scholar 

  • Yager RR (2009) OWA aggregation of intuitionistic fuzzy sets. Int J Intell Syst 38(6):617–641

    MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Yang ZL, Chang JP (2020) Interval-valued Pythagorean normal fuzzy information aggregation operators for multi-attribute decision making. IEEE Access 8:51295–51314

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Yang Z, Li X, Cao Z, Li J (2019) Q-rung Orthopair Normal Fuzzy Aggregation Operators and Their Application in Multi-Attribute Decision-Making. Mathematics 7:1142

    Article  Google Scholar 

  • Yang MS, Ali Z, Mahmood T (2021) Complex q-Rung Orthopair Uncertain Linguistic Partitioned Bonferroni Mean Operators with Application in Antivirus Mask Selection. Symmetry 13:249

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy Sets. Inf. Control 8(3):338–353

    Article  MathSciNet  MATH  Google Scholar 

  • Zeng S, Hu Y, Xie X (2021) Q-rung orthopair fuzzy weighted induced logarithmic distance measures and their application in multiple attribute decision making. Eng Appl Artif Intell 100:104–167

    Article  Google Scholar 

Download references

Acknowledgements

We thank anonymous reviewers for their valuable comments and constructive suggestions, which greatly improved the quality of this paper. The first author is grateful to the Council of Scientific & Industrial Research (CSIR), India, for financial support, to carry out this work. The second author is also thankful to the Uttarakhand State Council for Science and Technology, Dehradun, India to provide financial support to carry out this work under the project no. UCS&T/R7D19/20-21/19222/1.

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  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247667, India

    Manish Kumar & S. K. Gupta

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  1. Manish Kumar
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  2. S. K. Gupta
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Correspondence to S. K. Gupta.

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Kumar, M., Gupta, S.K. Multicriteria decision-making based on the confidence level Q-rung orthopair normal fuzzy aggregation operator. Granul. Comput. 8, 77–96 (2023). https://doi.org/10.1007/s41066-022-00314-5

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  • DOI: https://doi.org/10.1007/s41066-022-00314-5

Keywords

  • Q-rung orthopair fuzzy set
  • Q-rung orthopair normal fuzzy set
  • Confidence level
  • Aggregation operator
  • Multicriteria decision making