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Maclaurin symmetric mean aggregation operators based on t-norm operations for the dual hesitant fuzzy soft set

  • Harish GargEmail author
  • Rishu Arora
Original Research

Abstract

The objective of this paper is to present a Maclaurin symmetric mean (MSM) operator to aggregate dual hesitant fuzzy (DHF) soft numbers. The salient feature of MSM operators is that it can reflect the interrelationship between the multi-input arguments. Under DHF soft set environment, we develop some aggregation operators named as DHF soft MSM averaging (DHFSMSMA) operator, the weighted DHF soft MSM averaging (WDHFSMSMA) operator, DHF soft MSM geometric (DHFSMSMG) operator, and the weighted DHF soft MSM geometric (WDHFSMSMG) operator. Further, some properties and the special cases of these operators are discussed. Then, by utilizing these operators, we develop an approach for solving the multicriteria decision-making problem and illustrate it with a numerical example. Finally, a comparison analysis has been done to analyze the advantages of the proposed operators.

Keywords

Maclaurin symmetric mean Aggregation operator Multicriteria decision-making Dual hesitant fuzzy soft set 

Notes

Acknowledgements

The authors are thankful to the editor and anonymous reviewers for their constructive comments and suggestions that helped us in improving the paper significantly. The authors (Rishu Arora) would like to thank the Department of Science & Technology, New Delhi, India for providing financial support under WOS-A scheme wide File No. SR/WOS-A/PM-77/2016 during the preparation of this manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human/animal rights statement

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

References

  1. Arora R, Garg H (2018a) Prioritized averaging/geometric aggregation operators under the intuitionistic fuzzy soft set environment. Scientia Iranica 25(1):466–482Google Scholar
  2. Arora R, Garg H (2018b) Robust aggregation operators for multi-criteria decision making with intuitionistic fuzzy soft set environment. Scientia Iranica E 25(2):931–942Google Scholar
  3. Arora R, Garg H (2018c) A robust correlation coefficient measure of dual hesistant fuzzy soft sets and their application in decision making. Eng Appl Artif Intell 72:80–92CrossRefGoogle Scholar
  4. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96zbMATHCrossRefGoogle Scholar
  5. Babitha KV, John SJ (2013) Hesistant fuzzy soft sets. J New Results Sci 3:98–107Google Scholar
  6. Capuano N, Loia V, Orciuoli F (2017) A fuzzy group decision making model for ordinal peer assessment. IEEE Trans Learn Technol 10(2):247–259CrossRefGoogle Scholar
  7. Capuano N, Chiclana F, Fujita H, Herrera-Viedma E, Loia V (2018a) Fuzzy group decision making with incomplete information guided by social influence. IEEE Trans Fuzzy Syst 26(3):1704–1718CrossRefGoogle Scholar
  8. Capuano N, Chiclana F, Herrera-Viedma E, Fujita H, Loia V (2018b) Fuzzy rankings for preferences modeling in group decision making. Int J Intell Syst 33(7):1555–1570CrossRefGoogle Scholar
  9. Chen CT, Huang SF, Hung WZ (2018a) Linguistic VIKOR method for project evaluation of ambient intelligence product. J Ambient Intell Humaniz Comput.  https://doi.org/10.1007/s12652-018-0889-x
  10. Chen N, Xu Z, Xia M (2013) Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model 37(4):2197–2211MathSciNetzbMATHCrossRefGoogle Scholar
  11. Chen YS, Chuang HM, Sangaiah AK, Lin CK, Huang WB (2018b) A study for project risk management using an advanced MCDM-based DEMATEL-ANP approach. J Ambient Intell Humaniz Comput.  https://doi.org/10.1007/s12652-018-0973-2
  12. Farhadinia B, Xu Z (2017) Distance and aggregation-based methodologies for hesitant fuzzy decision making. Cogn Comput 9(1):81–94CrossRefGoogle Scholar
  13. Garg H (2018) Hesitant Pythagorean fuzzy sets and their aggregation operators in multiple attribute decision making. Int J Uncertain Quantif 8(3):267–289MathSciNetCrossRefGoogle Scholar
  14. Garg H (2019a) Hesitant Pythagorean fuzzy Maclaurin symmetric mean operators and its applications to multiattribute decision making process. Int J Intell Syst 34(4):601–626.  https://doi.org/10.1002/int.22067 CrossRefGoogle Scholar
  15. Garg H (2019b) Intuitionistic fuzzy hamacher aggregation operators with entropy weight and their applications to multi-criteria decision-making problems. Iran J Sci Technol Trans Electr Eng.  https://doi.org/10.1007/s40998-018-0167-0 CrossRefGoogle Scholar
  16. Garg H, Arora R (2017) Distance and similarity measures for dual hesistant fuzzy soft sets and their applications in multi criteria decision-making problem. Int J Uncertain Quantif 7(3):229–248MathSciNetCrossRefGoogle Scholar
  17. Garg H, Arora R (2018a) Bonferroni mean aggregation operators under intuitionistic fuzzy soft set environment and their applications to decision-making. J Oper Res Soc 69(11):1711–1724CrossRefGoogle Scholar
  18. Garg H, Arora R (2018b) Dual hesitant fuzzy soft aggregation operators and their application in decision making. Cogn Comput 10(5):769–789CrossRefGoogle Scholar
  19. Garg H, Arora R (2018c) Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decision-making. Appl Intell 48(2):343–356CrossRefGoogle Scholar
  20. Garg H, Arora R (2018d) Novel scaled prioritized intuitionistic fuzzy soft interaction averaging aggregation operators and their application to multi criteria decision making. Eng Appl Artif Intell 71C:100–112CrossRefGoogle Scholar
  21. Garg H, Arora R (2019) Generalized intuitionistic fuzzy soft power aggregation operator based on t-norm and their application in multi criteria decision-making. Int J Intell Syst 34(2):215–246CrossRefGoogle Scholar
  22. Garg H, Kaur G (2018) Algorithm for probabilistic dual hesitant fuzzy multi-criteria decision making based on aggregation operators with new distance measures. Mathematics 6(12):280.  https://doi.org/10.3390/math6120280 CrossRefGoogle Scholar
  23. Garg H, Kumar K (2018a) An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making. Soft Comput 22(15):4959–4970zbMATHCrossRefGoogle Scholar
  24. Garg H, Kumar K (2018b) A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory. Artif Intell Rev.  https://doi.org/10.1007/s10462-018-9668-5
  25. Garg H, Kumar K (2018c) Some aggregation operators for linguistic intuitionistic fuzzy set and its application to group decision-making process using the set pair analysis. Arab J Sci Eng 43(6):3213–3227zbMATHCrossRefGoogle Scholar
  26. Garg H, Nancy (2018) Linguistic single-valued neutrosophic prioritized aggregation operators and their applications to multiple-attribute group decision-making. J Ambient Intell Humaniz Comput 9(6):1975–1997CrossRefGoogle Scholar
  27. Garg H, Rani D (2019) Complex interval- valued intuitionistic fuzzy sets and their aggregation operators. Fundamenta Informaticae 164(1):61–101MathSciNetzbMATHCrossRefGoogle Scholar
  28. Jana C, Pal M, Wang JQ (2018) Bipolar fuzzy Dombi aggregation operators and its application in multiple-attribute decision-making process. J Ambient Intell Humaniz Comput.  https://doi.org/10.1007/s12652-018-1076-9
  29. Ju Y, Zhang W, Yang S (2014) Some dual hesitant fuzzy hamacher aggregation operators and their applications to multiple attribute decision making. J Intell Fuzzy Syst 27(5):2481–2495MathSciNetzbMATHGoogle Scholar
  30. Kaur G, Garg H (2018) Generalized cubic intuitionistic fuzzy aggregation operators using t-norm operations and their applications to group decision-making process. Arab J Sci Eng.  https://doi.org/10.1007/s13369-018-3532-4
  31. Klir GJ, Yuan B (2005) Fuzzy sets and fuzzy logic: theory and applications. Prentice Hall of India Private Limited, New DelhizbMATHGoogle Scholar
  32. Kumar K, Garg H (2018a) Connection number of set pair analysis based TOPSIS method on intuitionistic fuzzy sets and their application to decision making. Appl Intell 48(8):2112–2119CrossRefGoogle Scholar
  33. Kumar K, Garg H (2018b) TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment. Comput Appl Math 37(2):1319–1329MathSciNetzbMATHCrossRefGoogle Scholar
  34. Liu P, Qin X (2017) Maclaurin symmetric mean operators of linguistic intuitionistic fuzzy numbers and their application to multiple-attribute decision-making. J Exp Theor Artif Intell 29(6):1173–1202MathSciNetCrossRefGoogle Scholar
  35. Liu W, Dong Y, Chiclana F, Cabrerizo FJ, Herrera-Viedma E (2017) Group decision-making based on heterogeneous preference relations with self-confidence. Fuzzy Optim Decis Mak 16(4):429–447MathSciNetzbMATHCrossRefGoogle Scholar
  36. Maclaurin C (1729) A second letter to martin folkes, esq.; concerning the roots of equations, with demonstration of other rules of algebra. Philos Trans R Soc Lond Ser A 36:59–96Google Scholar
  37. Maji PK, Biswas R, Roy A (2001a) Intuitionistic fuzzy soft sets. J Fuzzy Math 9(3):677–692MathSciNetzbMATHGoogle Scholar
  38. Maji PK, Biswas R, Roy AR (2001b) Fuzzy soft sets. J Fuzzy Math 9(3):589–602MathSciNetzbMATHGoogle Scholar
  39. Meng F, Chen X (2015) Correlation coefficients of hesitant fuzzy sets and their application based on fuzzy measures. Cogn Comput 7(4):445–463CrossRefGoogle Scholar
  40. Molodtsov D (1999) Soft set theory—first results. Comput Math Appl 27(4–5):19–31MathSciNetzbMATHCrossRefGoogle Scholar
  41. Pecaric J, Wen JJ, Wang WL, Lu T (2005) A generalization of Maclaurin’s inequalities and its applications. Math Inequal Appl 8:583–598MathSciNetzbMATHGoogle Scholar
  42. Peng XD, Yang Y (2015) Research on dual hesistant fuzzy soft set. Comput Eng 41:262–267Google Scholar
  43. Pourhassan MR, Raissi S (2017) An integrated simulation-based optimization technique for multi-objective dynamic facility layout problem. J Ind Inf Integr 8:49–58Google Scholar
  44. Qin J, Liu X (2014) An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators. J Intell Fuzzy Syst 27(5):2177–2190MathSciNetzbMATHGoogle Scholar
  45. Qin J, Liu X (2015) Approaches to uncertain linguistic multiple attribute decision making based on dual Maclaurin symmetric mean. J Intell Fuzzy Syst 29(1):171–186MathSciNetzbMATHCrossRefGoogle Scholar
  46. Qin J, Liu X, Pedrycz W (2015) Hesistant fuzzy Maclaurin symmetric mean operators and its application to multiple-attribute decision-making. Int J Fuzzy Syst 17(4):509–520MathSciNetCrossRefGoogle Scholar
  47. Rani D, Garg H (2018) Complex intuitionistic fuzzy power aggregation operators and their applications in multi-criteria decision-making. Expert Syst 35(6):e12,325.  https://doi.org/10.1111/exsy.12325
  48. Teixeira C, Lopes I, Figueiredo M (2018) Classification methodology for spare parts management combining maintenance and logistics perspectives. J Manag Anal 5(2):116–135Google Scholar
  49. Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539zbMATHGoogle Scholar
  50. Torra V, Narukawa Y (2009) On hesistant fuzzy sets and decision. In: Proceedings of the 8th IEEE international conference on fuzzy systems, pp 1378 – 1382Google Scholar
  51. Viriyasitavat W (2016) Multi-criteria selection for services selection in service workflow. J Ind Inf Integr 1:20–25Google Scholar
  52. Wang HJ, Zhao XF, Wei GW (2014) Dual hesistant fuzzy aggregation opertors in multi attribute decision making. J Intell Fuzzy Syst 26:2281–2290zbMATHGoogle Scholar
  53. Wei G, Garg H, Gao H, Wei C (2018) Interval-valued Pythagorean fuzzy Maclaurin symmetric mean operators in multiple attribute decision making. IEEE Access 6(1):67,866–67,884CrossRefGoogle Scholar
  54. Xia M, Xu ZS (2011) Hesitant fuzzy information aggregation in decision-making. Int J Approx Reason 52:395–407MathSciNetzbMATHCrossRefGoogle Scholar
  55. Xu LD (1988) A fuzzy multiobjective programming algorithm in decision support systems. Ann Oper Res 12(1):315–320MathSciNetCrossRefGoogle Scholar
  56. Xu Z, Xia M (2011a) On distance and correlation measures of hesitant fuzzy information. Int J Intell Syst 26(5):410–425zbMATHCrossRefGoogle Scholar
  57. Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187CrossRefGoogle Scholar
  58. Xu ZS, Xia MM (2011b) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181(11):2128–2138MathSciNetzbMATHCrossRefGoogle Scholar
  59. Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433MathSciNetzbMATHCrossRefGoogle Scholar
  60. Yu D (2014) Some generalized dual hesitant fuzzy geometric aggregation operators and applications. Int J Uncertain Fuzziness Knowl Based Syst 22(3):367–384zbMATHCrossRefGoogle Scholar
  61. Yu D (2015) Archimedean aggregation operators based on dual hesitant fuzzy set and their application to GDM. Int J Uncertain Fuzziness Knowl Based Syst 23(5):761–780MathSciNetzbMATHCrossRefGoogle Scholar
  62. Yu D, Wu Y, Zhou W (2011) Multi criteria decision making based on choquet integral under hesitant fuzzy environment. J Comput Inf Syst 7(12):4506–4513Google Scholar
  63. Yu D, Zhang W, Huang G (2016) Dual hesistant fuzzy aggregation operators. Technol Econ Dev Econ 22(2):194–209CrossRefGoogle Scholar
  64. Zhang C, Wang C, Zhang Z, Tian D (2018) A novel technique for multiple attribute group decision making in interval-valued hesitant fuzzy environments with incomplete weight information. J Ambient Intell Humaniz Comput.  https://doi.org/10.1007/s12652-018-0912-2
  65. Zhang HD, Shu L (2016) Dual hesitant fuzzy soft set and its properties. In: Cao BY, Liu ZL, Zhong YB, Mi HH (eds) Fuzzy systems & operations research and management. Advances in intelligent systems and computing, vol 367. Springer, Berlin, pp 171–182Google Scholar
  66. Zhao H, Xu Z, Liu S (2017) Dual hesitant fuzzy information aggregation with einstein t-conorm and t-norm. J Syst Sci Syst Eng 26(2):240–264CrossRefGoogle Scholar
  67. Zhao N, Xu Z, Liu F (2016) Group decision making with dual hesitant fuzzy preference relations. Cogn Comput 8(6):1119–1143CrossRefGoogle Scholar
  68. Zhu B, Xu Z, Xia M (2012) Dual hesitant fuzzy sets. J Appl Math 2012:879629.  https://doi.org/10.1155/2012/879629 MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of MathematicsThapar Institute of Engineering and Technology, Deemed UniversityPatialaIndia

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