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

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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.

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References

  • Arora R, Garg H (2018a) Prioritized averaging/geometric aggregation operators under the intuitionistic fuzzy soft set environment. Scientia Iranica 25(1):466–482

    Google Scholar 

  • Arora R, Garg H (2018b) Robust aggregation operators for multi-criteria decision making with intuitionistic fuzzy soft set environment. Scientia Iranica E 25(2):931–942

    Google Scholar 

  • 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 72:80–92

    Google Scholar 

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

    MATH  Google Scholar 

  • Babitha KV, John SJ (2013) Hesistant fuzzy soft sets. J New Results Sci 3:98–107

    Google Scholar 

  • Capuano N, Loia V, Orciuoli F (2017) A fuzzy group decision making model for ordinal peer assessment. IEEE Trans Learn Technol 10(2):247–259

    Google Scholar 

  • 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):1704–1718

    Google Scholar 

  • 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):1555–1570

    Google Scholar 

  • 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

  • Chen N, Xu Z, Xia M (2013) Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model 37(4):2197–2211

    MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • Farhadinia B, Xu Z (2017) Distance and aggregation-based methodologies for hesitant fuzzy decision making. Cogn Comput 9(1):81–94

    Google Scholar 

  • Garg H (2018) Hesitant Pythagorean fuzzy sets and their aggregation operators in multiple attribute decision making. Int J Uncertain Quantif 8(3):267–289

    MathSciNet  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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):229–248

    MathSciNet  Google Scholar 

  • 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):1711–1724

    Google Scholar 

  • Garg H, Arora R (2018b) Dual hesitant fuzzy soft aggregation operators and their application in decision making. Cogn Comput 10(5):769–789

    Google Scholar 

  • Garg H, Arora R (2018c) Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decision-making. Appl Intell 48(2):343–356

    Google Scholar 

  • 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:100–112

    Google Scholar 

  • 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):215–246

    Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • 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):4959–4970

    MATH  Google Scholar 

  • 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

  • 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):3213–3227

    MATH  Google Scholar 

  • 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):1975–1997

    Google Scholar 

  • Garg H, Rani D (2019) Complex interval- valued intuitionistic fuzzy sets and their aggregation operators. Fundamenta Informaticae 164(1):61–101

    MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • 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):2481–2495

    MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • Klir GJ, Yuan B (2005) Fuzzy sets and fuzzy logic: theory and applications. Prentice Hall of India Private Limited, New Delhi

    MATH  Google Scholar 

  • 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):2112–2119

    Google Scholar 

  • 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):1319–1329

    MathSciNet  MATH  Google Scholar 

  • 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):1173–1202

    MathSciNet  Google Scholar 

  • 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):429–447

    MathSciNet  MATH  Google Scholar 

  • 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 36:59–96

    Google Scholar 

  • Maji PK, Biswas R, Roy A (2001a) Intuitionistic fuzzy soft sets. J Fuzzy Math 9(3):677–692

    MathSciNet  MATH  Google Scholar 

  • Maji PK, Biswas R, Roy AR (2001b) Fuzzy soft sets. J Fuzzy Math 9(3):589–602

    MathSciNet  MATH  Google Scholar 

  • Meng F, Chen X (2015) Correlation coefficients of hesitant fuzzy sets and their application based on fuzzy measures. Cogn Comput 7(4):445–463

    Google Scholar 

  • Molodtsov D (1999) Soft set theory—first results. Comput Math Appl 27(4–5):19–31

    MathSciNet  MATH  Google Scholar 

  • Pecaric J, Wen JJ, Wang WL, Lu T (2005) A generalization of Maclaurin’s inequalities and its applications. Math Inequal Appl 8:583–598

    MathSciNet  MATH  Google Scholar 

  • Peng XD, Yang Y (2015) Research on dual hesistant fuzzy soft set. Comput Eng 41:262–267

    Google Scholar 

  • Pourhassan MR, Raissi S (2017) An integrated simulation-based optimization technique for multi-objective dynamic facility layout problem. J Ind Inf Integr 8:49–58

    Google Scholar 

  • 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):2177–2190

    MathSciNet  MATH  Google Scholar 

  • 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):171–186

    MathSciNet  MATH  Google Scholar 

  • 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):509–520

    MathSciNet  Google Scholar 

  • 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

    Google Scholar 

  • Teixeira C, Lopes I, Figueiredo M (2018) Classification methodology for spare parts management combining maintenance and logistics perspectives. J Manag Anal 5(2):116–135

    Google Scholar 

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

    MATH  Google Scholar 

  • Torra V, Narukawa Y (2009) On hesistant fuzzy sets and decision. In: Proceedings of the 8th IEEE international conference on fuzzy systems, pp 1378 – 1382

  • Viriyasitavat W (2016) Multi-criteria selection for services selection in service workflow. J Ind Inf Integr 1:20–25

    Google Scholar 

  • Wang HJ, Zhao XF, Wei GW (2014) Dual hesistant fuzzy aggregation opertors in multi attribute decision making. J Intell Fuzzy Syst 26:2281–2290

    MATH  Google Scholar 

  • 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):67,866–67,884

    Google Scholar 

  • Xia M, Xu ZS (2011) Hesitant fuzzy information aggregation in decision-making. Int J Approx Reason 52:395–407

    MathSciNet  MATH  Google Scholar 

  • Xu LD (1988) A fuzzy multiobjective programming algorithm in decision support systems. Ann Oper Res 12(1):315–320

    MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

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

    Google Scholar 

  • Xu ZS, Xia MM (2011b) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181(11):2128–2138

    MathSciNet  MATH  Google Scholar 

  • Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433

    MathSciNet  MATH  Google Scholar 

  • Yu D (2014) Some generalized dual hesitant fuzzy geometric aggregation operators and applications. Int J Uncertain Fuzziness Knowl Based Syst 22(3):367–384

    MATH  Google Scholar 

  • 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):761–780

    MathSciNet  MATH  Google Scholar 

  • 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):4506–4513

    Google Scholar 

  • Yu D, Zhang W, Huang G (2016) Dual hesistant fuzzy aggregation operators. Technol Econ Dev Econ 22(2):194–209

    Google Scholar 

  • 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

    Google Scholar 

  • 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 171–182

    Google Scholar 

  • 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):240–264

    Google Scholar 

  • Zhao N, Xu Z, Liu F (2016) Group decision making with dual hesitant fuzzy preference relations. Cogn Comput 8(6):1119–1143

    Google Scholar 

  • Zhu B, Xu Z, Xia M (2012) Dual hesitant fuzzy sets. J Appl Math 2012:879629. https://doi.org/10.1155/2012/879629

    Article  MathSciNet  MATH  Google Scholar 

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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.

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  1. School of Mathematics, Thapar Institute of Engineering and Technology, Deemed University, Patiala, Punjab, 147004, India

    Harish Garg & Rishu Arora

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  1. Harish Garg
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  2. Rishu Arora
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Correspondence to Harish Garg.

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Garg, H., Arora, R. Maclaurin symmetric mean aggregation operators based on t-norm operations for the dual hesitant fuzzy soft set. J Ambient Intell Human Comput 11, 375–410 (2020). https://doi.org/10.1007/s12652-019-01238-w

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