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Application of Interval Neutrosophic Power Hamy Mean Operators in MAGDM
Volume 30, Issue 2 (2019), pp. 293–325
Pub. online: 5 August 2022      Type: Research Article      Open accessOpen Access
Received
1 August 2018
Accepted
1 January 2019
Published
5 August 2022

Abstract

The Hamy mean (HM) operator, as a convenient mathematical aggregation tool, can deal with the interrelationship among multiple input parameters, and the power average (PA) operator can relieve the influence of awkward assessment values in the decision consequences. The interval neutrosophic sets (INSs) are a more powerful mathematical tool to handle insufficient, indeterminate and vague information that exists in real life problems. Yet, in some complicated decision-making situations, we require to consider the correlation between multi-input arguments and remove the influence of awkward data at the same time. To deal with such situations, in this paper, we combine the conventional HM operator to the traditional PA operator in interval neutrosophic settings and present two novel interval neutrosophic aggregation operators, that is, the interval neutrosophic power Hamy mean (INPHM) operator and the weighted interval neutrosophic power Hamy mean (WINPHM) operators. Then, some preferable properties of the developed aggregation operators are discussed. Moreover, based on these developed aggregation operators, we propose a new method for multiple attribute group decision making (MAGDM) under the INSs. Lastly, some examples are given to show the effectiveness of the developed method by comparing it with other existing methods.

References

 
Atanassov, K.T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, (20) (1), 87–96.
 
Bausys, R., Zavadskas, K.E., Kaklauskas, A. (2015). Application of neutrosophic set to multicriteria decision making by COPRAS. Journal of Economic Computation and Economic Cybernetics Studies and Research, 49, 84–98.
 
Cabrerizo, F.J., Al-Hmouz, R., Morfeq, A., Balamash, A.S., Martinez, M.A., Herrera-Viedma, E. (2017). Soft consensus measures in group decision making using unbalanced fuzzy linguistic information. Soft Computing, 21(11), 3037–3050.
 
Capuano, N., Chiclana, F., Fujita, H., Herrera-Viedma, E., Loia, V. (2018). Fuzzy group decision making with incomplete information guided by social influence. IEEE Transactions on Fuzzy Systems, 26(3), 1704–1718.
 
Dong, Y., Zhang, H., Herrera-Viedma, E. (2016). Integrating experts’ weights generated dynamically into the consensus reaching process and its applications in managing non-cooperative behaviors. Decision Support Systems, 84, 1–15.
 
Dong, Y., Zhao, S., Zhang, H., Chiclana, F., Herrera-Viedma, E. (2018). A self-management mechanism for non-cooperative behaviors in large-scale group consensus reaching processes. IEEE Transactions on Fuzzy Systems, (26) (6), 3276–3288.
 
Feng, J., Li, M., Li, Y. (2018). Study of decision framework of shopping mall photovoltaic plan selection based on DEMATEL and ELECTRE III with symmetry under neutrosophic set environment. Symmetry, 10(5), 150.
 
Garg, H. (2016). An improved score function for ranking neutrosophic sets and its application to decision-making process. International Journal for Uncertainty Quantification, 6(5), 377–385.
 
Hara, T., Uchiyama, M., Takahasi, S.E. (1998). A refinement of various mean inequalities. Journal of Inequalities and Applications, 2(4), 387–395.
 
He, Y.D., Chen, H., Zhou, L., Liu, J., Tao, Z. (2013). Generalized interval-valued Atanassovs intuitionistic fuzzy power operators and their application to group decision making. International Journal of Fuzzy Systems, 15(4), 401–411.
 
He, Y.D., Jin, Y., Chen, H. (2015a). Intuitionistic fuzzy power geometric Bonferroni means and their application to multiple attribute group decision making. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 23(02), 285–315.
 
He, Y., Wang, Z.G., Chen, H. (2015b). Hesitant fuzzy power Bonferroni means and their application to multiple attribute decision making. IEEE Transactions on Fuzzy Systems, 23(5), 1655–1668.
 
Huang, Wei W. G, Y.H., Wei, C. (2017). VIKOR method for interval neutrosophic multiple attribute group decision-making. Information, 8(4), 144.
 
Ji, P., Cheng, P.F., Zhang, H.Y., Wang, J.Q. (2018a). Interval-valued neutrosophic Bonferroni mean operators and the application in the selection of renewable energy. New Trends in Neutrosophic Theory and Applications, 2, 12–39.
 
Ji, Cheng, P., Zhang H. Y, P.F., Wang, J.Q. (2018b). A projection-based TODIM method under multi-valued neutrosophic environments and its application in personnel selection. Neural Computing and Applications, 29(1), 221–234.
 
Li, Y., Liu, P., Chen, Y. (2016). Some single valued neutrosophic number heronian mean operators and their application in multiple attribute group decision making. Informatica, 27(1), 85–110.
 
Liu, P. (2017). Multiple attribute group decision making method based on interval-valued intuitionistic fuzzy power Heronian aggregation operators. Computers & Industrial Engineering, 108, 199–212.
 
Liu, P., Liu, Y. (2014). An approach to multiple attribute group decision making based on intuitionistic trapezoidal fuzzy power generalized aggregation operator. International Journal of Computational Intelligence Systems, 7(2), 291–304.
 
Liu, P., Wang, Y. (2014). Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean. Neural Computing and Applications, 25(7–8), 2001–2010.
 
Liu, P., Tang, G. (2016). Some power generalized aggregation operators based on the interval neutrosophic sets and their application to decision making. Journal of Intelligent & Fuzzy Systems, 30(5), 2517–2528.
 
Liu, P., Chen, S.M. (2017). Group decision making based on Heronian aggregation operators of intuitionistic fuzzy numbers. IEEE Transactions on Cybernetics, 47(9), 2514–2530.
 
Liu, P., Li, H. (2017). Interval-valued intuitionistic fuzzy power Bonferroni aggregation operators and their application to group decision making. Cognitive Computation, 9(4), 494–512.
 
Liu, P., Gao, H. (2018). Multicriteria decision making based on generalized Maclaurin symmetric means with multi-hesitant fuzzy linguistic information. Symmetry, 10(4), 81.
 
Liu, P., You, X. (2017). Interval neutrosophic muirhead mean operators and their application in multiple attribute group decision-making. International Journal for Uncertainty Quantification, 7(4), 303–334.
 
Liu, P., You, X. (2018). Some linguistic neutrosophic Hamy mean operators and their application to multi-attribute group decision making. PloS One, 13(3), e0193027.
 
Liu, P., Zhang, X. (2018). Some Maclaurin symmetric mean operators for single-valued trapezoidal neutrosophic numbers and their applications to group decision making. International Journal of Fuzzy Systems, 20(1), 45–61.
 
Liu, Z., Teng, F., Liu, P., Ge, Q. (2018). Interval-valued intuitionistic fuzzy power Maclaurin symmetric mean aggregation operators and their application to multiple attribute group decision-making. International Journal for Uncertainty Quantification, 8(3), 211–232.
 
Maclaurin, C. (1729). A second letter to Martin Folkes, Esq; concerning the roots of equations, with demonstration of otherrules of algebra. Philosophical Transactions of the Royal Society of London A, 36, 59–96.
 
Morente-Molinera, J.A., Kou, G., Pang, C., Cabrerizo, F.J., Herrera-Viedma, E. (2019). An automatic procedure to create fuzzy ontologies from users’ opinions using sentiment analysis procedures and multi-granular fuzzy linguistic modelling methods. Information Sciences, 476, 222–238.
 
Nie, R.X., Wang, J.Q., Zhang, H.Y. (2017). Solving solar-wind power station location problem using an extended weighted aggregated sum product assessment (WASPAS) technique with interval neutrosophic sets. Symmetry, 9(7), 106.
 
Peng, J.J., Wang, J.Q., Wang, J., Zhang, H.Y., Chen, X.H. (2014). An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets. Applied Soft Computing, 25, 336–346.
 
Peng, J.J., Wang, J.Q., Wang, J., Zhang, H.Y., Chen, X.H. (2016). Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems. International Journal of Systems Science, 47(10), 2342–2358.
 
Qin, J. (2017). Interval type-2 fuzzy Hamy mean operators and their application in multiple criteria decision making. Granular Computing, 2(4), 249–269.
 
Qin, J., Liu, X. (2014). An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators. Journal of Intelligent & Fuzzy Systems, 27(5), 2177–2190.
 
Smarandache, F. (1998). Neutrosophy: Neutrosophic Probability, Set, and Logic: Analytic Synthesis & Synthetic Analysis.
 
Smarandache, F. (1999). A unifying field in logics: neutrosophic logic. In: Philosophy. American Research Press, pp. 1–141.
 
Stanujkic, D., Zavadskas, E.K., Smarandache, F., Brauers, W.K., Karabasevic, D. (2017). A neutrosophic extension of the MULTIMOORA method. Informatica, 28(1), 181–192.
 
Urena, R., Kou, G., Dong, Y., Chiclana, F., Herrera-Viedma, E. (2019). A review on trust propagation and opinion dynamics in social networks and group decision making frameworks. Information Sciences, 478, 461–475.
 
Wang, H., Smarandache, F., Sunderraman, R., Zhang, Y.Q. (2005). Interval neutrosophic sets and logic: theory and applications in computing. Theory and Applications in Computing, 5.
 
Wang, H., Smarandache, F., Zhang, Y.Q., Sunderraman, R. (2010). Single valued neutrosophic sets. Infinite Study.
 
Wei, G., Lu, M. (2018). Pythagorean fuzzy maclaurin symmetric mean operators in multiple attribute decision making. International Journal of Intelligent Systems, 33(5), 1043–1070.
 
Wu, S., Wang, J., Wei, G., Wei, Y. (2018). Research on construction engineering project risk assessment with some 2-tuple linguistic neutrosophic Hamy mean operators. Sustainability, 1(5), 1–26.
 
Xu, Z. (2007). Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems, 15(6), 1179–1187.
 
Xu, Z. (2011). Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowledge-Based Systems, 24(6), 749–760.
 
Xu, Z., Yager, R.R. (2006). Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems, 35(4), 417–433.
 
Xu, Z., Yager, R.R. (2011). Intuitionistic fuzzy Bonferroni means. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 41(2), 568–578.
 
Yager, R.R. (2001). The power average operator. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 31(6), 724–731.
 
Ye, J. (2014). A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. Journal of Intelligent & Fuzzy Systems, 26(5), 2459–2466.
 
Yu, D. (2015). Triangular Atanassov’s intuitionistic fuzzy Bonferroni mean and application to supplier selection. Journal of Intelligent & Fuzzy Systems, 28(6), 2785–2791.
 
Yu, D., Wu, Y. (2012). Interval-valued intuitionistic fuzzy Heronian mean operators and their application in multi-criteria decision making. African Journal of Business Management, 6(11), 4158–4168.
 
Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
 
Zhang, H.Y., Wang, J.Q., Chen, X.H. (2014). Interval neutrosophic sets and their application in multicriteria decision making problems. The Scientific World Journal, 1–15.
 
Zhang, X., Liu, P., Wang, Y. (2015). Multiple attribute group decision making methods based on intuitionistic fuzzy frank power aggregation operators. Journal of Intelligent & Fuzzy Systems, 29(5), 2235–2246.
 
Zhang, H., Wang, J., Chen, X. (2016). An outranking approach for multi-criteria decision-making problems with interval-valued neutrosophic sets. Neural Computing and Applications, 27(3), 615–627.
 
Zavadskas, E.K., Bausys, R., Lazauskas, M. (2015). Sustainable assessment of alternative sites for the construction of a waste incineration plant by applying WASPAS method with single-valued neutrosophic set. Sustainability, 7(12), 15923–15936.
 
Zavadskas, E.K., Bausys, R., Kaklauskas, A., Ubarte, I., Kuzminske, A., Gudiene, N. (2017). Sustainable market valuation of buildings by the single-valued neutrosophic MAMVA method. Applied Soft Computing, 57, 74–87.

Biographies

Liu Peide
peide.liu@gmail.com

P. Liu received the BS and MS degrees in signal and information processing from Southeast University, Nanjing, China, in 1988 and 1991, respectively, and the PhD degree in information management from Beijng Jiaotong University, Beijing, China, in 2010.

He is currently a professor with the School of Management Science and Engineering, Shandong University of Finance and Economics, Shandong, China. He is an associate editor of the Journal of Intelligent and Fuzzy Systems, a member of the editorial board of the Journal Technological and Economic Development of Economy, and a member of the editorial board of other 12 journals. He has authored or coauthored more than 200 publications. His research interests include aggregation operators, fuzzy logic, fuzzy decision making, and their applications.

Khan Qaisar
qaisarkhan421@gmail.com

Q. Khan is currently a PhD candidate at the Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan. He received his MS degree in mathematics from International Islamic University Islamabad, Pakistan, in 2014 under the supervision of Dr. Tahir Mahmood. He has 25 international publications to his credit. His areas of interest are automata theory, decision making and neutrosophc theory.

Mahmood Tahir
tahirbakhat@iiu.edu.pk

T. Mahmood is assistant professor of Mathematics at Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan. He received his PhD degree in mathematics from Quaid-i-Azam University, Islamabad, Pakistan in 2012 under the supervision of professor Dr. Muhammad Shabir. His areas of interest are algebraic structures, fuzzy algebraic structures and soft sets. He has more than 65 international publications to his credit and he has also produced 38 MS students.


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Keywords
interval neutrosophic sets Hamy mean operators power average operators MAGDM

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