Abstract
In this chapter, we discuss the VIKOR method for solving MCDM problem with interval valued neutrosophic number . First we define interval-valued neutrosophic number . The different properties of that type of numbers are also discussed. For solving MCDM problem we propose Interval-valued neutrosophic weighted arithmetic average (INNWAA) operator and Interval-valued neutrosophic weighted geometric average (INNWGA) operator in neutrosophic environment.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Zadeh, L.A.: Fuzzy Sets. Inform Control 8, 338–353 (1965)
Atanassov, K.T.: Intuitionistic Fuzzy Sets. Pysica-Verlag A Springer-Verlag Company, New York (1999)
Smarandache, F.: A Unifying Field in Logics Neutrosophy: Neutrosophic Probability, Set and Logic. American Research Press, Rehoboth (1998)
Wang, H.B., Smarandache, F., Zhang, Y.Q., Sunderraman, R.: Singlevalued neutrosophic sets. Multispace Multistruct. 4, 410–413 (2010)
Ye, J.: A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. J. Intell. Fuzzy Syst. 26(5), 2459–2466 (2014)
Peng, J.J., Wang, J.Q., Wang, J., Zhang, H.Y., Chen, X.H.: Simplified neutrosophic sets and their applications in multi-criteria group decision making problems. Int. J. Syst. Sci. (2015)
Peng, J.J., Wang, J.Q., Wu, X.H., Zhang, H.Y., Chen, X.H.: Thefuzzy cross-entropy for intuitionistic hesitant fuzzy sets and their application in multi-criteria decision-making. Int. J. Syst. Sci. 46(13), 2335–2350 (2014)
Wang, J.Q., Peng, J.J., Zhang, H.Y., Liu, T., Chen, X.H.: An uncertain linguistic multi-criteria group decision-making method based ona cloud model. Group Decis. Negot. 24(1), 171–192 (2015)
Deli, I., Ali, M., Smarandache, F.: Bipolar Neutrosophic Sets and Their Application Based on Multi-criteria Decision Making Problems (2015)
Peng, J.J., Wang, J.Q., Wu, X.H., Wang, J., Chen, X.H.: Multivaluedneutrosophic sets and power aggregation operators with their applications in multi-criteria group decision-making problems. Int. Comput. Intell. Syst. 8(2), 345–363 (2015)
Wang, J.Q., Li, X.E.: The TODIMmethod with multi-valued neutrosophicsets. Control Decis. 30(6), 1139–1142 (2015)
Selin Soner Kara and Naoufel Cheikhrouhou: A multi criteria group decision making approach for collaborative software selection problem. J. Intell. Fuzzy Syst. 26, 37–47 (2014)
Wang, **n-Fan, Wang, Jian-Qiang, Yang, Wu-E: Multi-criteria group decision making method based on intuitionistic linguistic aggregation operators. J. Intell. Fuzzy Syst. 26, 115–125 (2014)
Chen, X., Yang, L., Wang, P., Yue, W.: A Fuzzy multicriteria group decision-making method with new entropy of interval-valued intuitionistic fuzzy sets. J. Appl. Math. 1–8 (2013)
Wang, J., Han, Z., Zhang, H.: Multi-criteria group decision-making method based on intuitionistic interval fuzzy information. Group Decis. Negot. 23, 715–733 (2014)
Chaio, K.-P.: The multi-criteria group decision making methodology using type 2 fuzzy linguistic judgments, Appl. Soft Comput. (2016)
Wibowo, S., Grandhi, S., Deng, H.: Multicriteria Group Decision Making for Selecting Human Resources Management Information Systems Projects. IEEE (2016)
Hanine, M., Boutkhoum, O., Tikniouine, A., Agouti, T.: A new web-based framework development for fuzzy multi-criteria group decision-making. SpringerPlus 5, 601 (2016)
Büyüközkan, G., Güleryüz, S.: Multi criteria group decision making approach for smart phone selection using intuitionistic fuzzy TOPSIS. Int. J. Comput. Intell. Syst. 9(4), 709–725 (2016)
Efe, B.: An integrated fuzzy multi criteria group decision making approach for ERP system selection. Appl. Soft Comput. (2016)
Seddiki, M., Anouche, K., Bennadji, A., Boateng, P.: A multi-criteria group decision-making method for the thermal innovation of masonry buildings: the case of Algeria. Energy Build. 129, 471–483 (2016)
Shen, F., Xu, J., Xu, Z.: An outranking sorting method for multi-criteria group decision making using intuitionistic fuzzy sets. Inf. Sci. (2016)
You, X., Chen, T., Yang, Q.: Approach to multi-criteria group decision-making problems based on the best-worst-method and ELECTRE method. Symmetry 8(95), 1–16 (2016)
Chuu, S.J.: Selecting the advanced manufacturing technology using fuzzy multiple attributes group decision making with multiple fuzzy information. Comput. Ind. Eng. 57(3), 1033–1042 (2007)
Liu, P., X.: Multi attribute group decision making methods based on linguistic intuitionistic fuzzy power Bonferroni mean operators. Complexity 2017, Article ID 3571459, 15 (2017) Hindawi Publishing Corporation
Chang, C.L., Hsu, C.H.: Multi-criteria analysis via the VIKOR method for prioritizing land-use restraint strategies in the Tseng-Wen reservoir watershed. J. Environ. Manage. 90, 3226–3230 (2009)
Chen, L.Y., Wang, T.-C.: Optimizing partners’ choice in IS/IT outsourcing projects: the strategic decision of fuzzy VIKOR. Int. J. Prod. Econ. 120, 233–242 (2009)
Sayadi, M.K., Heydari, M., Shahanaghi, K.: Extension of VIKOR method for decision making problem with interval numbers. Appl. Math. Model. 33, 2257–2262 (2009)
Chatterjee, P., Athawale, V.M., Chakraborty, S.: Selection of materials using compromise ranking and outranking methods. Mater. Des. 30, 4043–53 (2009)
Civic, A., Vucijak, B.: Multi-criteria optimization of insulation options for warmth of buildings to increase energy efficiency. Procedia Eng. 69, 911–920 (2014)
Sanayei, A., Mousavi, S.F., Yazdankhah, A.: Group decision making process for supplier selection with VIKOR under fuzzy environment. Expert Syst. Appl. 37, 24–30 (2010)
Shemshadi, A., Shirazi, H., Toreihi, M., Tarokh, M.J.: A fuzzy VIKOR method for supplier selection based on entropy measure for objective weighting. Expert Syst. Appl. 38, 12160–12167 (2011)
Devi, K.: Extension of VIKOR method in intuitionist fuzzy environment for robot selection. Expert Syst. Appl. 38, 14163–14168 (2011)
Wang, J., Han, Z., Zhang, H.: Multi-criteria group decision-making method based on intuitionistic interval fuzzy information. Group Decis. Negot. 23, 715–733 (2014)
Aiwua, Z., Jianguoa, D., Hongjunb, G.: Interval valued neutrosophic sets and multi-attribute decision-making based on generalized weighted aggregation operator. J. Intell. Fuzzy Syst. 29, 2697–2706 (2015)
Zeshui, Xu: On method for uncertain multiple attribute decision making problems with uncertain multiplicative preference information on alternatives. Fuzzy Optim. Decis. Making 4, 131–139 (2005)
Acknowledgements
The second author of the article wishes to convey his heartiest thanks to Miss. Gullu for inspiring him to write the chapter.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendices
Appendix 1
Appendix 2
Appendix 3
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Hussain, S.A.I., Mondal, S.P., Mandal, U.K. (2019). VIKOR Method for Decision Making Problems in Interval Valued Neutrosophic Environment. In: Kahraman, C., Otay, Ä°. (eds) Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets. Studies in Fuzziness and Soft Computing, vol 369. Springer, Cham. https://doi.org/10.1007/978-3-030-00045-5_22
Download citation
DOI: https://doi.org/10.1007/978-3-030-00045-5_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-00044-8
Online ISBN: 978-3-030-00045-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)