1. Home
  2. Issues
  3. Volume 31, Issue 1 (2020)
  4. TOPSIS Method for Neutrosophic Hesitant ...

Informatica


TOPSIS Method for Neutrosophic Hesitant Fuzzy Multi-Attribute Decision Making
Volume 31, Issue 1 (2020), pp. 35–63
Pub. online: 23 March 2020      Type: Research Article      Open accessOpen Access
Received
1 May 2019
Accepted
1 September 2019
Published
23 March 2020

Abstract

Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a very common and useful method for solving multi-criteria decision making problems in certain and uncertain environments. Single valued neutrosophic hesitant fuzzy set (SVNHFS) and interval neutrosophic hesitant fuzzy set (INHFS) are developed on the integration of neutrosophic set and hesitant fuzzy set. In this paper, we extend TOPSIS method for multi-attribute decision making based on single valued neutrosophic hesitant fuzzy set and interval neutrosophic hesitant fuzzy set. Furthermore, we assume that the attribute weights are known, incompletely known or completely unknown. We establish two optimization models for SVNHFS and INHFS with the help of maximum deviation method. Finally, we provide two numerical examples to validate the proposed approach.

References

 
Atanassov, K.T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.
 
Beg, I., Rashid, T. (2013). TOPSIS for hesitant fuzzy linguistic term sets. International Journal of Intelligent Systems, 28(12), 1162–1171.
 
Biswas, P., Pramanik, S., Giri, B.C. (2016a). TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment. Neural Computing and Applications, 27(3), 727–737.
 
Biswas, P., Pramanik, S., Giri, B.C. (2016b). GRA method of multiple attribute decision making with single valued neutrosophic hesitant fuzzy set information. New Trends in Neutrosophic Theory and Applications, Brussells, Pons Editions, 55–63.
 
Biswas, P., Pramanik, S., Giri, B.C. (2018). TOPSIS strategy for multi-attribute decision making with trapezoidal neutrosophic numbers Neutrosophic. Sets and Systems, 19, 29–39.
 
Biswas, P., Pramanik, S., Giri, B.C. (2019a). Non-linear programming approach for single-valued neutrosophic TOPSIS method. New Mathematics and Natural Computation. https://doi.org/10.1142/S1793005719500169.
 
Biswas, P., Pramanik, S., Giri, B.C. (2019b). NH-MADM strategy in neutrosophic hesitant fuzzy set environment based on extended GRA. Informatica, 30(2), 213–242.
 
Boran, F.E., Genç, S., Kurt, M., Akay, D. (2009). A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Systems with Applications, 36(8), 11363–11368.
 
Brans, J.P., Vincke, P., Mareschal, B. (1986). How to select and how to rank projects: the PROMETHEE method. European Journal of Operational Research, 24(2), 228–238.
 
Brauers, W.K., Zavadskas, E.K. (2006). The MOORA method and its application to privatization in a transition economy. Control and Cybernetics, 35, 445–469.
 
Brauers, W.K.M., Zavadskas, E.K. (2010). Project management by MULTIMOORA as an instrument for transition economies. Technological and Economic Development of Economy, 16(1), 5–24.
 
Chen, C.T. (2000). Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets and Systems, 114(1), 1–9.
 
Chen, N., Xu, Z., Xia, M. (2013). Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Applied Mathematical Modelling, 37(4), 2197–2211.
 
Chi, P., Liu, P. (2013). An extended TOPSIS method for the multiple attribute decision making problems based on interval neutrosophic set. Neutrosophic Sets and Systems, 1(1), 63–70.
 
Fu, Z., Liao, H. (2019). Unbalanced double hierarchy linguistic term set: the TOPSIS method for multi-expert qualitative decision making involving green mine selection. Information Fusion, 51, 271–286.
 
Gabus, A., Fontela, E. (1972). World problems. In: An Invitation to Further Thought Within the Framework of DEMATEL, Battelle Geneva Research Center, Geneva, Switzerland, pp. 1–8.
 
Giri, B.C., Molla, M.U., Biswas, P. (2018). TOPSIS method for MADM based on interval trapezoidal neutrosophic number. Neutrosophic Sets and Systems, 22, 151.
 
Gomes, L.F.A.M., Lima, M.M.P.P. (1992a). TODIM: basics and application to multi–criteria ranking of projects with environmental impacts. Foundations of Computing and Decision Sciences, 16(4), 113–127.
 
Gomes, L.F.A.M., Lima, M.M.P.P. (1992b). From modeling individual preferences to multi–criteria ranking of discrete alternatives: a look at prospect theory and the additive difference model. Foundations of Computing and Decision Sciences, 17(3), 171–184.
 
Hafezalkotob, A., Hafezalkotob, A., Liao, H., Herrera, F. (2019). An overview of MULTIMOORA for multi-criteria decision-making: theory, developments, applications, and challenges. Information Fusion, 51, 145–177.
 
Haibin, W., Smarandache, F., Zhang, Y., Sunderraman, R. (2010). Single valued neutrosophic sets. Multispace and Multi-Structure, 4, 410–413.
 
Hwang, C.L., Yoon, K. (1981). Methods for multiple attribute decision making. In: Multiple Attribute Decision Making. Springer, Berlin, Heidelberg, 48–191.
 
Ji, P., Zhang, H.Y., Wang, J.Q. (2018). A projection-based TODIM method under multi-valued neutrosophic environments and its application in personnel selection. Neural Computing and Applications, 29(1), 221–234.
 
Joshi, D., Kumar, S. (2016). Interval-valued intuitionistic hesitant fuzzy Choquet integral based TOPSIS method for multi-criteria group decision making. European Journal of Operational Research, 248(1), 183–191.
 
Kahraman, C., Otay, İ. (Eds.) (2019). Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets. Springer.
 
Kanapeckiene, L., Kaklauskas, A., Zavadskas, E.K., Raslanas, S. (2011). Method and system for multi-attribute market value assessment in analysis of construction and retrofit projects. Expert Systems with Applications, 38(11), 14196–14207.
 
Keshavarz Ghorabaee, M., Zavadskas, E.K., Olfat, L., Turskis, Z. (2015). Multi-criteria inventory classification using a new method of evaluation based on distance from average solution (EDAS). Informatica, 26(3), 435–451.
 
Liu, P., Shi, L. (2015). The generalized hybrid weighted average operator based on interval neutrosophic hesitant set and its application to multiple attribute decision making. Neural Computing and Applications, 26(2), 457–471.
 
Liao, H., Xu, Z. (2015). Approaches to manage hesitant fuzzy linguistic information based on the cosine distance and similarity measures for HFLTSs and their application in qualitative decision making. Expert Systems with Applications, 42(12), 5328–5336.
 
Liao, H., Wu, X. (2019). DNMA: a double normalization-based multiple aggregation method for multi-expert multi-criteria decision making. Omega. https://doi.org/10.1016/j.omega.2019.04.001.
 
Mi, X., Tang, M., Liao, H., Shen, W., Lev, B. (2019). The state-of-the-art survey on integrations and applications of the best worst method in decision making: why, what, what for and what’s next? Omega. https://doi.org/10.1016/j.omega.2019.01.009.
 
Opricovic, S., Tzeng, G.H. (2004). Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, 156(2), 445–455.
 
Peng, J.J., Wang, J.Q., 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.
 
Rodriguez, R.M., Martinez, L., Herrera, F. (2012). Hesitant fuzzy linguistic term sets for decision making. IEEE Transactions on Fuzzy Systems, 20(1), 109–119.
 
Roy, B. (1990). The outranking approach and the foundations of ELECTRE methods. In: Readings in Multiple Criteria Decision Aid. Springer, Berlin, Heidelberg, 155–183.
 
Sahin, R., Liu, P. (2017). Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making. Neural Computing and Applications, 28(6), 1387–1395.
 
Satty, T.L. (1980). The Analytic Hierarchy Process. McGrawHill, New York.
 
Smarandache, F. (1998). In: Neutrosophy. Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA (Vol. 105), pp. 118–123.
 
Smarandache, F. (2017). Plithogeny, Plithogenic Set, Logic, Probability, and Statistics. Infinite Study.
 
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.
 
Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25(6), 529–539.
 
Wang, H., Smarandache, F., Sunderraman, R., Zhang, Y.Q. (2005). Interval Neutrosophic Sets and Logic: Theory and Applications in Computing. Hexis, Phoenix, AZ.
 
Wei, G. (2012). Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowledge-Based Systems, 31, 176–182.
 
Wu, X., Liao, H. (2019). A consensus-based probabilistic linguistic gained and lost dominance score method. European Journal of Operational Research, 272(3), 1017–1027.
 
Xia, M., Xu, Z. (2011). Hesitant fuzzy information aggregation in decision making. International Journal of Approximate Reasoning, 52(3), 395–407.
 
Xu, Z., Xia, M. (2011a). Distance and similarity measures for hesitant fuzzy sets. Information Sciences, 181(11), 2128–2138.
 
Xu, Z., Xia, M. (2011b). On distance and correlation measures of hesitant fuzzy information. International Journal of Intelligent Systems, 26(5), 410–425.
 
Xu, Z., Zhang, X. (2013). Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowledge-Based Systems, 52, 53–64.
 
Ye, F. (2010). An extended TOPSIS method with interval-valued intuitionistic fuzzy numbers for virtual enterprise partner selection. Expert Systems with Applications, 37(10), 7050–7055.
 
Ye, J. (2014). Single valued neutrosophic cross-entropy for multi-criteria decision making problems. Applied Mathematical Modelling, 38(3), 1170–1175.
 
Ye, J. (2015a). An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers. Journal of Intelligent and Fuzzy Systems, 28(1), 247–255.
 
Ye, J. (2015b). Multiple-attribute decision-making method under a single-valued neutrosophic hesitant fuzzy environment. Journal of Intelligent Systems, 24(1), 23–36.
 
Ye, J. (2016). Correlation coefficients of interval neutrosophic hesitant fuzzy sets and its application in a multiple attribute decision making method. Informatica, 27(1), 179–202.
 
Yingming, W. (1997). Using the method of maximizing deviation to make decision for multi-indices. Journal of Systems Engineering and Electronics, 8(3), 21–26.
 
Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(3), 338–355.
 
Zhang, N., Wei, G. (2013). Extension of VIKOR method for decision making problem based on hesitant fuzzy set. Applied Mathematical Modelling, 37(7), 4938–4947.
 
Zavadskas, E.K., Kaklauskas, A., Sarka, V. (1994). The new method of multicriteria complex proportional assessment of projects. Technological and Economic Development of Economy, 1(3), 131–139.
 
Zavadskas, E.K., Antucheviciene, J., Hajiagha, S.H.R., Hashemi, S.S. (2014). Extension of weighted aggregated sum product assessment with interval-valued intuitionistic fuzzy numbers (WASPAS-IVIF). Applied Soft Computing, 24, 1013–1021.
 
Zavadskas, E.K., Mardani, A., Turskis, Z., Jusoh, A., Nor, K.M. (2016). Development of TOPSIS method to solve complicated decision-making problems—an overview on developments from 2000 to 2015. International Journal of Information Technology & Decision Making, 15(03), 645–682.

Biographies

Giri Bibhas C.
bcgiri.jumath@gmail.com

B.C. Giri is a professor at the Department of Mathematics, Jadavpur University, Kolkata, India. He has published many high-level papers in international peer-reviewed journals. His current research interests include supply chain management, inventory theory, multiple criteria decision making, soft computing, and optimization.

Molla Mahatab Uddin
mahatab.jumath@gmail.com

M.U. Molla is a junior research fellow at the Department of Mathematics, Jadavpur University, Kolkata. He obtained his BSc and MSc in Mathematics from University of Calcutta. His research interests include multiple criteria decision making, fuzzy set, intuitionistic fuzzy set, and neutrosophic set.

Biswas Pranab
prabiswas.jdvu@gmail.com

P. Biswas obtained his bachelor degree in mathematics and master degree in applied mathematics from University of Kalyani, India. He obtained his PhD degree from Jadavpur University, India. His research interests include multiple criteria decision making, aggregation operators, soft computing, optimization, fuzzy set, intuitionistic fuzzy set, and neutrosophic set.


Full article Related articles Cited by PDF XML
Full article Related articles Cited by PDF XML

Copyright
© 2020 Vilnius University
Open access article under the CC BY license.

Keywords
hesitant fuzzy set neutrosophic set single valued neutrosophic hesitant fuzzy set interval neutrosophic hesitant fuzzy set multi-attribute decision making TOPSIS

Funding
This research was supported by the Council of Scientific and Industrial Research (CSIR), Govt. of India, File No. 09/096(0945)/2018-EMR-I.

Metrics
since January 2020
1842

Article info
views

 919

Full article
views
1065

PDF
downloads

 351

XML
downloads


Share


RSS