1. Introduction
2. Preliminaries
3. The TOPSIS Method Customized to the Use of SVNNs and Group Decision-Making
3.1. The TOPSIS Method
3.2. An Extension of the TOPSIS Method Adapted for the Use of SVNNs
4. A Numerical Illustration
5. Discussion and Comparison Analysis
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Magnusson, D.; Hermelin, B. ICT development from the perspective of connectivity and inclusion—The operation of a local digital agenda in Sweden. Nor. Geogr. Tidsskr. Nor. J. Geogr. 2019, 81–95. [Google Scholar] [CrossRef]
- Sandberg, K.W.; Håkansson, F. Strategical Use of ICT in Microenterprises: A Case Study. Int. J. E Entrep. Innov. 2020, 10, 1–13. [Google Scholar] [CrossRef]
- Nica, E. ICT innovation, internet sustainability, and economic development. J. Self Gov. Manag. Econ. 2015, 3, 242–249. [Google Scholar]
- Chaffey, D.; Hemphill, T.; Edmundson-Bird, D. Digital Business and E-Commerce Management; Pearson: London, UK, 2019. [Google Scholar]
- Goyal, S.; Sergi, B.S.; Esposito, M. Literature review of emerging trends and future directions of e-commerce in global business landscape. World Rev. Entrep. Manag. Sustain. Dev. 2019, 15, 226–255. [Google Scholar] [CrossRef]
- Laudon, K.C.; Traver, C.G. E-Commerce: Business, Technology, Society; Pearson: Essex, UK, 2016. [Google Scholar]
- Hua, N.; Hight, S.; Wei, W.; Ozturk, A.B.; Zhao, X.R.; Nusair, K.; DeFranco, A. The power of e-commerce. Int. J. Contemp. Hosp. Manag. 2019, 31, 1906–1923. [Google Scholar] [CrossRef]
- Johnson, G.; Whittington, R.; Scholes, K.; Angwin, D.N.; Regnér, P. Exploring Strategy, 11th ed.; Pearson: London, UK, 2017. [Google Scholar]
- Thompson, F.M.; Tuzovic, S.; Braun, C. Trustmarks: Strategies for exploiting their full potential in e-commerce. Bus. Horiz. 2019, 62, 237–247. [Google Scholar] [CrossRef]
- Ćurčić, N.; Piljan, I.; Simonović, Z. Marketing concept in insurance companies. Ekonomika 2019, 65, 21–23. [Google Scholar] [CrossRef]
- Jauković Jocić, K.; Jocić, G.; Karabašević, D.; Popović, G.; Stanujkić, D.; Zavadskas, E.K.; Thanh Nguyen, P. A Novel Integrated PIPRECIA—Interval-Valued Triangular Fuzzy ARAS Model: E-Learning Course Selection. Symmetry 2020, 12, 928. [Google Scholar] [CrossRef]
- Hassanpour, M.; Pamucar, D. Evaluation of Iranian household appliance industries using MCDM models. Oper. Res. Eng. Sci. Theory Appl. 2019, 2, 12–15. [Google Scholar] [CrossRef]
- Karabašević, D.; Maksimović, M.; Stanujkić, D.; Brzaković, P.; Brzaković, M. The evaluation of websites in the textile industry by applying ISO/IEC 91264-standard and the EDAS method. Ind. Text. 2018, 69, 4894. [Google Scholar]
- Fazlollahtabar, H.; Smailbašić, A.; Stević, Ž. FUCOM method in group decision-making: Selection of forklift in a warehouse. Decis. Mak. Appl. Manag. Eng. 2019, 2, 49–65. [Google Scholar] [CrossRef]
- Karabasević, D.; Stanujkić, D.; Maksimović, M.; Popović, G.; Momčilović, O. An Approach to Evaluating the Quality of Websites Based on the Weighted Sum Preferred Levels of Performances Method. Acta Polytech. Hung. 2019, 16, 195–215. [Google Scholar]
- Saaty, T.L. The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation; McGraw-Hill: New York, NY, USA, 1980. [Google Scholar]
- Roy, B. The outranking approach and the foundation of ELECTRE methods. Theory Decis. 1991, 31, 49–73. [Google Scholar] [CrossRef]
- Brans, J.P.; Vincke, P. Note—A Preference Ranking Organisation Method: (The PROMETHEE Method for Multiple Criteria Decision-Making). Manag. Sci. 1985, 31, 647–656. [Google Scholar] [CrossRef]
- Hwang, C.L.; Yoon, K. Multiple Attribute Decision Making: Methods and Applications; Springer: New York, NY, USA, 1981. [Google Scholar]
- Zavadskas, E.K.; Kaklauskas, A.; Sarka, V. The new method of multicriteria complex proportional assessment of projects. Technol. Econ. Dev. Econ. 1994, 1, 131–139. [Google Scholar]
- Opricović, S. Multicriteria Optimization of Civil Engineering Systems; Faculty of Civil Engineering: Belgrade, Serbia, 1998. [Google Scholar]
- Brauers, W.K.M.; Zavadskas, E.K. The MOORA method and its application to privatization in a transition economy. Control Cybern. 2006, 35, 445–469. [Google Scholar]
- Brauers, W.K.M.; Zavadskas, E.K. Project management by MULTIMOORA as an instrument for transition economies. Technol. Econ. Dev. Econ. 2010, 16, 52–54. [Google Scholar] [CrossRef]
- Nanayakkara, C.; Yeoh, W.; Lee, A.; Moayedikia, A. Deciding discipline, course and university through TOPSIS. Stud. High. Educ. 2019, 1–16. [Google Scholar] [CrossRef]
- Dos Santos, B.M.; Godoy, L.P.; Campos, L.M. Performance evaluation of green suppliers using entropy-TOPSIS-F. J. Clean. Prod. 2019, 207, 498–509. [Google Scholar] [CrossRef]
- Cavallaro, F.; Zavadskas, E.K.; Streimikiene, D.; Mardani, A. Assessment of concentrated solar power (CSP) technologies based on a modified intuitionistic fuzzy topsis and trigonometric entropy weights. Technol. Forecast. Soc. Chang. 2019, 140, 258–270. [Google Scholar] [CrossRef]
- Kwok, P.K.; Lau, H.Y. Hotel selection using a modified TOPSIS-based decision support algorithm. Decis. Support Syst. 2019, 120, 95–105. [Google Scholar] [CrossRef]
- Solangi, Y.A.; Tan, Q.; Mirjat, N.H.; Ali, S. Evaluating the strategies for sustainable energy planning in Pakistan: An integrated SWOT-AHP and Fuzzy-TOPSIS approach. J. Clean. Prod. 2019, 236, 117655. [Google Scholar] [CrossRef]
- Gupta, H.; Barua, M.K. Supplier selection among SMEs on the basis of their green innovation ability using BWM and fuzzy TOPSIS. J. Clean. Prod. 2017, 152, 242–258. [Google Scholar] [CrossRef]
- Efe, B. Website Evaluation Using Interval Type-2 Fuzzy-Number-Based TOPSIS Approach. In Multi-Criteria Decision-Making Models for Website Evaluation; IGI Global: Hershey, PA, USA, 2019; pp. 166–185. [Google Scholar]
- Wang, Y.M.; Elhag, T.M. Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment. Expert Syst. Appl. 2006, 31, 309–319. [Google Scholar] [CrossRef]
- Abdulsalam, K.; Ighravwe, D.; Babatunde, M. A fuzzy-TOPSIS approach for techno-economic viability of lighting energy efficiency measure in public building projects. J. Proj. Manag. 2018, 3, 197–206. [Google Scholar] [CrossRef]
- Ranjbar, H.R.; Nekooie, M.A. An improved hierarchical fuzzy TOPSIS approach to identify endangered earthquake-induced buildings. Eng. Appl. Artif. Intell. 2018, 76, 21–39. [Google Scholar] [CrossRef]
- Kelemenis, A.; Askounis, D. A new TOPSIS-based multi-criteria approach to personnel selection. Expert Syst. Appl. 2010, 37, 4999–5008. [Google Scholar] [CrossRef]
- Sang, X.; Liu, X.; Qin, J. An analytical solution to fuzzy TOPSIS and its application in personnel selection for knowledge-intensive enterprise. Appl. Soft Comput. 2015, 30, 190–204. [Google Scholar] [CrossRef]
- Samanlioglu, F.; Taskaya, Y.E.; Gulen, U.C.; Cokcan, O. A fuzzy AHP–TOPSIS-based group decision-making approach to IT personnel selection. Int. J. Fuzzy Syst. 2018, 20, 1576–1591. [Google Scholar] [CrossRef]
- Kelemenis, A.; Ergazakis, K.; Askounis, D. Support managers’ selection using an extension of fuzzy TOPSIS. Expert Syst. Appl. 2011, 38, 2774–2782. [Google Scholar] [CrossRef]
- Smarandache, F. Neutrosophy, Neutrosophic Probability, Set and Logic; American Res. Press: Rehoboth, DE, USA, 1998. [Google Scholar]
- Abdel-Basset, M.; Mohamed, M. A novel and powerful framework based on neutrosophic sets to aid patients with cancer. Future Gener. Comput. Syst. 2019, 98, 144–153. [Google Scholar] [CrossRef]
- Abdel-Basset, M.; Gamal, A.; Manogaran, G.; Long, H.V. A novel group decision making model based on neutrosophic sets for heart disease diagnosis. Multimed. Tools Appl. 2019, 1–26. [Google Scholar] [CrossRef]
- Abdel-Basset, M.; Mohamed, M.; Elhoseny, M.; Chiclana, F.; Zaied AE, N.H. Cosine similarity measures of bipolar neutrosophic set for diagnosis of bipolar disorder diseases. Artif. Intell. Med. 2019, 101, 101735. [Google Scholar] [CrossRef] [PubMed]
- Ulucay, V.; Kılıç, A.; Şahin, M.; Deniz, H. A new hybrid distance-based similarity measure for refined neutrosophic sets and its application in medical diagnosis. Matematika 2019, 35, 83–94. [Google Scholar] [CrossRef]
- Pratihar, J.; Kumar, R.; Dey, A.; Broumi, S. Transportation problem in neutrosophic environment. In Neutrosophic Graph Theory and Algorithms; IGI Global: Hershey, PA, USA, 2020; pp. 180–212. [Google Scholar]
- Smith, P. Exploring public transport sustainability with neutrosophic logic. Transp. Plan. Technol. 2019, 42, 257–273. [Google Scholar] [CrossRef]
- Elhassouny, A.; Idbrahim, S.; Smarandache, F. Machine learning in Neutrosophic Environment: A Survey. Neutrosophic Sets Syst. 2019, 28, 58–68. [Google Scholar]
- Jayaparthasarathy, G.; Little Flower, V.F.; Dasan, M.A. Neutrosophic Supra Topological Applications in Data Mining Process. Neutrosophic Sets Syst. 2019, 27, 80–97. [Google Scholar]
- Sengur, A.; Budak, U.; Akbulut, Y.; Karabatak, M.; Tanyildizi, E. A survey on neutrosophic medical image segmentation. In Neutrosophic Set in Medical Image Analysis; Academic Press: Cambridge, MA, USA, 2019; pp. 145–165. [Google Scholar]
- Tuan, T.M.; Chuan, P.M.; Ali, M.; Ngan, T.T.; Mittal, M. Fuzzy and neutrosophic modeling for link prediction in social networks. Evol. Syst. 2019, 10, 629–634. [Google Scholar] [CrossRef]
- Kahraman, C.; Otay, İ. Fuzzy Multi-Criteria Decision-Making Using Neutrosophic Sets; Springer: Berlin, Germany, 2019. [Google Scholar]
- Luo, M.; Wu, L.; Zhou, K.; Zhang, H. Multi-criteria decision making method based on the single valued neutrosophic sets. J. Intell. Fuzzy Syst. 2019, 37, 2403–2417. [Google Scholar] [CrossRef]
- Zhang, H.Y.; Ji, P.; Wang, J.Q.; Chen, X.H. An improved weighted correlation coefficient based on integrated weight for interval neutrosophic sets and its application in multi-criteria decision-making problems. Int. J. Comput. Intell. Syst. 2015, 8, 1027–1043. [Google Scholar] [CrossRef]
- Peng, J.J.; Wang, J.Q.; Zhang, H.Y.; Chen, X.H. An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets. Appl. Soft Comput. 2014, 25, 336–346. [Google Scholar] [CrossRef]
- Smarandache, F. A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic; American Research Press: Rehoboth, DE, USA, 1999. [Google Scholar]
- Wang, H.; Smarandache, F.; Zhang, Y.; Sunderraman, R. Single valued neutrosophic sets. Rev. Air Force Acad. 2010, 1, 10–14. [Google Scholar]
- Sahin, R. Multi-criteria neutrosophic decision making method based on score and accuracy functions under neutrosophic environment. arXiv, 2014; arXiv:1412.5202. [Google Scholar]
- Ye, J. Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment. Int. J. Gen. Syst. 2013, 42, 386–394. [Google Scholar] [CrossRef]
- Chang, C.H.; Lin, J.J.; Linc, J.H.; Chiang, M.C. Domestic open-end equity mutual fund performance evaluation using extended TOPSIS method with different distance approaches. Expert Syst. Appl. 2010, 37, 4642–4649. [Google Scholar] [CrossRef]
- Shanian, A.; Savadogo, O. TOPSIS multiple-criteria decision support analysis for material selection of metallic bipolar plates for polymer electrolyte fuel cell. J. Power Sources 2006, 159, 1095–1104. [Google Scholar] [CrossRef]
- Gautam, S.S.; Singh, S.R. An improved-based TOPSIS method in interval-valued intuitionistic fuzzy environment. Life Cycle Reliab. Saf. Eng. 2018, 7, 81–88. [Google Scholar] [CrossRef]
- Izadikhah, M. Using the Hamming distance to extend TOPSIS in a fuzzy environment. J. Comput. Appl. Math. 2009, 231, 200–207. [Google Scholar] [CrossRef]
- Chen, T.Y.; Tsao, C.Y. The interval-valued fuzzy TOPSIS method and experimental analysis. Fuzzy Sets Syst. 2008, 159, 1410–1428. [Google Scholar] [CrossRef]
- Yang, T.; Hung, C.C. Multiple-attribute decision making methods for plant layout design problem. Robot. Comput. Integr. Manuf. 2007, 23, 126–137. [Google Scholar] [CrossRef]
- Broumi, S.; Ye, J.; Smarandache, F. An extended TOPSIS method for multiple attribute decision making based on interval neutrosophic uncertain linguistic variables. Neutrosophic Sets Syst. 2015, 8, 22–31. [Google Scholar]
- Elhassouny, A.; Smarandache, F. Neutrosophic-simplified-TOPSIS multi-criteria decision-making using combined simplified-TOPSIS method and neutrosophics. In Proceedings of the 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Vancouver, BC, Canada, 24–29 July 2016; pp. 2468–2474. [Google Scholar]
- Srinivasan, V.; Shocker, A.D. Linear programming techniques for multidimensional analysis of preferences. Psychometrika 1973, 38, 337–369. [Google Scholar] [CrossRef]
- Kersuliene, V.; Turskis, Z. Integrated fuzzy multiple criteria decision making model for architect selection. Technol. Econ. Dev. Econ. 2011, 17, 645–666. [Google Scholar] [CrossRef]
- Pamucar, D.; Stevic, Z.; Sremac, S. A new model for determining weight coefficients of criteria in MCDM models: Full consistency method (FUCOM). Symmetry 2018, 10, 393. [Google Scholar] [CrossRef]
- Stanujkić, D.; Zavadskas, E.K.; Karabašević, D.; Smarandache, F.; Turskis, Z. The use of Pivot Pair-wise Relative Criteria Importance Assessment method for determining weights of criteria. Rom. J. Econ. Forecast. 2017, 20, 116–133. [Google Scholar]
- Stanujkić, D.; Karabašević, D.; Maksimović, M.; Popović, G.; Brzaković, M. Evaluation of the e-commerce development strategies. Quaestus 2019, 1, 144–152. [Google Scholar]
- Ansari, A.; Mela, C.F. E-customization. J. Mark. Res. 2003, 40, 131–145. [Google Scholar] [CrossRef]
- Hajli, M. A research framework for social commerce adoption. Inf. Manag. Comput. Secur. 2013, 21, 144–154. [Google Scholar] [CrossRef]
- Sen, R. Optimal search engine marketing strategy. Int. J. Electron. Commer. 2005, 10, 9–25. [Google Scholar] [CrossRef]


Alternatives | Designation |
---|---|
A1—E-customization and personalization—Ansari & Mela [70] | ECDS1 |
A2—Social E-commerce adoption model—Hajli [71] | ECDS2 |
A3—Strong search engine optimization (SEO)—Sen [72] | ECDS3 |
Criteria | Designation |
---|---|
C1—Feasibility of the strategy | FS |
C2—Implementation speed | IS |
C3—Compliance with the corporate strategy | CS |
C4—Compliance of the strategy with the mission and vision of the company | MV |
C5—General acceptance | GA |
FS | IS | CS | MV | GA | |
---|---|---|---|---|---|
ECDS1 | <0.6, 0.1, 0.1> | <0.6, 0.1, 0.1> | <0.6, 0.1, 0.1> | <0.4, 0.1, 0.1> | <0.4, 0.1, 0.1> |
ECDS2 | <1.0, 0.0, 0.0> | <0.8, 0.0, 0.0> | <1.0, 0.1, 0.1> | <1.0, 0.1, 0.3> | <1.0, 0.0, 0.1> |
ECDS3 | <0.6, 0.0, 0.2> | <0.6, 0.2, 0.1> | <0.8, 0.2, 0.1> | <1.0, 0.2, 0.3> | <1.0, 0.0, 0.2> |
FS | IS | CS | MV | GA | |
---|---|---|---|---|---|
ECDS1 | <0.5, 0.0, 0.1> | <0.7, 0.1, 0.1> | <0.5, 0.0, 0.1> | <0.4, 0.1, 0.1> | <0.4, 0.0, 0.1> |
ECDS2 | <0.9, 0.0, 0.0> | <0.7, 0.1, 0.0> | <0.9, 0.0, 0.0> | <1.0, 0.0, 0.1> | <0.7, 0.0, 0.2> |
ECDS3 | <0.7, 0.0, 0.0> | <0.6, 0.1, 0.1> | <0.8, 0.1, 0.2> | <0.9, 0.1, 0.3> | <0.8, 0.0, 0.2> |
FS | IS | CS | MV | GA | |
---|---|---|---|---|---|
ECDS1 | <0.5, 0.0, 0.0> | <0.8, 0.1, 0.1> | <0.6, 0.0, 0.1> | <0.5, 0.0, 0.0> | <0.5, 0.1, 0.1> |
ECDS2 | <0.8, 0.0, 0.1> | <0.7, 0.0, 0.0> | <1.0, 0.0, 0.0> | <0.9, 0.0, 0.1> | <0.6, 0.0, 0.1> |
ECDS3 | <0.8, 0.1, 0.1> | <0.7, 0.0, 0.0> | <0.8, 0.0, 0.1> | <0.9, 0.1, 0.2> | <0.8, 0.0, 0.0> |
FS | IS | CS | MV | GA | |
---|---|---|---|---|---|
ECDS1 | <0.5, 0.0, 0.0> | <0.7, 0.1, 0.1> | <0.6, 0.0, 0.1> | <0.4, 0.0, 0.0> | <0.4, 0.0, 0.1> |
ECDS2 | <1.0, 0.0, 0.0> | <0.7, 0.0, 0.0> | <1.0, 0.0, 0.0> | <1.0, 0.0, 0.1> | <1.0, 0.0, 0.1> |
ECDS3 | <0.7, 0.0, 0.0> | <0.6, 0.0, 0.0> | <0.8, 0.0, 0.1> | <1.0, 0.1, 0.3> | <1.0, 0.0, 0.0> |
FS | IS | CS | MV | GA | |
---|---|---|---|---|---|
ECDS+ | <1.0, 0.0, 0.0> | <0.7, 0.0, 0.0> | <1.0, 0.0, 0.0> | <1.0, 0.0, 0.0> | <1.0, 0.0, 0.0> |
ECDS− | <0.5, 0.0, 0.0> | <0.6, 0.1, 0.1> | <0.6, 0.0, 0.1> | <0.4, 0.1, 0.3> | <0.4, 0.0, 0.1> |
Rank | ||||
---|---|---|---|---|
ECDS1 | 0.87 | 0.69 | 0.44 | 3 |
ECDS2 | 0.38 | 1.08 | 0.74 | 1 |
ECDS3 | 0.63 | 0.66 | 0.51 | 2 |
Rank | ||||
---|---|---|---|---|
ECDS1 | 3.38 | 3.24 | 0.490 | 3 |
ECDS2 | 1.70 | 4.25 | 0.714 | 1 |
ECDS3 | 2.60 | 2.54 | 0.495 | 2 |
w1 | w2 | w3 | w4 | w5 | Σwj | |
---|---|---|---|---|---|---|
W1 | 0.40 | 0.15 | 0.15 | 0.15 | 0.15 | 1.00 |
W2 | 0.15 | 0.40 | 0.15 | 0.15 | 0.15 | 1.00 |
W3 | 0.15 | 0.15 | 0.40 | 0.15 | 0.15 | 1.00 |
W4 | 0.15 | 0.15 | 0.15 | 0.40 | 0.15 | 1.00 |
W5 | 0.15 | 0.15 | 0.15 | 0.15 | 0.40 | 1.00 |
W1 | W2 | W3 | W4 | W5 | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Rank | Rank | Rank | Rank | Rank | ||||||
ECDS1 | 0.45 | 3 | 0.51 | 2 | 0.44 | 3 | 0.39 | 3 | 0.43 | 3 |
ECDS2 | 0.74 | 1 | 0.70 | 1 | 0.72 | 1 | 0.75 | 1 | 0.78 | 1 |
ECDS3 | 0.50 | 2 | 0.43 | 3 | 0.54 | 2 | 0.59 | 2 | 0.49 | 2 |
W1 | W2 | W3 | W4 | W5 | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Rank | Rank | Rank | Rank | Rank | ||||||
ECDS1 | 0.49 | 3 | 0.56 | 2 | 0.48 | 3 | 0.44 | 3 | 0.48 | 2 |
ECDS2 | 0.72 | 1 | 0.67 | 1 | 0.70 | 1 | 0.73 | 1 | 0.76 | 1 |
ECDS3 | 0.50 | 2 | 0.41 | 3 | 0.54 | 2 | 0.57 | 2 | 0.46 | 3 |
Overall Ratings | Score | Rank | Cosine | Rank | |
---|---|---|---|---|---|
ECDS1 | <0.55, 0.00, 0.00> | 0.78 | 3 | 0.55 | 3 |
ECDS2 | <1.00, 0.00, 0.00> | 1.00 | 1 | 1.00 | 1 |
ECDS3 | <1.00, 0.00, 0.00> | 1.00 | 1 | 1.00 | 1 |
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