# A Novel Extension of the TOPSIS Method Adapted for the Use of Single-Valued Neutrosophic Sets and Hamming Distance for E-Commerce Development Strategies Selection

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

**Definition**

**1.**

**Definition**

**2.**

_{A}, I

_{A}, and F

_{A}$\in \text{}{[}^{-}0,{1}^{+}]$and satisfy the following constraint$0\le {\mu}_{A}(x)+{\pi}_{A}(x)+{\nu}_{A}(x)\le 3$.

**Definition**

**3.**

**Definition**

**4.**

**Definition**

**5.**

_{1}, x

_{2}, ..., x

_{n}) and Y = (y

_{1}, y

_{2}, ..., y

_{n}) be two n-dimensional vectors,${x}_{i}=<{t}_{xi},{i}_{xi},{f}_{xi}>$and${y}_{i}=<{t}_{yi},{i}_{yi},{f}_{yi}>$. The Hamming distance between X and Y is defined as

**Definition**

**6.**

_{1}, x

_{2}, ..., x

_{n}) and Y = (y

_{1}, y

_{2}, ..., y

_{n}) be two n-dimensional vectors,${x}_{i}=<{t}_{xi},{i}_{xi},{f}_{xi}>$and${y}_{i}=<{t}_{yi},{i}_{yi},{f}_{yi}>$. The Euclidean distance between X and Y is defined as

**Definition**

**7.**

**Definition**

**8.**

**Definition**

**9.**

_{j}is

_{j}is the element j of the weighting vector,${w}_{j}\in [0,\text{}1]$and${\sum}_{j=1}^{n}{w}_{j}}=1$.

## 3. The TOPSIS Method Customized to the Use of SVNNs and Group Decision-Making

#### 3.1. The TOPSIS Method

_{i}of the ith alternative to the ideal and anti-ideal solutions is calculated as

#### 3.2. An Extension of the TOPSIS Method Adapted for the Use of SVNNs

_{ij}in the evaluation matrix D means the rating of the alternative i with respect to the criterion j and entries w

_{j}in W of the weight vector denote the weights of the criterion j, for each i = 1, … m and j = 1, ..., n.

## 4. A Numerical Illustration

_{j}= 0.20.

## 5. Discussion and Comparison Analysis

_{2}and W

_{5}. In the first case (W

_{2}), both distances gave the same ranking order, whereas in the second case (W

_{5}), there was a difference in the second- and third-ranked alternatives.

_{j}= 0.20. The achieved ranking results are shown in Table 13.

## 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][Green Version] - 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][Green Version] - 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][Green Version] - 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][Green Version] - 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][Green Version] - 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 |
---|---|

A_{1}—E-customization and personalization—Ansari & Mela [70] | ECDS1 |

A_{2}—Social E-commerce adoption model—Hajli [71] | ECDS2 |

A_{3}—Strong search engine optimization (SEO)—Sen [72] | ECDS3 |

Criteria | Designation |
---|---|

C_{1}—Feasibility of the strategy | FS |

C_{2}—Implementation speed | IS |

C_{3}—Compliance with the corporate strategy | CS |

C_{4}—Compliance of the strategy with the mission and vision of the company | MV |

C_{5}—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> |

${\mathit{d}}_{\mathit{i}}^{+}$ | ${\mathit{d}}_{\mathit{i}}^{-}$ | ${\mathit{C}}_{\mathit{i}}$ | 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 |

${\mathit{d}}_{\mathit{i}}^{+}$ | ${\mathit{d}}_{\mathit{i}}^{-}$ | ${\mathit{C}}_{\mathit{i}}$ | 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 |

w_{1} | w_{2} | w_{3} | w_{4} | w_{5} | Σw_{j} | |
---|---|---|---|---|---|---|

W_{1} | 0.40 | 0.15 | 0.15 | 0.15 | 0.15 | 1.00 |

W_{2} | 0.15 | 0.40 | 0.15 | 0.15 | 0.15 | 1.00 |

W_{3} | 0.15 | 0.15 | 0.40 | 0.15 | 0.15 | 1.00 |

W_{4} | 0.15 | 0.15 | 0.15 | 0.40 | 0.15 | 1.00 |

W_{5} | 0.15 | 0.15 | 0.15 | 0.15 | 0.40 | 1.00 |

W_{1} | W_{2} | W_{3} | W_{4} | W_{5} | ||||||
---|---|---|---|---|---|---|---|---|---|---|

${\mathit{C}}_{\mathit{i}}$ | Rank | ${\mathit{C}}_{\mathit{i}}$ | Rank | ${\mathit{C}}_{\mathit{i}}$ | Rank | ${\mathit{C}}_{\mathit{i}}$ | Rank | ${\mathit{C}}_{\mathit{i}}$ | 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 |

W_{1} | W_{2} | W_{3} | W_{4} | W_{5} | ||||||
---|---|---|---|---|---|---|---|---|---|---|

${\mathit{C}}_{\mathit{i}}$ | Rank | ${\mathit{C}}_{\mathit{i}}$ | Rank | ${\mathit{C}}_{\mathit{i}}$ | Rank | ${\mathit{C}}_{\mathit{i}}$ | Rank | ${\mathit{C}}_{\mathit{i}}$ | 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 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Karabašević, D.; Stanujkić, D.; Zavadskas, E.K.; Stanimirović, P.; Popović, G.; Predić, B.; Ulutaş, A.
A Novel Extension of the TOPSIS Method Adapted for the Use of Single-Valued Neutrosophic Sets and Hamming Distance for E-Commerce Development Strategies Selection. *Symmetry* **2020**, *12*, 1263.
https://doi.org/10.3390/sym12081263

**AMA Style**

Karabašević D, Stanujkić D, Zavadskas EK, Stanimirović P, Popović G, Predić B, Ulutaş A.
A Novel Extension of the TOPSIS Method Adapted for the Use of Single-Valued Neutrosophic Sets and Hamming Distance for E-Commerce Development Strategies Selection. *Symmetry*. 2020; 12(8):1263.
https://doi.org/10.3390/sym12081263

**Chicago/Turabian Style**

Karabašević, Darjan, Dragiša Stanujkić, Edmundas Kazimieras Zavadskas, Predrag Stanimirović, Gabrijela Popović, Bratislav Predić, and Alptekin Ulutaş.
2020. "A Novel Extension of the TOPSIS Method Adapted for the Use of Single-Valued Neutrosophic Sets and Hamming Distance for E-Commerce Development Strategies Selection" *Symmetry* 12, no. 8: 1263.
https://doi.org/10.3390/sym12081263