Systematic Review of Decision Making Algorithms in Extended Neutrosophic Sets
Abstract
:1. Introduction
2. Preliminary
- 1.
- 2.
- 3.
3. Reviewof Multi-Attribute Decision Making Algorithmsin Extended Neutrosophic Sets
4. Some Typical Decision Making Methodson Extended Neutrosopic Sets
4.1. Single Valued Neutrosophic Set (SVNS)
- For benefit criteria (the better is larger), where and where is the wanted or chosen level, and is thepoorest level.
- For cost criteria (the better is smaller), .
… | ||||
… | ||||
- for and .
4.2. Interval Neutrosophic Set
4.3. Bipolar Neutrosophic Set
4.4. Refined Neutrosophic Set
4.5. Triangular Fuzzy Number Neutrosophic Set
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Smarandache, F. Neutrosophic set—A generalization of the intuitionistic fuzzy set. Int. J. Pure Appl. Math. 2004, 24, 287. [Google Scholar]
- Atanassov, K.T. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986, 20, 87–96. [Google Scholar] [CrossRef]
- Smarandache, F. Neutrosophy: A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability; American Research Press: Rehoboth, NM, USA, 2005. [Google Scholar]
- Wang, H.; Smarandache, F.; Zhang, Y.; Sunderraman, R. Single valued neutrosophic sets. In Proceedings of the 10th International. Conference on Fuzzy Theory and Technology, Salt Lake City, UT, USA, 21–26 July 2005. [Google Scholar]
- Wang, H.; Madiraju, P.; Zhang, Y.; Sunderraman, R. Interval neutrosophic sets. arXiv, 2004; arXiv:math/0409113. [Google Scholar]
- Maji, P.K. Neutrosophic soft set. Ann. Fuzzy Math. Inform. 2013, 5, 157–168. [Google Scholar]
- Broumi, S.; Smarandache, F. Intuitionistic neutrosophic soft set. J. Comput. Inf. Sci. Eng. 2013, 8, 130–140. [Google Scholar]
- Broumi, S.; Smarandache, F.; Dhar, M. Rough neutrosophic sets. Neutrosophic Sets Syst. 2014, 3, 62–67. [Google Scholar]
- Broumi, S.; Smarandache, F. Interval valued neutrosophic rough set. J. New Res. Sci. 2014, 7, 58–71. [Google Scholar]
- Broumi, S.; Smarandache, F. Interval valued neutrosophic soft rough set. Int. J. Comput. Math. 2015, 2015. [Google Scholar] [CrossRef]
- Ali, M.; Smarandache, F. Complex neutrosophic set. Neural Comput. Appl. 2017, 28, 1817–1834. [Google Scholar] [CrossRef]
- Deli, I.; Ali, M.; Smarandache, F. Bipolar neutrosophic sets and their application based on multi-criteria decision making problems. In Proceedings of the 2015 International Conference on Advanced Mechatronic Systems (ICAMechS), Beijing, China, 22–24 August 2015; pp. 249–254. [Google Scholar]
- Ali, M.; Deli, I.; Smarandache, F. The theory of neutrosophic cubic sets and their applications in pattern recognition. J. Intell. Fuzzy Syst. 2016, 30, 1957–1963. [Google Scholar] [CrossRef]
- Wang, H.; Smarandache, F.; Zhang, Y.; Sunderraman, R. Single valued neutrosophic sets. Rev. Air Force Acad. 2010, 1, 10. [Google Scholar]
- Wang, H.; Smarandache, F.; Sunderraman, R.; Zhang, Y.Q. Interval Neutrosophic Sets and Logic: Theory and Applications in Computing; Hexis: Phoenix, AR, USA, 2005; Volume 5. [Google Scholar]
- Biswas, P.; Pramanik, S.; Giri, B.C. TOPSIS method for multi-attribute group decision making under single-valued neutrosophic environment. Neural Comput. Appl. 2016, 27, 727–737. [Google Scholar] [CrossRef]
- Ye, J. Multi-criteria decision making method using the correlation coefficient under single-valued neutrosophic environment. Int. J. Gen. Syst. 2013, 42, 386–394. [Google Scholar] [CrossRef]
- Deli, I.; Subas, Y. Single valued neutrosophic numbers and their applications to multicriteria decision making problem. Neutrosophic Sets Syst. 2014, 2, 1–13. [Google Scholar]
- Huang, H. New distance measure of single-valued neutrosophic sets and its application. Int. J. Intell. Syst. 2016, 31, 1021–1032. [Google Scholar] [CrossRef]
- Yang, L.; Li, B. A Multi-Criteria Decision-Making Method Using Power Aggregation Operators for Single-valued Neutrosophic Sets. Int. J. Database Theory Appl. 2016, 9, 23–32. [Google Scholar] [CrossRef]
- Ye, J. Single valued neutrosophic cross-entropy for multi-criteria decision making problems. Appl. Math. Model. 2014, 38, 1170–1175. [Google Scholar] [CrossRef]
- Deli, I.; Şubaş, Y. A ranking method of single valued neutrosophic numbers and its applications to multi-attribute decision making problems. Int. J. Mach. Learn. Cybern. 2017, 8, 1309–1322. [Google Scholar] [CrossRef]
- Ye, J. Improved correlation coefficients of single valued neutrosophic sets and interval neutrosophic sets for multiple attribute decision making. J. Intell. Fuzzy Syst. 2014, 27, 2453–2462. [Google Scholar]
- Ye, J.; Zhang, Q. Single valued neutrosophic similarity measures for multiple attribute decision making. Neutrosophic Sets Syst. 2014, 2, 48–54. [Google Scholar]
- Ye, J. An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers. J. Intell. Fuzzy Syst. 2015, 28, 247–255. [Google Scholar]
- Ye, J. Improved cross entropy measures of single valued neutrosophic sets and interval neutrosophic sets and their multicriteria decision making methods. Cybern. Inf. Technol. 2015, 15, 13–26. [Google Scholar] [CrossRef]
- Ye, J.; Fu, J. Multi-period medical diagnosis method using a single valued neutrosophic similarity measure based on tangent function. Comput. Methods Programs Biomed. 2016, 123, 142–149. [Google Scholar] [CrossRef] [PubMed]
- Sahin, R.; Karabacak, M. A multi attribute decision making method based on inclusion measure for interval neutrosophic sets. Int. J. Eng. Appl. Sci. 2015, 2, 13–15. [Google Scholar]
- Chi, P.; Liu, P. An extended TOPSIS method for the multiple attribute decision making problems based on interval neutrosophic set. Neutrosophic Sets Syst. 2013, 1, 63–70. [Google Scholar]
- Huang, Y.; Wei, G.; Wei, C. VIKOR method for interval neutrosophic multiple attribute group decision-making. Information 2017, 8, 144. [Google Scholar] [CrossRef]
- Liu, P.; Wang, Y. Interval neutrosophic prioritized OWA operator and its application to multiple attribute decision making. J. Syst. Sci. Complex. 2016, 29, 681–697. [Google Scholar] [CrossRef]
- Tian, Z.P.; Zhang, H.Y.; Wang, J.; Wang, J.Q.; Chen, X.H. Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets. Int. J. Syst. Sci. 2016, 47, 3598–3608. [Google Scholar] [CrossRef]
- Ye, J. Similarity measures between interval neutrosophic sets and their applications in multi-criteria decision making. J. Intell. Fuzzy Syst. 2014, 26, 165–172. [Google Scholar]
- Zhang, H.Y.; Wang, J.Q.; Chen, X.H. Interval neutrosophic sets and their application in multi-criteria decision making problems. Sci. World J. 2014, 2014, 1–15. [Google Scholar]
- 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]
- Dey, P.P.; Pramanik, S.; Giri, B.C. TOPSIS for Solving Multi-Attribute Decision Making Problems under Bi-Polar Neutrosophic Environment. In New Trends in Neutrosophic Theory and Applications; Smarandache, F., Pramanik, S., Eds.; Pons asbl: Brussels, Belgium, 2016; p. 65. [Google Scholar]
- Ali, M.; Son, L.H.; Deli, I.; Tien, N.D. Bipolar neutrosophic soft sets and applications in decision making. J. Intell. Fuzzy Syst. 2017, 33, 4077–4087. [Google Scholar] [CrossRef]
- Uluçay, V.; Deli, I.; Şahin, M. Similarity measures of bipolar neutrosophic sets and their application to multiple criteria decision making. Neural Comput. Appl. 2018, 29, 739–748. [Google Scholar] [CrossRef]
- Sahin, R.; Küçük, A. Generalised Neutrosophic Soft Set and its Integration to Decision Making Problem. Appl. Math. Inf. Sci. 2014, 8, 2751–2759. [Google Scholar] [CrossRef]
- Broumi, S.; Sahin, R.; Smarandache, F. Generalized interval neutrosophic soft set and its decision making problem. J. New Res. Sci. 2014, 3, 29–47. [Google Scholar]
- Mondal, K.; Pramanik, S. Neutrosophic refined similarity measure based on cotangent function and its application to multi-attribute decision making. J. New Theory 2015, 8, 41–50. [Google Scholar]
- Samuel, A.E.; Narmadhagnanam, R. Neutrosophic refined sets in medical diagnosis. Int. J. Fuzzy Math. Arch. 2017, 14, 117–123. [Google Scholar]
- Pramanik, S.; Banerjee, D.; Giri, B. TOPSIS Approach for Multi Attribute Group Decision Making in Refined Neutrosophic Environment. In New Trends in Neutrosophic Theory and Applications; Smarandache, F., Pramanik, S., Eds.; Pons asbl: Brussels, Belgium, 2016. [Google Scholar]
- Chen, J.; Ye, J.; Du, S. Vector similarity measures between refined simplified neutrosophic sets and their multiple attribute decision-making method. Symmetry 2017, 9, 153. [Google Scholar] [CrossRef]
- Biswas, P.; Pramanik, S.; Giri, B.C. Aggregation of triangular fuzzy neutrosophic set information and its application to multi-attribute decision making. Neutrosophic Sets Syst. 2016, 12, 20–40. [Google Scholar]
- Zhang, X.; Liu, P. Method for aggregating triangular fuzzy intuitionistic fuzzy information and its application to decision making. Technol. Econ. Dev. Econ. 2010, 16, 280–290. [Google Scholar] [CrossRef] [Green Version]
- Biswas, P.; Pramanik, S.; Giri, B.C. Cosine similarity measure based multi-attribute decision-making with trapezoidal fuzzy neutrosophic numbers. Neutrosophic Sets Syst. 2014, 8, 46–56. [Google Scholar]
- Ye, J. Trapezoidal neutrosophic set and its application to multiple attribute decision making. Neural Comput. Appl. 2015, 26, 1157–1166. [Google Scholar] [CrossRef]
- Mondal, K.; Surapati, P.; Giri, B.C. Role of Neutrosophic Logic in Data Mining. In New Trends in Neutrosophic Theory and Applications; Smarandache, F., Pramanik, S., Eds.; Pons asbl: Brussels, Belgium, 2016; pp. 15–23. [Google Scholar]
- Radwan, N.M. Neutrosophic Applications in E-learning: Outcomes, Challenges and Trends. In New Trends in Neutrosophic Theory and Applications; Smarandache, F., Pramanik, S., Eds.; Pons asbl: Brussels, Belgium, 2016; pp. 177–184. [Google Scholar]
- Koundal, D.; Gupta, S.; Singh, S. Applications of Neutrosophic Sets in Medical Image Diagnosing and segmentation. In New Trends in Neutrosophic Theory and Applications; Smarandache, F., Pramanik, S., Eds.; Pons asbl: Brussels, Belgium, 2016; pp. 257–275. [Google Scholar]
- Patro, S.K. On a Model of Love dynamics: A Neutrosophic analysis. In New Trends in Neutrosophic Theory and Applications; Smarandache, F., Pramanik, S., Eds.; Pons asbl: Brussels, Belgium, 2016; pp. 279–287. [Google Scholar]
- Zadeh, L.A. Fuzzy Sets. Inf. Control 1965, 8, 338–353. [Google Scholar] [CrossRef]
- Molodtsov, D. Soft set theory—First result. Comput. Math. Appl. 1999, 37, 19–31. [Google Scholar] [CrossRef]
- Karaaslan, F. Correlation coefficients of single-valued neutrosophic refined soft sets and their applications in clustering analysis. Neural Comput. Appl. 2017, 28, 2781–2793. [Google Scholar]
- Broumi, S.; Smarandache, F. Extended Hausdorff distance and similarity measures for neutrosophic refined sets and their application in medical diagnosis. J. New Theory 2015, 7, 64–78. [Google Scholar]
- Boran, F.E.; Genç, S.; Kurt, M.; Akay, D. A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Syst. Appl. 2009, 36, 11363–11368. [Google Scholar] [CrossRef]
- Dezert, J. Open Questions on Neutrosophic Inference. Mult.-Valued Log. 2002, 8, 439–472. [Google Scholar]
- Wang, Y.M. Using the method of maximizing deviations to make decision for multi-indices. Syst. Eng. Electron. 1998, 7, 31. [Google Scholar]
- Nădăban, S.; Dzitac, S. Neutrosophic TOPSIS: A general view. In Proceedings of the 2016 6th International Conference on Computers Communications and Control (ICCCC), Oradea, Romania, 10–14 May 2016; pp. 250–253. [Google Scholar]
- Broumi, S.; Smarandache, F. Neutrosophic refined similarity measure based on cosine function. Neutrosophic Sets Syst. 2014, 6, 42–48. [Google Scholar]
- Broumi, S.; Smarandache, F. Correlation coefficient of interval neutrosophic set. In Applied Mechanics and Materials; Trans Tech Publications, Inc.: Zürich, Switzerland, 2013; pp. 511–517. [Google Scholar]
- Broumi, S.; Smarandache, F. More on intuitionistic neutrosophic soft sets. Comput. Sci. Inf. Technol. 2013, 1, 257–268. [Google Scholar]
- Ali, M.; Son, L.H.; Thanh, N.D.; Nguyen, V.M. A neutrosophic recommender system for medical diagnosis based on algebraic neutrosophic measures. Appl. Soft Comput. 2018. [Google Scholar] [CrossRef]
- Al-Quran, A.; Hassan, N. Fuzzy parameterized single valued neutrosophic soft expert set theory and its application in decision making. Int. J. Appl. Decis. Sci. 2016, 9, 212–227. [Google Scholar]
- Ansari, A.Q.; Biswas, R.; Aggarwal, S. Proposal for applicability of neutrosophic set theory in medical AI. Int. J. Comput. Appl. 2011, 27, 5–11. [Google Scholar] [CrossRef]
- Bhowmik, M.; Pal, M. Intuitionistic neutrosophic set relations and some of its properties. J. Comput. Inform. Sci. 2010, 5, 183–192. [Google Scholar]
- Biswas, R.; Pandey, U.S. Neutrosophic Relational Database Decomposition. Int. J. Adv. Comput. Sci. Appl. 2011, 2, 121–125. [Google Scholar]
- Broumi, S.; Smarandache, F. Cosine similarity measure of interval valued neutrosophic sets. Neutrosophic Sets Syst. 2014, 5, 15–20. [Google Scholar]
- Broumi, S.; Smarandache, F. Several similarity measures of neutrosophic sets. Neutrosophic Sets Syst. 2013, 1, 54–62. [Google Scholar]
- Broumi, S.; Deli, I.; Smarandache, F. Neutrosophic parameterized soft set theory and its decision making. Ital. J. Pure Appl. Math. 2014, 32, 503–514. [Google Scholar]
- Deli, I.; Broumi, S.; Smarandache, F. On neutrosophic refined sets and their applications in medical diagnosis. J. New Theory 2015, 6, 88–98. [Google Scholar]
- Karaaslan, F. Possibility neutrosophic soft sets and PNS-decision making method. Appl. Soft Comput. 2017, 54, 403–414. [Google Scholar] [CrossRef]
- Maji, P.K. A neutrosophic soft set approach to a decision making problem. Ann. Fuzzy Math Inform. 2012, 3, 313–319. [Google Scholar]
- Pawlak, Z.; Grzymala-Busse, J.; Slowinski, R.; Ziarko, W. Rough sets. Commun. ACM 1995, 38, 88–95. [Google Scholar] [CrossRef]
- Peng, X.; Liu, C. Algorithms for neutrosophic soft decision making based on EDAS, new similarity measure and level soft set. J. Intell. Fuzzy Syst. 2017, 32, 955–968. [Google Scholar] [CrossRef]
- Peng, J.J.; Wang, J.; Wang, J.; Zhang, H.; Chen, X. Simplified neutrosophic sets and their applications in multi-criteria group decision-making problem. Int. J. Syst. Sci. 2016, 47, 2342–2358. [Google Scholar] [CrossRef]
- Sahin, R.; Liu, P. Maximizing deviation method for neutrosophic multiple attribute decision making with incomplete weight information. Neural Comput. Appl. 2015, 27, 2017–2029. [Google Scholar] [CrossRef]
- Schweizer, B.; Sklar, A. Statistical metric spaces. Pac. J. Math. 1960, 10, 313–334. [Google Scholar] [CrossRef] [Green Version]
- Thanh, N.D.; Ali, M.; Son, L.H. A novel clustering algorithm in a neutrosophic recommender system for medical diagnosis. Cogn. Comput. 2017, 9, 526–544. [Google Scholar] [CrossRef]
- Ye, J. A multi-criteria decision making method using aggregation operators for simplified neutrosophic sets. J. Intell. Fuzzy Syst. 2014, 26, 2459–2466. [Google Scholar]
- Ye, J. Fault diagnoses of hydraulic turbine using the dimension root similarity measure of single-valued neutrosophic sets. Intell. Autom. Soft Comput. 2016, 1–8. [Google Scholar] [CrossRef]
- Ye, J. Single-valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine. Soft Comput. 2017, 21, 817–825. [Google Scholar] [CrossRef]
- Ye, J.; Du, S. Some distances, similarity and entropy measures for interval valued neutrosophic sets and their relationship. Int. J. Mach. Learn. Cybern. 2017, 1–9. [Google Scholar] [CrossRef]
- Zhang, C.; Zhai, Y.; Li, D.; Mu, Y. Steam turbine fault diagnosis based on single-valued neutrosophic multigranulation rough sets over two universes. J. Intell. Fuzzy Syst. 2016, 31, 2829–2837. [Google Scholar] [CrossRef]
- Zhang, C.; Li, D.; Sangaiah, A.K.; Broumi, S. Merger and acquisition target selection based on interval neutrosophic multi-granulation rough sets over two universes. Symmetry 2017, 9, 126. [Google Scholar] [CrossRef]
- Jha, S.; Kumar, R.; Son, L.; Chatterjee, J.M.; Khari, M.; Yadav, N.; Smarandache, F. Neutrosophic soft set decision making for stock trending analysis. Evolv. Syst. 2018. [Google Scholar] [CrossRef]
- Dey, A.; Broumi, S.; Son, L.H.; Bakali, A.; Talea, M.; Smarandache, F. A new algorithm for finding minimum spanning trees with undirected neutrosophic graphs. Granul Comput. 2018, 1–7. [Google Scholar] [CrossRef]
- Ali, M.; Son, L.H.; Khan, M.; Tung, N.T. Segmentation of dental X-ray images in medical imaging using neutrosophic orthogonal matrices. Expert Syst. Appl. 2018, 91, 434–441. [Google Scholar] [CrossRef]
- Ali, M.; Dat, L.Q.; Son, L.H.; Smarandache, F. Interval complex neutrosophic set: Formulation and applications in decision-making. Int. J. Fuzzy Syst. 2018, 20, 986–999. [Google Scholar] [CrossRef]
- Nguyen, G.N.; Son, L.H.; Ashour, A.S.; Dey, N. A survey of the state-of-the-arts on neutrosophic sets in biomedical diagnoses. Int. J. Mach. Learn. Cybern. 2017, 1–13. [Google Scholar] [CrossRef]
- Thanh, N.D.; Son, L.H.; Ali, M. Neutrosophic recommender system for medical diagnosis based on algebraic similarity measure and clustering. In Proceedings of the 2017 IEEE International Conference on Fuzzy Systerm (FUZZ-IEEE), Naples, Italy, 9–12 July 2017; pp. 1–6. [Google Scholar]
- Broumi, S.; Bakali, A.; Talea, M.; Smarandache, F.; Selvachandran, G. Computing Operational Matrices in Neutrosophic Environments: A Matlab Toolbox. Neutrosophic Sets Syst. 2017, 18, 58–66. [Google Scholar]
No. | Type of Neutrosophic Model | Literature |
---|---|---|
(a) | Neutrosophic based models |
|
(b) | Neutrosophic based decision making methods for SVNS, INS and SNS |
|
(c) | Bipolar neutrosophic set |
|
(d) | Refined neutrosophic sets |
|
(e) | Triangular fuzzy/trapezoidal neutrosophic sets |
|
Alternative | Score Values of | Accuracy Values of |
---|---|---|
0.7960 | 0.5921 | |
0.8103 | 0.6247 | |
0.6464 | 0.1864 | |
0.6951 | 0.3789 |
Aggregated Rating Values | |||
---|---|---|---|
Alternative | Score Value | Accuracy Values |
---|---|---|
0.7791 | 0.5518 | |
0.8010 | 0.6016 | |
0.5962 | 0.1683 | |
0.6627 | 0.3096 |
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Khan, M.; Son, L.H.; Ali, M.; Chau, H.T.M.; Na, N.T.N.; Smarandache, F. Systematic Review of Decision Making Algorithms in Extended Neutrosophic Sets. Symmetry 2018, 10, 314. https://doi.org/10.3390/sym10080314
Khan M, Son LH, Ali M, Chau HTM, Na NTN, Smarandache F. Systematic Review of Decision Making Algorithms in Extended Neutrosophic Sets. Symmetry. 2018; 10(8):314. https://doi.org/10.3390/sym10080314
Chicago/Turabian StyleKhan, Mohsin, Le Hoang Son, Mumtaz Ali, Hoang Thi Minh Chau, Nguyen Thi Nhu Na, and Florentin Smarandache. 2018. "Systematic Review of Decision Making Algorithms in Extended Neutrosophic Sets" Symmetry 10, no. 8: 314. https://doi.org/10.3390/sym10080314
APA StyleKhan, M., Son, L. H., Ali, M., Chau, H. T. M., Na, N. T. N., & Smarandache, F. (2018). Systematic Review of Decision Making Algorithms in Extended Neutrosophic Sets. Symmetry, 10(8), 314. https://doi.org/10.3390/sym10080314