A Note on Geometric Aggregation Operators in Spherical Fuzzy Environment and its Application in Multi-Attribute Decision Making
T-spherical fuzzy sets (T-SFSs) and spherical fuzzy sets (SFSs) are the generalizations of fuzzy sets (FSs), intuitionistic fuzzy set (IFS) and picture fuzzy sets (PFSs). This manuscript is a contribution to the area of SFSs and T-SFSs. In this manuscript, some properties of aggregation operators for SFSs and T-SFSs are discussed and some ordered weighted geometric (OWG) and hybrid geometric (HG) operators are developed. It is discussed that these aggregation operators are generalizations of the aggregation operators of IFSs and PFSs. Multi-attribute decision making (MADM) process is discussed in spherical fuzzy environment and illustrated with a numerical example. The results obtained are compared with the existing structures.
2. Chen, S.-M. and J.-M. Tan, Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy sets and systems, 1994. 67(2): p. 163-172.
3. Bellman, R.E. and L.A. Zadeh, Decision-making in a fuzzy environment. Management science, 1970. 17(4): p. B-141-B-164.
4. Zimmermann, H.-J., Fuzzy sets, decision making, and expert systems. Vol. 10. 2012: Springer Science & Business Media.
5. Kacprzyk, J. and M. Fedrizzi, Multiperson decision making models using fuzzy sets and possibility theory. Vol. 18. 2012: Springer Science & Business Media.
6. Grabisch, M., Fuzzy integral in multicriteria decision making. Fuzzy sets and Systems, 1995. 69(3): p. 279-298.
7. Yager, R.R., Quantifier guided aggregation using OWA operators. International Journal of Intelligent Systems, 1996. 11(1): p. 49-73.
8. Zimmermann, H.-J. and P. Zysno, Latent connectives in human decision making. Fuzzy sets and systems, 1980. 4(1): p. 37-51.
9. Calvo, T., G. Mayor, and R. Mesiar, Aggregation operators: new trends and applications. Vol. 97. 2012: Physica.
10. Mahmood, T., K. Ullah, and Q. Khan, Some Aggregation Operators For Bipolar-Valued Hesitant Fuzzy Information. Journal of Fundamental and Applied Sciences, 2018. 10(4S): p. 240-245.
11. Mahmood, T., et al., Some Aggregation Operators for Bipolar-Valued Hesitant Fuzzy Information based on Einstein Operational Laws. Journal of Engineering and Applied Sciences (JEAS), Peshawar, 2017. 36(2).
12. Atanassov, K.T., Intuitionistic fuzzy sets. Fuzzy sets and Systems, 1986. 20(1): p. 87-96.
13. Xu, Z., Intuitionistic fuzzy aggregation operators. IEEE Transactions on fuzzy systems, 2007. 15(6): p. 1179-1187.
14. Xu, Z. and R.R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets. International journal of general systems, 2006. 35(4): p. 417-433.
15. Wei, G., Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Applied soft computing, 2010. 10(2): p. 423-431.
16. Zhao, H., et al., Generalized aggregation operators for intuitionistic fuzzy sets. International Journal of Intelligent Systems, 2010. 25(1): p. 1-30.
17. Beliakov, G., et al., On averaging operators for Atanassov’s intuitionistic fuzzy sets. Information Sciences, 2011. 181(6): p. 1116-1124.
18. Li, D.-F., Multiattribute decision making method based on generalized OWA operators with intuitionistic fuzzy sets. Expert Systems with Applications, 2010. 37(12): p. 8673-8678.
19. Wei, G. and X. Wang. Some geometric aggregation operators based on interval-valued intuitionistic fuzzy sets and their application to group decision making. in Computational Intelligence and Security, 2007 International Conference on. 2007. IEEE.
20. Xu, Z. and M. Xia, Induced generalized intuitionistic fuzzy operators. Knowledge-Based Systems, 2011. 24(2): p. 197-209.
21. Yager, R.R. Pythagorean fuzzy subsets. in IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013 Joint. 2013. IEEE.
22. Yager, R.R., Pythagorean membership grades in multicriteria decision making. IEEE Transactions on Fuzzy Systems, 2014. 22(4): p. 958-965.
23. Yager, R.R. and A.M. Abbasov, Pythagorean membership grades, complex numbers, and decision making. International Journal of Intelligent Systems, 2013. 28(5): p. 436-452.
24. Peng, X. and Y. Yang, Some results for Pythagorean fuzzy sets. International Journal of Intelligent Systems, 2015. 30(11): p. 1133-1160.
25. Garg, H., A new generalized pythagorean fuzzy information aggregation using einstein operations and its application to decision making. International Journal of Intelligent Systems, 2016. 31(9): p. 886-920.
26. Garg, H., A Novel Correlation Coefficients between Pythagorean Fuzzy Sets and Its Applications to Decision‐Making Processes. International Journal of Intelligent Systems, 2016. 31(12): p. 1234-1252.
27. Cuong, B. Picture fuzzy sets-First results. Part 1. in Seminar Neuro-Fuzzy Systems with Applications. 2013.
28. Singh, P., Correlation coefficients for picture fuzzy sets. Journal of Intelligent & Fuzzy Systems, 2015. 28(2): p. 591-604.
29. Wei, G., Picture fuzzy cross-entropy for multiple attribute decision making problems. Journal of Business Economics and Management, 2016. 17(4): p. 491-502.
30. Thong, N.T., HIFCF: An effective hybrid model between picture fuzzy clustering and intuitionistic fuzzy recommender systems for medical diagnosis. Expert Systems with Applications, 2015. 42(7): p. 3682-3701.
31. Thong, P.H., A new approach to multi-variable fuzzy forecasting using picture fuzzy clustering and picture fuzzy rule interpolation method, in Knowledge and systems engineering. 2015, Springer. p. 679-690.
32. Wei, G., Some cosine similarity measures for picture fuzzy sets and their applications to strategic decision making. Informatica, 2017. 28(3): p. 547-564.
33. Wang, C., et al., Some geometric aggregation operators based on picture fuzzy sets and their application in multiple attribute decision making.
34. Garg, H., Some picture fuzzy aggregation operators and their applications to multicriteria decision-making. Arabian Journal for Science and Engineering, 2017. 42(12): p. 5275-5290.
35. Mahmood, T., Ullah, K. Khan, Q. and Jan, N., An Approach Towards Decision Making and Medical Diagnosis Problems Using the Concept of Spherical Fuzzy Sets. Neural Computing and Applications, 2018.
36. Ullah, K., T. Mahmood, and N. Jan, Similarity Measures for T-Spherical Fuzzy Sets with Applications in Pattern Recognition. Symmetry, 2018. 10(6): p. 193.