Document Type : Research Paper


Department of Mathematics, Research Scholar, Nirmala College for Women, Coimbatore, Tamilnadu, India.


Similarity measure is an important tool in multiple criteria decision-making problems, which can be used to measure the difference between the alternatives. In this paper, some new similarity measures of Spherical Fuzzy Sets (SFS) are defined based on the Euclidean distance measure and the proposed similarity measures satisfy the axiom of the similarity measure. Furthermore, we apply the proposed similarity measures to medical diagnosis decision making problem; the numerical example is used to illustrate the feasibility and effectiveness of the proposed similarity measures of SFS, which are then compared to other existing similarity measures.     


Main Subjects

[1]     Zadeh, L. A. (1996). Fuzzy sets. In Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers by Lotfi A Zadeh (pp. 394-432).
[2]     De, S. K., Biswas, R., & Roy, A. R. (1998). Multicriteria decision making using intuitionistic fuzzy set theory. Journal of fuzzy mathematics6, 837-842.
[3]     Phuong, N. H., Thang, V. V., & Hirota, K. (2000). Case based reasoning for medical diagnosis using fuzzy set theory. International journal of biomedical soft computing and human sciences: the official journal of the biomedical fuzzy systems association5(2), 1-7.
[4]     Song, Y., Wang, X., & Zhang, H. (2015). A distance measure between intuitionistic fuzzy belief functions. Knowledge-based systems86, 288-298.
[5]     Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning—I. Information sciences8(3), 199-249.
[6]     Atanassov, K. (2016). Intuitionistic fuzzy sets. International journal bioautomation20, 1-6.
[7]     Yang, Y., & Chiclana, F. (2009). Intuitionistic fuzzy sets: Spherical representation and distances. International journal of intelligent systems24(4), 399-420.
[8]     Gong, Z., Xu, X., Yang, Y., Zhou, Y., & Zhang, H. (2016). The spherical distance for intuitionistic fuzzy sets and its application in decision analysis. Technological and economic development of economy22(3), 393-415.
[9]     Beg, I., & Ashraf, S. (2009). Similarity measures for fuzzy sets. Appl. Comput. Math8(2), 192-202.
[10] Jun, Y. E. (2016). Multicriteria decision-making method based on cosine similarity measures between intervalvalued fuzzy sets with risk preference. Economic computation & economic cybernetics studies & research50(4), 205-215.
[11] Ye, J. (2011). Cosine similarity measures for intuitionistic fuzzy sets and their applications. Mathematical and computer modelling53(1-2), 91-97.
[12] Ye, J. (2014). Vector Similarty meaures of simplified neutrosophic sets and their application in multicriteria decision making, International journal of fuzzy systems, 16(2), 204-211.
[13] Ye, J. (2015). Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses. Artificial intelligence in medicine63(3), 171-179.
[14] Liu, D., Chen, X., & Peng, D. (2017). Interval-valued intuitionistic fuzzy ordered weighted cosine similarity measure and its application in investment decision-making. Complexity.
[15] Liu, D., Chen, X., & Peng, D. (2018). The intuitionistic fuzzy linguistic cosine similarity measure and its application in pattern recognition. Complexity2018. Complexity.
[16] Ashraf, S., & Abdullah, S. (2019). Spherical aggregation operators and their application in multiattribute group decision‐making. International journal of intelligent systems34(3), 493-523.
[17] Ashraf, S., Abdullah, S., Mahmood, T., Ghani, F., & Mahmood, T. (2019). Spherical fuzzy sets and their applications in multi-attribute decision making problems. Journal of intelligent & fuzzy systems36(3), 2829-2844. 1–16. DOI: 10.3233/JIFS-172009.
[18] Ashraf, S., Abdullah, S., & Mahmood, T. (2018). GRA method based on spherical linguistic fuzzy Choquet integral environment and its application in multi-attribute decision-making problems. Mathematical sciences12(4), 263-275.
[19] Kutlu Gündoğdu, F., & Kahraman, C. (2019). Spherical fuzzy sets and spherical fuzzy TOPSIS method. Journal of intelligent & fuzzy systems36(1), 337-352.
[20] Broumi, S., & Smarandache, F. (2013). Several similarity measures of neutrosophic sets. In Neutrosophic sets and systems (pp. 54-62). University of New Mexico
[21] Şahin, R., & Küçük, A. (2014). On similarity and entropy of neutrosophic soft sets. Journal of intelligent & fuzzy systems27(5), 2417-2430.
[22] Ye, J. (2015). Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses. Artificial intelligence in medicine63(3), 171-179.
[23] Yong-Wei, Y. A. N. G., Zhang, R. L., & Jing, G. U. O. (2017). A multrattribute decision-making approach based on hesitantneutrosophic sets. Fuzzy systems and mathematics31(2), 114-123.