How to cite this paper
Sahoo, L. (2022). Similarity measures for Fermatean fuzzy sets and its applications in group decision-making.Decision Science Letters , 11(2), 167-180.
Refrences
Atanassov, K. T. (1983). A Second type of Intuitionistic fuzzy sets. BUSE-FAL, 56, 66-70.
Atanassov, K. T. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems. 20, 87-96.
Atanassov, K. T. (2012). On Intuitionistic fuzzy sets theory. Springer, Berlin.
Atanassov, K. T. (2016). Geometric interpretation of the elements of the intuitionistic fuzzy objects. International Journal of Bioautomation, 20(S1), S27-S42.
Atanassov, K. T., & Gargov, G. (1987). Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31, 1-17.
Atanassov, K. T., Vassilev, P.M., & Tsvetkov, R. T. (2013). Intuitionistic fuzzy sets, measures and integrals, Professor Marin Drinov Academic publishing House, Sofia.
Bai, Z.Y. (2013). An interval valued intuitionistic fuzzy TOPSIS method based on an improved score function. The Scientific World Journal, 2013, 1-6.
Bellman, R.E., & Zadeh, L.A. (1970). Decision making in a fuzzy environment. Management Science, 17, 141-164.
Boltruk, E. (2018). Pythagorean fuzzy CODAS and its application to supplier selection in a manufacturing firm. Journal of Enterprise Information Management, 31, 550-564.
Chen, S. M. (1995). Measures of similarity between vague sets. Fuzzy Sets and Systems, 74(2), 217–223.
Chen, T-Y (2018). An outranking approach using a risk attitudinal assignment model involving Pythagorean fuzzy information and its application to financial decision making. Applied Soft Computing, 71, 460-487.
Ejegwa, P. A. (2019). Personnel Appointments: A Pythagorean fuzzy sets approach using similarity measure. Journal of information and Computing Science, 14(2), 094-102.
Ejegwa, P. A. (2020), Distance and similarity measures of Pythagorean fuzzy sets, Granular Computing, 5, 225-238.
Fei, L.,Wang, H., Chen, L., & Deng, Y., A new vector valued similarity measure for intuitionistic fuzzy sets based on OWA operators. Iranian Journal of Fuzzy Systems, 15(5), 31-49.
Garg, H. (2017). Anew improved score function of an interval valued Pythagorean fuzzy set based topsis method. International Journal of Uncertainty Quantification, 7, 463-474.
Garg, H. (2018). A linear programming method based on an improved score function for interval valued Pythagorean fuzzy numbers and its application to decision-making. International Journal of Uncertainty Fuzziness Knowledge Based System, 26, 67-80.
Geng, Y., Liu, P., Teng, F., & Liu, Z. (2017). Pythagorean fuzzy uncertain linguistic TODIM method and their application to multiple criteria group decision making. International Journal of Intelligent Systems, 33, 3383-3395.
Gorzalczany, M. B. (1987). A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets and Systems, 21(1), 1-17.
Gou, X., Xu, Z., & Liao, H.(2016). Alternative queuing method for multiple criteria decision making with hybrid fuzzy and ranking information. Information Science, 357, 144-160.
Hung, W. L., & Yang, M. S. (2004). Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recognition Letters, 25(14), 1603–1611.
Jing, N., Xian, S., & Xiao, Y. (2017). Pythagorean triangular fuzzy linguistic bonferroni mean operators and their application for multi-attribute decision making, In: 2nd IEEE international conference on computational intelligence and applications (ICCIA), 435-439.
Li, D., & Cheng, C.(2002). New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Letters, 23(1-3), 221–225.
Li, Z., Wei, G.,& Lu, M.(2018). Pythagorean fuzzy Hamy mean operators in multiple attribute group decision making and their application to supplier selection. Symmetry, 10, 505.
Liang, Z., & Shi, P. (2003). Similarity measures on intuitionistic fuzzy sets. Pattern Recognition Letters, 24(15), 2687–2693.
Lin, Y-L, Ho, L-H, Yeh, S-L, & Chen, T-Y ( 2018). A Pythagorean fuzzy topsis method based on novel correlation measures and its application to multiple criteria decision analysis of inpatient stoke rehabilitiation. International Journal of Computer Intelligence System, 12(1), 410-425.
Liu, D., Chen, X., & Peng, D.(2018). Cosine Similarity Measure between Hybrid Intuitionistic Fuzzy Sets and Its Application in Medical Diagnosis. Computational and Mathematical Methods in Medicine, 2018, Article ID 3146873, 7 pages.
Liu, D., Chen, X.,& Peng, D.(2018). The intuitionistic fuzzy linguistic cosine similarity measure and its application in pattern recognition. Complexity, 2018, Article ID 9073597, 11 pages.
Liu, D., Liu, Y., & Wang L.(2019). Distance measure for Fermatean fuzzy linguistic term sets based on linguistic scale function: An illustration to the TODIM and TOPSIS methods. International Journal of Intelligent Systems, 34(11), 2807-2834.
Nguyen, H. (2016). A novel similarity/dissimilarity measure for intuitionistic fuzzy sets and its application in pattern recognition. Expert Systems with Applications, 45, 97–107.
Pappis, C. P., & Karacapilidis, N. I. (1993). A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets and Systems, 56(2), 171–174.
Qin, J. (2018). Generalized Pythagorean fuzzy Maclaurin symmetric means and its application to multiple attribute sir group decision model. International Journal of Fuzzy System, 20, 943-957.
Senapati, T., & Yager, R. R. (2019). Fermatean fuzzy weighted averaging/geometric operators and its application in multi-criteria decision-making methods. Engineering Applications of Artificial Intelligence, 85, 112-121.
Senapati, T., & Yager, R. R. (2020). Fermatean fuzzy sets. Journal of Ambient Intelligence and Humanized Computing, 11, 663-674.
Turksen, I.B. (1986). Interval valued fuzzy sets based on normal forms, Fuzzy Sets and Systems, 20(2), 191-210.
Wan, S-P, Li, S-Q, & Dong, J-Y (2018). A three phase method for Pythagorean fuzzy multi attribute group decision making and application to haze management. Computers and Industrial Engineering, 123, 348-363.
Yager, R. R. (2013). Pythagorean fuzzy subsets, In: 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/ NAFIPS), 57-61.
Yager, R. R. (2014). Pythagorean membership grades in multi-criteria decision making, IEEE Transactions on Fuzzy Systems, 22, 958-965.
Ye, J. (2009). Multicriteria fuzzy-decision making method based on a novel accuracy function under interval valued intuitionistic fuzzy environment. Expert Systems with Applications, 36(3), 6899-6902.
Ye, J. (2011). Cosine similarity measures for intuitionistic fuzzy sets and their applications. Mathematical and Computer Modeling, 53(1-2), 91–97.
Ye, J. (2013). Interval-valued intuitionistic fuzzy cosine similarity measures for multiple attribute decision-making, International Journal of General Systems, 42(8), 883-891.
Zadeh, L. A. (1965). Fuzzy Sets, Information and Control, 8, 338-353.
Zhang, R., Ashuri, B., & Deng, Y. (2018). A novel method for forecasting time series based on fuzzy logic and visibility graph. Advances in Data Analysis and Classification, 11(4), 759-783.
Zhang, X, & Xu, Z. (2014). Extention of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. International Journal of Intelligent System, 29, 1061-1078.
Zhang, X.(2016). A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. International Journal of Intelligent System, 31, 593-611.
Zhang, Z., Yang, J., Ye, Y., Hu, Y., & Zhang, Q. (2012). A type of score function on intuitionistic fuzzy sets with double parameters and its application to pattern recognition and medical diagnosis. Procedia Engineering, 29, 4336-4342.
Zhou, J., Su, W., Balezentis, T., & Streimikiene, D. (2018). Multiple criteria group decision making considering symmetry with regards to the positive and negative ideal solution via the Pythagorean normal cloud model for application to economic decision. Symmetry, 10(5), 140.
Zhou, L., Z. Tao, H. Chen, & Liu, J. (2014). Intuitionistic fuzzy ordered weighted cosine similarity measure. Group Decision and Negotiation, 23(4), 879–900.
Atanassov, K. T. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems. 20, 87-96.
Atanassov, K. T. (2012). On Intuitionistic fuzzy sets theory. Springer, Berlin.
Atanassov, K. T. (2016). Geometric interpretation of the elements of the intuitionistic fuzzy objects. International Journal of Bioautomation, 20(S1), S27-S42.
Atanassov, K. T., & Gargov, G. (1987). Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31, 1-17.
Atanassov, K. T., Vassilev, P.M., & Tsvetkov, R. T. (2013). Intuitionistic fuzzy sets, measures and integrals, Professor Marin Drinov Academic publishing House, Sofia.
Bai, Z.Y. (2013). An interval valued intuitionistic fuzzy TOPSIS method based on an improved score function. The Scientific World Journal, 2013, 1-6.
Bellman, R.E., & Zadeh, L.A. (1970). Decision making in a fuzzy environment. Management Science, 17, 141-164.
Boltruk, E. (2018). Pythagorean fuzzy CODAS and its application to supplier selection in a manufacturing firm. Journal of Enterprise Information Management, 31, 550-564.
Chen, S. M. (1995). Measures of similarity between vague sets. Fuzzy Sets and Systems, 74(2), 217–223.
Chen, T-Y (2018). An outranking approach using a risk attitudinal assignment model involving Pythagorean fuzzy information and its application to financial decision making. Applied Soft Computing, 71, 460-487.
Ejegwa, P. A. (2019). Personnel Appointments: A Pythagorean fuzzy sets approach using similarity measure. Journal of information and Computing Science, 14(2), 094-102.
Ejegwa, P. A. (2020), Distance and similarity measures of Pythagorean fuzzy sets, Granular Computing, 5, 225-238.
Fei, L.,Wang, H., Chen, L., & Deng, Y., A new vector valued similarity measure for intuitionistic fuzzy sets based on OWA operators. Iranian Journal of Fuzzy Systems, 15(5), 31-49.
Garg, H. (2017). Anew improved score function of an interval valued Pythagorean fuzzy set based topsis method. International Journal of Uncertainty Quantification, 7, 463-474.
Garg, H. (2018). A linear programming method based on an improved score function for interval valued Pythagorean fuzzy numbers and its application to decision-making. International Journal of Uncertainty Fuzziness Knowledge Based System, 26, 67-80.
Geng, Y., Liu, P., Teng, F., & Liu, Z. (2017). Pythagorean fuzzy uncertain linguistic TODIM method and their application to multiple criteria group decision making. International Journal of Intelligent Systems, 33, 3383-3395.
Gorzalczany, M. B. (1987). A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets and Systems, 21(1), 1-17.
Gou, X., Xu, Z., & Liao, H.(2016). Alternative queuing method for multiple criteria decision making with hybrid fuzzy and ranking information. Information Science, 357, 144-160.
Hung, W. L., & Yang, M. S. (2004). Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recognition Letters, 25(14), 1603–1611.
Jing, N., Xian, S., & Xiao, Y. (2017). Pythagorean triangular fuzzy linguistic bonferroni mean operators and their application for multi-attribute decision making, In: 2nd IEEE international conference on computational intelligence and applications (ICCIA), 435-439.
Li, D., & Cheng, C.(2002). New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Letters, 23(1-3), 221–225.
Li, Z., Wei, G.,& Lu, M.(2018). Pythagorean fuzzy Hamy mean operators in multiple attribute group decision making and their application to supplier selection. Symmetry, 10, 505.
Liang, Z., & Shi, P. (2003). Similarity measures on intuitionistic fuzzy sets. Pattern Recognition Letters, 24(15), 2687–2693.
Lin, Y-L, Ho, L-H, Yeh, S-L, & Chen, T-Y ( 2018). A Pythagorean fuzzy topsis method based on novel correlation measures and its application to multiple criteria decision analysis of inpatient stoke rehabilitiation. International Journal of Computer Intelligence System, 12(1), 410-425.
Liu, D., Chen, X., & Peng, D.(2018). Cosine Similarity Measure between Hybrid Intuitionistic Fuzzy Sets and Its Application in Medical Diagnosis. Computational and Mathematical Methods in Medicine, 2018, Article ID 3146873, 7 pages.
Liu, D., Chen, X.,& Peng, D.(2018). The intuitionistic fuzzy linguistic cosine similarity measure and its application in pattern recognition. Complexity, 2018, Article ID 9073597, 11 pages.
Liu, D., Liu, Y., & Wang L.(2019). Distance measure for Fermatean fuzzy linguistic term sets based on linguistic scale function: An illustration to the TODIM and TOPSIS methods. International Journal of Intelligent Systems, 34(11), 2807-2834.
Nguyen, H. (2016). A novel similarity/dissimilarity measure for intuitionistic fuzzy sets and its application in pattern recognition. Expert Systems with Applications, 45, 97–107.
Pappis, C. P., & Karacapilidis, N. I. (1993). A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets and Systems, 56(2), 171–174.
Qin, J. (2018). Generalized Pythagorean fuzzy Maclaurin symmetric means and its application to multiple attribute sir group decision model. International Journal of Fuzzy System, 20, 943-957.
Senapati, T., & Yager, R. R. (2019). Fermatean fuzzy weighted averaging/geometric operators and its application in multi-criteria decision-making methods. Engineering Applications of Artificial Intelligence, 85, 112-121.
Senapati, T., & Yager, R. R. (2020). Fermatean fuzzy sets. Journal of Ambient Intelligence and Humanized Computing, 11, 663-674.
Turksen, I.B. (1986). Interval valued fuzzy sets based on normal forms, Fuzzy Sets and Systems, 20(2), 191-210.
Wan, S-P, Li, S-Q, & Dong, J-Y (2018). A three phase method for Pythagorean fuzzy multi attribute group decision making and application to haze management. Computers and Industrial Engineering, 123, 348-363.
Yager, R. R. (2013). Pythagorean fuzzy subsets, In: 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/ NAFIPS), 57-61.
Yager, R. R. (2014). Pythagorean membership grades in multi-criteria decision making, IEEE Transactions on Fuzzy Systems, 22, 958-965.
Ye, J. (2009). Multicriteria fuzzy-decision making method based on a novel accuracy function under interval valued intuitionistic fuzzy environment. Expert Systems with Applications, 36(3), 6899-6902.
Ye, J. (2011). Cosine similarity measures for intuitionistic fuzzy sets and their applications. Mathematical and Computer Modeling, 53(1-2), 91–97.
Ye, J. (2013). Interval-valued intuitionistic fuzzy cosine similarity measures for multiple attribute decision-making, International Journal of General Systems, 42(8), 883-891.
Zadeh, L. A. (1965). Fuzzy Sets, Information and Control, 8, 338-353.
Zhang, R., Ashuri, B., & Deng, Y. (2018). A novel method for forecasting time series based on fuzzy logic and visibility graph. Advances in Data Analysis and Classification, 11(4), 759-783.
Zhang, X, & Xu, Z. (2014). Extention of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. International Journal of Intelligent System, 29, 1061-1078.
Zhang, X.(2016). A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. International Journal of Intelligent System, 31, 593-611.
Zhang, Z., Yang, J., Ye, Y., Hu, Y., & Zhang, Q. (2012). A type of score function on intuitionistic fuzzy sets with double parameters and its application to pattern recognition and medical diagnosis. Procedia Engineering, 29, 4336-4342.
Zhou, J., Su, W., Balezentis, T., & Streimikiene, D. (2018). Multiple criteria group decision making considering symmetry with regards to the positive and negative ideal solution via the Pythagorean normal cloud model for application to economic decision. Symmetry, 10(5), 140.
Zhou, L., Z. Tao, H. Chen, & Liu, J. (2014). Intuitionistic fuzzy ordered weighted cosine similarity measure. Group Decision and Negotiation, 23(4), 879–900.