Cubic Intuitionistic Fuzzy Soft Set and its Distance Measures

Muhammad Saqlain; Raiha Imran; Sabahat Hassan

doi:10.32350/sir.62.04

Muhammad Saqlain School of Mathematics, Northwest University, Xi’an 710069, China
Raiha Imran Department of Mathematics, Lahore Garrison University, DHA Phase-VI, Sector C, Lahore, 54000, Pakistan.
Sabahat Hassan Department of Mathematics, Lahore Garrison University, DHA Phase-VI, Sector C, Lahore, 54000, Pakistan.

DOI: https://doi.org/10.32350/sir.62.04

Keywords: cubic set, cubic intuitionistic fuzzy soft set, fuzzy set, intuitionistic set, intuitionistic fuzzy soft set

Abstract

Abstract Views: 324

To deal with vagueness, falsity, attributive values, and inconsistency, this study introduced the cubic intuitionistic fuzzy soft set (CIFS-set) which is the extension of the cubic intuitionistic fuzzy set and proposed a distance measure, Hamming distance, Euclidean distance, and separation measures of CIFS-set. Moreover, we presented the aggregate operator (P-union, R-intersection) of CIFS-sets. The proposed CIFS-set is more reliable, efficient, and accurate. For the future research MCDM and MCGDM techniques could be proposed to deal with real-life issues, and this CIFS-set can also be extended for its hybrids.

Downloads

Download data is not yet available.

References

Zadeh, L. A. (1996). Fuzzy sets. In Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers by Lotfi A Zadeh (pp. 394-432).

Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy sets and systems, 1(1), 3-28.

Mamdani, E. H., &Assilian, S. (1975). An experiment in linguistic synthesis with a fuzzy logic controller. International journal of man-machine studies, 7(1), 1-13.

Kickert, W. J. M., & Mamdani, E. H. (1993). Analysis of a fuzzy logic controller. In Readings in Fuzzy Sets for Intelligent Systems (pp. 290-297). Morgan Kaufmann.

Saqlain, M., Naz, K., Gaffar, K., & Jafar, M. N. (2019). Fuzzy Logic Controller. Scientific Inquiry and Review, 3(3), 16-29.

Atanassov, K. (2016). Intuitionistic fuzzy sets. International journal bioautomation, 20, 1.

Atanassov, K. T. (2012). On intuitionistic fuzzy sets theory (Vol. 283). Springer.

Ejegwa, P. A., Akowe, S. O., Otene, P. M., & Ikyule, J. M. (2014). An overview on intuitionistic fuzzy sets. Int. J. Sci. Technol. Res, 3(3), 142-145.

De, S. K., Biswas, R., & Roy, A. R. (2000). Some operations on intuitionistic fuzzy sets. Fuzzy sets and Systems, 114(3), 477-484.

Atanassov, K. T. (1999). Interval valued intuitionistic fuzzy sets. In Intuitionistic Fuzzy Sets (pp. 139-177). Physica, Heidelberg.

Zhang, Q. S., Jiang, S., Jia, B., & Luo, S. (2010). Some information measures for interval-valued intuitionistic fuzzy sets. Information sciences, 180(24), 5130-5145.

Nayagam, V. L. G., Muralikrishnan, S., &Sivaraman, G. (2011). Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets. Expert Systems with Applications, 38(3), 1464-1467.

Jun, Y. B., Kim, C. S., & Yang, K. O. (2012). Cubic sets. Ann. Fuzzy Math. Inform, 4(1), 83-98.

Garg, H., & Kaur, G. (2019). Cubic Intuitionistic Fuzzy Sets and its Fundamental Properties. Journal of Multiple-Valued Logic & Soft Computing, 33(6).

Kaur, G., & Garg, H. (2018). Cubic intuitionistic fuzzy aggregation operators. International Journal for Uncertainty Quantification, 8(5).

Molodtsov, D. (1999). Soft set theory—first results. Computers & Mathematics with Applications, 37(4-5), 19-31.

Maji, P. K., Biswas, R. K., & Roy, A. (2001). Fuzzy soft sets.

Maji, P. K., Biswas, R., & Roy, A. R. (2001). Intuitionistic fuzzy soft sets. Journal of fuzzy mathematics, 9(3), 677-692.

Cubic Intuitionistic Fuzzy Soft Set and its Distance Measures

Abstract

Downloads

References

Editor-in-Chief: Prof. Dr. Muhammad Aziz ur Rehman