SIMILARITY MEASURE ON CUBIC INTUITIONISTIC FUZZY SETS AND ITS RELATIONSHIP WITH ENTROPY MEASURE

Priyadharshini Manoharan; Jayanthi Duraisamy; P. Gajalaxmi

SIMILARITY MEASURE ON CUBIC INTUITIONISTIC FUZZY SETS AND ITS RELATIONSHIP WITH ENTROPY MEASURE

Abstract

The objective of the study is to introduce the axioms defining similarity measures on cubic intuitionistic fuzzy sets. The proposed similarity measure integrates the principles of similarity measures on interval-valued intuitionistic fuzzy sets and intuitionistic fuzzy sets. Additionally, a novel approach is presented to construct similarity measures using entropy measures specific to cubic intuitionistic fuzzy sets. The transformation of entropy measures into similarity measures is formalized through several key theorems that adhere to the established axioms. Illustrative example is provided to demonstrate and validate the proposed definitions.

Keywords

Thanks

The author will be extremely grateful to the learned reviewers for their valuable comments and suggestions which help us a lot for improving the standard of this paper.

References

Alolyian, H., Razaq, A., Ashfaq, H., Alghazzawi, D., Shuaib, U and Liu, J. B., (2024), Improving similarity measures for modeling real-world issues with interval-valued intuitionistic fuzzy sets, IEEE Access, 12, pp.10482-10496.
Atanassov, K., (1986), Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20, pp.87-96.
Atanassov, K. and Gargov, G., (1989), Interval – valued intuitionistic fuzzy sets, Fuzzy Sets Syst., 31, pp.343-349.
Chen, Z and Liu, P., (2022), Intuitionistic fuzzy value similarity measures for intuitionistic fuzzy sets, Comput. Appl. Math., 45,pp.1-20.
De Luca, A. and Termini, S., (1972), A definition of a non-probabilistic entropy in the setting of fuzzy set theory, Inf. Control, 20, pp.301-312.
Garg, H. and Kaur, G., (2019), Cubic intuitionistic fuzzy sets and its fundamental properties, Journal of Multiple-Valued Logic \& Soft Comput., 33, pp.507-537.
Garg, H. and Kaur, G., (2018), Novel distance measures for cubic intuitionistic fuzzy sets and their applications to pattern recognitions and medical diagnosis, Granular Computing, 5, pp.169-184.
Garg, H. and Kaur, G., (2019), TOPSIS based on nonlinear-programming methodology for solving decision-making problems under cubic intuitionistic fuzzy set environment, Comput. Appl. Math., 38, pp.1-19.

Gohain, B., Chutia, R., Dutta, P and Gogoi, S., (2022), Two new similarity measures for intuitionistic fuzzy sets and its various applications, Int. J. Intell. Syst., 37, pp.5557-5596.
Gul, R., (2024), An extension of VIKOR approach for MCDM using bipolar fuzzy preference $\delta$-covering based bipolar fuzzy rough set model, Spec. Oper. Res., 2, pp.72-91.
Hu, K. and Li, J., (2013), The entropy and similarity measure of interval valued intuitionistic fuzzy sets and their relationship, Int. J. Fuzzy Syst., 15, pp.279-288.
Huang, W., Zhang, F., Wang, S. and Kong, F., (2024), A novel knowledge-based similarity measure on intuitionistic fuzzy sets and its applications in pattern recognition, Expert Syst. Appl., 249, pp.1-25.
Hyung, L. K, Song, Y. S. and Lee, K. M., (1994). Similarity measures between fuzzy sets and between elements, Fuzzy Sets Syst., 62, pp.291-293.
Jing, L., (2013), Entropy and similarity measures for interval-valued intuitionistic fuzzy sets based on intuitionism and fuzziness, Adv. Model. Optim., 15, pp.635-643.
Jeevaraj, S., (2020), Similarity measure on interval valued intuitionistic fuzzy numbers based on non-hesitance score and its application to pattern recognition, Comput. Appl. Math., 39, 1-15.
Jun, Y. B., Kim, C. S. and Yang, K. O., (2012), Cubic Sets. Ann. Fuzzy Math. Inform., 4, pp. 83-98.
Kannan, J., Jayakumar, V. and Pethaperumal, M., (2024), Advanced fuzzy-based decision-making: The linear diophantine fuzzy CODAS method for logistic specialist selection, Spec. Oper. Res., 2, pp.41-60.
Kaur, G. and Garg, H., (2018), Cubic intuitionistic fuzzy aggregation operators, Int. J. Uncertainty Quantif., 8, pp.405-427.
Li, J. Deng, G. Li, H. Zeng, W., (2012), The relationship between similarity measure and entropy of intuitionistic fuzzy sets, Inf. Sci., 188, pp.314-321.
Meng, F. and Chen, X. (2015), Entropy and similarity measure for Atannasov’s interval-valued intuitionistic fuzzy sets and their application, Fuzzy Optim. Decis. Mak., 15, pp.75-101.
Mishra, A. R., Rani, P., Cavallaro, F. and Alrasheedi, A. F., (2023), Assessment of sustainable wastewater treatment technologies using interval-valued intuitionistic fuzzy distance measure-based MAIRCA method, Facta Univ. Ser. Mech. Eng., 21(3), pp.359 -386.
Nayagam, V. L. G., Muralikrishnan, S. and Sivaraman, G., (2011), Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets, Expert Syst. Appl., 38(3), pp.1464-1467.
Palanisamy, S and Periyasamy, J., (2024), Interval-valued intuitionistic fuzzy cosine similarity measures for real world problem solving, Int. J. Robot. Control Syst., 4(2), pp.655 – 677.
Park, J. H., Lim, K. M., Park, J. S. and Kwun, Y. C., (2007), Entropy and similarity measures of interval-valued intuitionistic fuzzy set, In Proceedings of the Korean Institute of Intelligent Systems Conference, pp. 187-190.
Patel, A., Jana, S. and Mahanta, J., (2024), Construction of similarity measure for intuitionistic fuzzy sets and its application in face recognition and software quality evaluation, Expert Syst. Appl., 237, pp.1-25.
Priyadharshini, M. and Jayanthi, D., A measure of entropy for cubic intuitionistic fuzzy sets. (Communicated)
Shannon, C. E., (1948), A mathematical theory of communication, Bell Syst. Tech. J., 27, pp.379-423.
Song, Y., Wang, X., Quan, W and Huang, W., (2019), A new approach to construct similarity measure for intuitionistic fuzzy sets, Soft Computing, 23(6), pp.1985-1998.
Szmidt, E. and Kacprzyk, J., (2001), Entropy for intuitionistic fuzzy sets, Fuzzy Sets Syst., 118, pp.467- 477.
Sun, M. and Liu, J., (2012), New entropy and similarity measures for interval-valued intuitionistic fuzzy set, JJ. Inf. Comput. Sci., 9, pp.5799-5806.
Talukdar, P. and Dutta, P., (2023), An advanced entropy measure of IFSs via similarity measure, Int. J. Fuzzy Syst. Appl., 12, pp.1-23.
Tiwari, P. and Gupta, P., (2018), Entropy, distance and similarity measures under interval-valued intuitionistic fuzzy environment, Informatica, 42, pp.617-628.
Vishnukumar, P. Edwin Antony Raj, M. and Sivaraman, G.,(2024), A novel similarity measure based on new accuracy function on interval-valued intuitionistic fuzzy number and its application to multicriteria decision-making problem, Neural Comput. Appl., 36(10), pp.5183-5195.
Verma, R. and Merigo, J. M., (2020), A new decision-making method using interval-valued intuitionistic fuzzy cosine similarity measure based on the weighted reduced intuitionistic fuzzy sets, Informatica, 31(2), pp.399-433.
Wei, C. P, Wang, P. and Zhang, Y. Z., (2011), Entropy, similarity measures of interval-valued intuitionistic fuzzy sets and their applications, Inf. Sci., 181, pp.4273-4286.
Xu, Z. S. and Yager, R. R., (2009), Intuitionistic and interval-valued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group, Fuzzy Optim. Dec. Making, 8, pp.123-139.
Zadeh, L. A., (1965), Fuzzy sets, Inf. Control., 8, pp. 338-353.
Zadeh, L. A., (1968), Probability measures of fuzzy events, J. Math. Anal. Appl., 23, pp.421-427.
Zeng, W., Yu, X., Yu, F. and Cui, B., (2008), Entropy of intuitionistic fuzzy set based on similarity measure, 3rd International Conference on Innovative Computing Information and Control, IEEE, 398-398.
Zhang, Q. S. and Jiang, S. Y., (2010), Relationships between entropy and similarity measure of interval‐valued intuitionistic fuzzy sets, Int. J. Intell. Syst., 25, pp.1121-1140.
Zhang, H. Y., Zhang, W. X. and Mei, C. L., (2009), Entropy of interval - valued fuzzy sets based on distance and its relationship with similarity measure, Knowl.-Based Syst., 22, pp.449-454.
Zhang, Q., Xing, H., Liu, F., Ye, J. and Tang P., (2014), Some new entropy measures for interval-valued intuitionistic fuzzy sets based on distances and their relationships with similarity and inclusion measures, Inf. Sci., 283, pp.55-69.
Zhang, Q., Xing, H. and Wu, L., (2012), Entropy, similarity measure, inclusion measure of intuitionistic fuzzy sets and their relationship, Int. J. Comput. Intell. Syst., 5, pp. 519-529.

Details

Primary Language

English

Subjects

Mathematical Logic, Set Theory, Lattices and Universal Algebra

Journal Section

Research Article

Authors

Priyadharshini Manoharan ^*
0000-0002-9667-0820
India

Jayanthi Duraisamy
0000-0002-3066-1139
India

P. Gajalaxmi This is me
0000-0002-5274-8550
India

Publication Date

December 6, 2025

Submission Date

August 21, 2024

Acceptance Date

January 15, 2025

Published in Issue

Year 2025 Volume: 15 Number: 12

IZ

https://izlik.org/JA44ZC55MZ

Cite

RIS / Bibtex

APA

Manoharan, P., Duraisamy, J., & Gajalaxmi, P. (2025). SIMILARITY MEASURE ON CUBIC INTUITIONISTIC FUZZY SETS AND ITS RELATIONSHIP WITH ENTROPY MEASURE. TWMS Journal of Applied and Engineering Mathematics, 15(12), 2771-2785. https://izlik.org/JA44ZC55MZ

AMA

1.Manoharan P, Duraisamy J, Gajalaxmi P. SIMILARITY MEASURE ON CUBIC INTUITIONISTIC FUZZY SETS AND ITS RELATIONSHIP WITH ENTROPY MEASURE. JAEM. 2025;15(12):2771-2785. https://izlik.org/JA44ZC55MZ

Chicago

Manoharan, Priyadharshini, Jayanthi Duraisamy, and P. Gajalaxmi. 2025. “SIMILARITY MEASURE ON CUBIC INTUITIONISTIC FUZZY SETS AND ITS RELATIONSHIP WITH ENTROPY MEASURE”. TWMS Journal of Applied and Engineering Mathematics 15 (12): 2771-85. https://izlik.org/JA44ZC55MZ.

EndNote

Manoharan P, Duraisamy J, Gajalaxmi P (December 1, 2025) SIMILARITY MEASURE ON CUBIC INTUITIONISTIC FUZZY SETS AND ITS RELATIONSHIP WITH ENTROPY MEASURE. TWMS Journal of Applied and Engineering Mathematics 15 12 2771–2785.

IEEE

[1]P. Manoharan, J. Duraisamy, and P. Gajalaxmi, “SIMILARITY MEASURE ON CUBIC INTUITIONISTIC FUZZY SETS AND ITS RELATIONSHIP WITH ENTROPY MEASURE”, JAEM, vol. 15, no. 12, pp. 2771–2785, Dec. 2025, [Online]. Available: https://izlik.org/JA44ZC55MZ

ISNAD

Manoharan, Priyadharshini - Duraisamy, Jayanthi - Gajalaxmi, P. “SIMILARITY MEASURE ON CUBIC INTUITIONISTIC FUZZY SETS AND ITS RELATIONSHIP WITH ENTROPY MEASURE”. TWMS Journal of Applied and Engineering Mathematics 15/12 (December 1, 2025): 2771-2785. https://izlik.org/JA44ZC55MZ.

JAMA

1.Manoharan P, Duraisamy J, Gajalaxmi P. SIMILARITY MEASURE ON CUBIC INTUITIONISTIC FUZZY SETS AND ITS RELATIONSHIP WITH ENTROPY MEASURE. JAEM. 2025;15:2771–2785.

MLA

Manoharan, Priyadharshini, et al. “SIMILARITY MEASURE ON CUBIC INTUITIONISTIC FUZZY SETS AND ITS RELATIONSHIP WITH ENTROPY MEASURE”. TWMS Journal of Applied and Engineering Mathematics, vol. 15, no. 12, Dec. 2025, pp. 2771-85, https://izlik.org/JA44ZC55MZ.

Vancouver

1.Priyadharshini Manoharan, Jayanthi Duraisamy, P. Gajalaxmi. SIMILARITY MEASURE ON CUBIC INTUITIONISTIC FUZZY SETS AND ITS RELATIONSHIP WITH ENTROPY MEASURE. JAEM [Internet]. 2025 Dec. 1;15(12):2771-85. Available from: https://izlik.org/JA44ZC55MZ