From Ambiguity to Clarity: Unraveling the Power of Similarity Measures in Multi-Polar Interval-Valued Intuitionistic Fuzzy Soft Sets

Authors

DOI:

https://doi.org/10.31181/dma21202421

Keywords:

Decision-making, Soft Set, Similarity Measure, Distance Measures;, Intuitionistic Set

Abstract

The utilization of similarity measures in the context of multi-polar interval-valued intuitionistic fuzzy soft sets (mPIVIFSS) is a significant theoretical approach that offers a valuable structure for tackling intricate situations that are characterized by imprecise information and uncertainty. Nevertheless, these issues frequently entail conditions that are not limited in scope and exhibit a considerable level of uncertainty in scenarios involving multiple dimensions, hence presenting substantial difficulties. The objective of this research study is to provide a comprehensive understanding of similarity measures in the context of mPIVIFSS. Additionally, we will examine several operations, such as complement, subset, union, intersection, AND, OR, and De-Morgan’s Laws, as they relate to mPIVIFSS. This study not only includes theoretical debates but also explores practical applications. These efforts contribute to the improvement of decision-making, pattern recognition, and data analysis in settings characterized by ambiguous and uncertain information, hence emphasizing the importance of similarity measures in efficiently addressing multi-dimensional problems.

Downloads

Download data is not yet available.

References

Zadeh, L. A. (1965). Fuzzy Sets. Information and control, 8, 338-353.

Antanssov. K. (1986). Intuitionistic fuzzy set. Fuzzy Sets, and System, 20(1), 87-96.

Molodtsov, D. (1999). Soft Set Theory-First Results. Computers and Mathematics with Applications, 37, 19-31.

Maji, P. K., R. Biswas R., and Roy, A. R. (2001). Fuzzy Soft Sets. The Journal of Fuzzy Mathematics, 9, 3, 589-602.

Çağman, N., & Karataş, S. (2013). Intuitionistic fuzzy soft set theory and its decision making. Journal of Intelligent & Fuzzy Systems, 24(4), 829-836.

Agarwal, M., Biswas, K. K., & Hanmandlu, M. (2013). Generalized intuitionistic fuzzy soft sets with applications in decision-making. Applied Soft Computing, 13(8), 3552-3566.

Maji, P. K. (2009). More on intuitionistic fuzzy soft sets. In Rough Sets, Fuzzy Sets, Data Mining and Granular Computing: 12th International Conference, RSFDGrC 2009, Delhi, India, December 15-18, 2009. Proceedings 12 (pp. 231-240). Springer Berlin Heidelberg.

Garg, H., & Arora, R. (2018). Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decision-making. Applied Intelligence, 48, 343-356.

Khan, M. J., Kumam, P., Liu, P., Kumam, W., & Ashraf, S. (2019). A novel approach to generalized intuitionistic fuzzy soft sets and its application in decision support systems. Mathematics, 7(8), 742.

Jiang, Y., Tang, Y., Chen, Q., Liu, H., & Tang, J. (2010). Interval-valued intuitionistic fuzzy soft sets and their properties. Computers & Mathematics with Applications, 60(3), 906-918.

Akram, M., and Shahzadi, G. (2017). Certain characterization of m-polar fuzzy graphs by level graphs. Punjab University Journal of Mathematics, 49(1), 1-12.

Akram, M., & Waseem, N. (2019). Similarity measures for new hybrid models: mF sets and mF soft sets. Punjab University Journal of Mathematics, 51(6), 115-130.

Papakostas, G. A., Hatzimichailidis, A. G., & Kaburlasos, V. G. (2013). Distance and similarity measures between intuitionistic fuzzy sets: A comparative analysis from a pattern recognition point of view. Pattern Recognition Letters, 34(14), 1609-1622.

Luo, L., & Ren, H. (2016). A new similarity measure of intuitionistic fuzzy set and application in MADM problem. AMSE Ser Adv A, 59, 204-223.

Li Dengfeng, Cheng Chuntian. (2002). New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Letters, 23(1-3),221-225.

Ma, X., Qin, H., & Abawajy, J. H. (2020). Interval-valued intuitionistic fuzzy soft sets based decision-making and parameter reduction. IEEE Transactions on Fuzzy Systems, 30(2), 357-369.

Szmidt, E., & Kacprzyk, J. (2000). Distances between intuitionistic fuzzy sets. Fuzzy sets and systems, 114(3), 505-518.

Szmidt, E., & Kacprzyk, J. (2004). A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. In International conference on artificial intelligence and soft computing (pp. 388-393). Berlin, Heidelberg: Springer Berlin Heidelberg.

Szmidt, E., & Kacprzyk, J. (2005). A new concept of a similarity measure for intuitionistic fuzzy sets and its use in group decision-making. In International Conference on Modeling Decisions for Artificial Intelligence (pp. 272-282). Berlin, Heidelberg: Springer Berlin Heidelberg.

Çağman, N., & Deli, I. (2013). Similarity measures of intuitionistic fuzzy soft sets and their decision-making. arXiv preprint arXiv:1301.0456

Muthukumar, P., & Krishnan, G. S. S. (2016). A similarity measure of intuitionistic fuzzy soft sets and its application in medical diagnosis. Applied Soft Computing, 41, 148-156.

Hooda, D. S., Kumari, R., & Sharma, D. K. (2018). Intuitionistic fuzzy soft set theory and its application in medical diagnosis. International Journal, 7(3), 71.

Selvachandran, G., Maji, P. K., Faisal, R. Q., & Razak Salleh, A. (2017). Distance and distance induced intuitionistic entropy of generalized intuitionistic fuzzy soft sets. Applied Intelligence, 47, 132-147.

Peng, X. (2019). Some novel decision-making algorithms for intuitionistic fuzzy soft set. Journal of Intelligent & Fuzzy Systems, 37(1), 1327-1341.

Garg, H., & Kumar, K. (2018). An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision-making. Soft Computing, 22(15), 4959-4970.

Aydın, T., & Enginoğlu, S. (2021). Interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft sets and their application in decision-making. Journal of Ambient Intelligence and Humanized Computing, 12(1), 1541-1558.

Zhang, Z., Wang, C., Tian, D., & Li, K. (2014). A novel approach to interval-valued intuitionistic fuzzy soft set-based decision making. Applied Mathematical Modelling, 38(4, 1255-1270.

Aydın, T., & Enginoğlu, S. (2021). Interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft sets and their application in decision-making. Journal of Ambient Intelligence and Humanized Computing, 12(1), 1541-1558.

Wu, X., Liao, H., Benjamin, L., Zavadskas, E. K. (2023). A Multiple Criteria Decision-Making Method with Heterogeneous Linguistic Expressions. IEEE Transactions on Engineering Management, 70(5), 1857-1870.

Saqlain M., S. Moin, M. N. Jafar, M. Saeed, and F. Smarandache. (2020). Aggregate Operators of Neutrosophic Hypersoft Set. Neutrosophic Sets and Systems, 32,294-306.

Saqlain M, Sana M, Jafar N, Saeed. M, Said. B, (2020). Single and Multi-valued Neutrosophic Hypersoft set and Tangent Similarity Measure of Single valued Neutrosophic Hypersoft Sets. Neutrosophic Sets and Systems, 32, 317-329.

Saqlain M, Saeed. M, Zulqarnain M R, Sana M. (2021). Neutrosophic Hypersoft Matrix Theory: Its Definition, Operators, and Application in Decision-Making of Personnel Selection Problem. Neutrosophic Operational Research, Springer.

Saqlain M., M. Riaz, M. A. Saleem, and M. S. Yang. (2021). Distance and Similarity Measures for Neutrosophic HyperSoft Set (NHSS) with Construction of NHSS TOPSIS and Applications.IEEE Access, 9, 30803-30816.

Jafar N M., M. Saeed, M. Saqlain and M. -S. Yang. (2021). Trigonometric Similarity Measures for Neutrosophic Hypersoft Sets with Application to Renewable Energy Source Selection. IEEE Access, 9, 129178-129187.

Saqlain, M. (2023). Sustainable Hydrogen Production: A Decision-Making Approach Using VIKOR and Intuitionistic Hypersoft Sets. Journal of Intelligent Management Decision, 2(3), 130-138.

Jain, A., Kumar, V., & Kumar, R. (2017). A novel approach for medical decision support system using intuitionistic fuzzy soft matrix. Health Information Science and Systems, 5(1), 1-10.

Ali, M. I., Feng, F., X. Liu, W. K. Min, M. Shabir. (2009). On some new operations in soft set theory. Computers & Mathematics with Applications, 57, 1547–1553.

Vijayabalaji, S., and Ramesh, A. (2018). Uncertain multiplicative linguistic soft sets and their application to group decision-making. Journal of Intelligent & Fuzzy Systems, 35(3), 3883–3893.

Aiwu Z., Hongjun G. (2016). Fuzzy-valued linguistic soft set theory and multi-attribute decision-making application. Chaos, Solitons & Fractals, 89, 2-7.

Published

2024-01-05

How to Cite

Saqlain, M., & Saeed, M. (2024). From Ambiguity to Clarity: Unraveling the Power of Similarity Measures in Multi-Polar Interval-Valued Intuitionistic Fuzzy Soft Sets. Decision Making Advances, 2(1), 48–59. https://doi.org/10.31181/dma21202421