Extended Fuzzy Binary Soft Sets and Their Applications in Multi Parameter Decision Making Problems
Abstract
Multi-criteria decision-making (MCDM) problems involve evaluating and selecting alternatives based on multiple criteria. This article aims to solve MCDM problems by extending the definition of fuzzy binary soft sets to two parameter sets, which are called extended fuzzy binary soft sets. Operations such as "AND" and "MaxMin" are defined and illustrated with examples. Additionally, an algorithm is presented to solve MCDM problems using extended fuzzy binary soft sets. Finally, an application of the proposed algorithm for decision-making is discussed.
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References
L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965.
K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, pp. 87–96, 1986. https://link.springer.com/chapter/10.1007/978-3-7908-1870-3_1.
R. Bihari, S. Jeevaraj, and A. Kumar, “A new ranking principle for ordering generalized trapezoidal fuzzy numbers based on diagonal distance, mean and its applications to supplier selection,” Soft Computing, pp. 1–26, 2023. https://doi.org/10.1007/s00500-023-08749-x.
S. Jeevaraj, R. Rajesh, and V. L. G. Nayagam, “A complete ranking of trapezoidal-valued intuitionistic fuzzy number: an application in evaluating social sustainability,” Neural Computing and Applications, vol. 35, no. 8, pp. 5939–5962, 2023. https://link.springer.com/article/10.1007/s00521-022-07983-y.
D. Marimuthu and G. S. Mahapatra, “Multi-criteria decision-making using a complete ranking of generalized trapezoidal fuzzy numbers,” Soft Computing, vol. 25, no. 15, pp. 9859–9871, 2021. https://doi.org/10.1007/s00500-020-05322-8.
V. L. G. Nayagam, S. Muralikrishnan, and G. Sivaraman, “Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets,” Expert Systems with Applications, vol. 38, pp. 1464–1467, 2011. https://link.springer.com/article/10.1007/s00500-019-04193-y.
P. G. Patil, V. Elluru, and S. . Salahshour, “Applications of similarity measure of trapezoidal fuzzy numbers in site selection problems and risk analysis,” Journal of Fuzzy Extension and Applications, 2025. https://doi.org/10.22105/jfea.2025.480618.1650.
P. G. Patil, S. Shivashankar, and V. Elluru, “Ranking of generalized trapezoidal fuzzy numbers by point of intersection and its application in multi criteria decision making problems,” Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, vol. 95, no. 1, pp. 71–83, 2025. https://doi.org/10.1007/s40010-025-00907-0.
D. Ponnialagan, J. Selvaraj, and N. V. L. G., “A complete ranking of trapezoidal fuzzy numbers and its applications to multi-criteria decision making,” Neural Computing and Applications, vol. 30, pp. 3303–3315, 2018. https://www.semanticscholar.org/paper/A-complete-ranking-of-trapezoidal-fuzzy-numbers-and-Ponnialagan-Selvaraj/134fee091a533c0ffd645886a3384948e9119ad8.
D. Molodtsov, “Soft set theory—first results,” Computers & Mathematics with Applications, vol. 37, no. 4–5, pp. 19–31, 1999. https://doi.org/10.1016/S0898-1221(99)00056-5.
P. K. Maji, A. R. Roy, and R. Biswas, “An application of soft sets in a decision making problem,” Computers & Mathematics with Applications, vol. 44, no. 8–9, pp. 1077–1083, 2002. https://doi.org/10.1016/S0898-1221(02)00216-X.
A. R. Roy and P. K. Maji, “A fuzzy soft set theoretic approach to decision making problems,” Journal of Computational and Applied Mathematics, vol. 203, no. 2, pp. 412–418, 2007. https://doi.org/10.1016/j.cam.2006.04.008.
P. N. Anil and P. G. Patil, “Multi parameter fuzzy soft set approach to decision making problem,” African Journal of Mathematics and Computer Science Research, vol. 11, no. 5, pp. 61–71, 2018. https://academicjournals.org/journal/AJMCSR/article-full-text-pdf/15971DC58179.
N. Cagman, S. Enginoglu, and F. Citak, “Fuzzy soft set theory and its applications,” Iranian journal of fuzzy systems, vol. 8, no. 3, pp. 137–147, 2011. https://ijfs.usb.ac.ir/article_292_22928400ec0d727700fd251a4f63fa07.pdf.
A. A. El-Atik, R. Abu-Gdairi, A. A. Nasef, S. Jafari, and M. Badr, “Fuzzy soft sets and decision making in ideal nutrition,” Symmetry, vol. 1523, pp. 452–463, 2023. https://doi.org/10.3390/sym15081523.
Z. Kong, L. Gao, and L. Wang, “Comment on “a fuzzy soft set theoretic approach to decision making problems,” Journal of Computational and Applied Mathematics, vol. 223, no. 42, pp. 540–542, 2009. https://doi.org/10.1016/j.cam.2011.09.016.
M. L. Staniskovski, L. Djurovic, and N. Stojanovic, “Energy of a fuzzy soft set and its application in decision-making,” Iranian Journal of Fuzzy Systems, vol. 21, no. 2, pp. 35–49, 2024. http://dx.doi.org/10.22111/ijfs.2024.46797.8243.
Z. Xiao, S. Xia, K. Gong, and D. Li, “The trapezoidal fuzzy soft set and its application in mcdm,” Applied Mathematical Modelling, vol. 36, no. 12, pp. 5844–5855, 2012. https://doi.org/10.1016/j.apm.2012.01.036.
H. Zhang, L. Shu, and S. Liao, “Generalized trapezoidal fuzzy soft set and its application in medical diagnosis,” Journal of Applied Mathematics, 2014. http://dx.doi.org/10.1155/2014312069.
A. A¸cikgoz and N. Tas, “Binary soft set theory,” European Journal of Pure and Applied Mathematics, vol. 9, no. 4, pp. 452–463, 2016. https://www.ejpam.com/index.php/ejpam/article/view/2148.
P. G. Metlida and J. Subhashini, “An application of fuzzy binary soft set in decision making problems,” Webology, vol. 18, no. 6, pp. 3672–3680, 2021.
P. G. Patil, V. Elluru, and S. Shivashankar, “A new approach to mcdm problems by fuzzy binary soft sets,” Journal of Fuzzy Extension and Applications, vol. 4, no. 3, pp. 207–216, 2023. https://www.journal-fea.com/article_175256_7bd232653b8c70fdbbd44d7c98686594.pdf.
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