CONVEXITY WITH SOFT APPROXIMATE FUNCTION UNDER FUZZY SOFT EXPERT SET ENVIRONMENT
Article Sidebar
-
Convexity, Fuzzy set, Fuzzy logic, Soft computingSoft computing, Convex hull
Abstract
Soft set theory is considered the best tool to deal with problems involving uncertainties by controlling all the complexities of optimization theory, fuzzy set theory, and probability theory. By utilising this theory, the majority of soft set-like models have been developed to address issues in decision-making and medical diagnosis with a single expert. This is a challenge for researchers who employ questionnaires. This issue is solved by soft expert sets, which enable the decision-maker to access the opinions of all experts in a single model. In this study, some types of convexity, like strictly (strongly) convexity, (λ,ψ)-convexity with different senses over fuzzy soft expert set, have been described with the numerical examples. Convex hull and convex cone on fuzzy soft expert set have been developed, and some important results have been proved by applying the algebraic approach
Full text article
References
Adam, F., & Hassan, N. (2016). Multi Q-fuzzy soft expert set and its application. Journal of Intelligent & Fuzzy Systems, 30(2), 943-950. https://doi.org/10.3233/ifs-151816
Ali, M. I., Feng, F., Liu, X., Min, W. K., & Shabir, M. (2009). On some new operations in soft set theory. Computers & Mathematics with Applications, 57(9), 1547-1553. https://doi.org/10.1016/j.camwa.2008.11.009
Alkhazaleh, S., & Salleh, A. R. (2011). Soft expert sets. Advances in Decision Sciences, 2011, 757868. https://doi.org/10.1155/2011/757868
Alkhazaleh, S., & Salleh, A. R. (2014). Fuzzy soft expert set and its application. Applied Mathematics, 5(9), 1349-1368. https://doi.org/10.4236/am.2014.59127
Al-Qudah, Y., & Hassan, N. (2017). Bipolar fuzzy soft expert set and its application in decision making. International Journal of Applied Decision Sciences, 10(2), 175-191. https://doi.org/10.1504/ijads.2017.084310
Aslam, M. F., Ali, M. I., Mahmood, T., Rehman, M. M. U., & Sarfraz, N. (2019). Study of fuzzy soft sets with some order on set of parameters. International Journal of Algebra and Statistics, 8(1), 50-65. https://doi.org/10.20454/ijas.2019.1593
Borah, M., Neog, T. J., & Sut, D. K. (2012). A study on some operations of fuzzy soft sets. International Journal of Modern Engineering Research (IJMER), 2(2), 157-168.
Çağman, N., Enginoğlu, S., & Çitak, F. (2011). Fuzzy soft set theory and its applications. Iranian Journal of Fuzzy Systems, 8(3), 137-147. https://doi.org/10.22111/ijfs.2011.292
Çelik, Y., & Yamak, S. (2013). Fuzzy soft set theory applied to medical diagnosis using fuzzy arithmetic operations. Journal of Inequalities and Applications, 2013(1), 82. https://doi.org/10.1186/1029-242x-2013-82
Das, A. K., Granados, C., & Bhattacharya, J. (2022). Some new operations on fuzzy soft sets and their applications in decision-making. Songklanakarin Journal of Science and Technology, 44(2), 440-449. https://doi.org/10.14456/sjst-psu.2022.61
Deli, I. (2019). Convex and concave sets based on soft sets and fuzzy soft sets. Journal of New Theory, 29, 101-110. https://izlik.org/JA75UN89LP
Gogoi, K., Dutta, A. K., & Chutia, C. (2014). Application of fuzzy soft set theory in day to day problems. International Journal of Computer Applications, 85(7), 27-31. https://doi.org/10.5120/14854-3221
Hassan, N., Sayed, O. R., Khalil, A. M., & Ghany, M. A. (2017). Fuzzy soft expert system in prediction of coronary artery disease. International Journal of Fuzzy Systems, 19(5), 1546-1559. https://doi.org/10.1007/s40815-016-0255-0
Ihsan, M., Rahman, A. U., Saeed, M., & Khalifa, H. A. E. W. (2021). Convexity-cum-concavity on fuzzy soft expert set with certain properties. International Journal of Fuzzy Logic and Intelligent Systems, 21(3), 233-242. https://doi.org/10.5391/ijfis.2021.21.3.233
Khan, A., Abidin, M. Z., & Sarwar, M. A. (2025). Another view on soft expert set and its application in multi-criteria decision-making. Mathematics, 13(2), 252. https://doi.org/10.3390/math13020252
Kong, Z., Ai, J., Wang, L., Li, P., Ma, L., & Lu, F. (2018). New normal parameter reduction method in fuzzy soft set theory. IEEE Access, 7, 2986-2998. https://doi.org/10.1109/access.2018.2888878
Liu, Z., Alcantud, J. C. R., Qin, K., & Pei, Z. (2019). The relationship between soft sets and fuzzy sets and its application. Journal of Intelligent & Fuzzy Systems, 36(4), 3751-3764. https://doi.org/10.3233/JIFS18559
Majeed, S. N. (2016). Some notions on convex soft sets. Annals of Fuzzy Mathematics and Informatics, 12(4), 517-526.
Maji, P. K., Biswas, R., & Roy, A. R. (2001). Fuzzy soft set. The Journal of Fuzzy Mathematics, 3, 589-602. https://doi.org/10.1016/s0165-0114(98)00235
Mizumoto, M., & Tanaka, K. (1981). Fuzzy sets and their operations. Information and Control, 48(1), 30-48. https://doi.org/10.1016/S0019-9958(81)90578-7
Molodtsov, D. (1999). Soft set theory—First results. Computers & Mathematics with Applications, 37(4-5), 19-31. https://doi.org/10.1016/s0898-1221(99)00056-5
Qayyum, A., Abdullah, S., & Aslam, M. (2016). Cubic soft expert sets and their application in decision making. Journal of Intelligent & Fuzzy Systems, 31(3), 1585-1596. https://doi.org/10.3233/JIFS-151652
Rahman, A. U., Saeed, M., Arshad, M., Ihsan, M., & Ahmad, M. R. (2021a). (m,n)-Convexity-cum-concavity on fuzzy soft set with applications in first and second sense. Punjab University Journal of Mathematics, 53(1), 19-33. https://doi.org/10.52280/pujm.2021.530102
Rahman, A. U., Saeed, M., Ihsan, M., Arshad, M., & Ayaz, S. (2021b). A conceptual framework of m-convex and m-concave sets under soft set environment with properties. Transactions in Mathematical and Computational Sciences, 1(1), 40-60. https://doi.org/10.5281/zenodo.4743406
Rahman, A. U., Saeed, M., & Smarandache, F. (2020). Convex and concave hypersoft sets with some properties. Neutrosophic Sets and Systems, 38, 555-562. https://doi.org/10.5281/zenodo.4300580
Rahman, A. U., Arshad, M., & Saeed, M. (2021c). A conceptual framework of convex and concave sets under refined intuitionistic fuzzy set environment. Journal of Prime Research in Mathematics, 17(2), 122-137. https://doi.org/10.5281/zenodo.6656141
Roy, A. R., & Maji, P. K. (2007). A fuzzy soft set theoretic approach to decision making problems. Journal of Computational and Applied Mathematics, 203(2), 412-418. https://doi.org/10.1016/j.cam.2006.04.008
Salih, H. M., & Sabir, P. O. (2020). Some new properties of convex and concave soft sets. Diyala Journal for Pure Sciences, 15(1), 84-94. https://doi.org/10.24237/djps.1501.471b
Sezgin, A. H., & Atagün, A. N. O. (2023). A new soft set operation: complementary soft binary piecewise plus (+) operation. Matrix Science Mathematic (MSMK), 7(2), 125-142. https://doi.org/10.26480/msmk.02.2023.125.142
Tanay, B., & Kandemir, M. B. (2011). Topological structure of fuzzy soft sets. Computers & Mathematics with Applications, 61(10), 2952-2957. https://doi.org/10.1016/j.camwa.2011.03.056
Tripathy, B. K., Sooraj, T. R., & Mohanty, R. K. (2015). A new approach to fuzzy soft set theory and its application in decision making. In Computational Intelligence in Data Mining—Volume 2: Proceedings of the International Conference on CIDM, 5-6 December 2015 (pp. 305-313). New Delhi: Springer India.
Xiao, Z., Gong, K., & Zou, Y. (2009). A combined forecasting approach based on fuzzy soft sets. Journal of Computational and Applied Mathematics, 228(1), 326-333. https://doi.org/10.1016/j.cam.2008.09.033
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. https://doi.org/10.1016/s0019-9958(65)90241-x
Authors
Copyright (c) 2026 Muhammad Ihsan, and Muhammad Arshad
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY-NC-SA 4.0] that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work, with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online.