Type-2 Intuitionistic Interpolation Cubic Fuzzy Bézier Curve Modeling using Shoreline Data
DOI:
https://doi.org/10.11113/mjfas.v19n6.3076Keywords:
Type-2 intuitionistic fuzzy set, Bézier curve, Real dataAbstract
The notion of fuzzy sets is fast becoming a key instrument in defining the uncertainty data and has increasingly been recognised by practitioners and researchers across different disciplines in recent decades. The uncertainty data cannot be modeled directly and this causes hindrance in obtaining accurate information for analysis or predictions. Hence, this paper contributes to another approach in which an application of type-2 intuitionistic fuzzy set (T-2IFS) in geometric modeling onto complex uncertainty data where the data are defined using the type-2 fuzzy concept. T-2IFS is the generalized forms of fuzzy sets, intuitionistic fuzzy sets, interval-valued fuzzy sets, and interval-valued intuitionistic fuzzy sets. Based on the concept of T2IFS, type-2 intuitionistic fuzzy point (T-2IFP) is defined in order to generate a type-2 intuitionistic fuzzy control point (T-2IFCP). Following, the T-2IFCP will be blended with the Bernstein blending function through the interpolation method, resulting to a type-2 intuitionistic interpolation cubic fuzzy Bézier curve. Shoreline data is used as the data and further verifies that the model can be conceivably accepted. In conclusion, the proposed methods are reliable and can be expanded to many other areas.
References
Atanassov, Krassimir T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87-96.
Awad, M., & El-Sayed, H. M. (2021). The analysis of shoreline change dynamics and future predictions using automated spatial techniques: Case of El-Omayed on the Mediterranean Coast of Egypt. Ocean & Coastal Management, 205, 105568.
Bakali, A., Broumi, S., Nagarajan, D., Talea, M., Lathamaheswari, M., & Kavikumar, J. (2021). Graphical representation of type-2 neutrosophic sets. Neutrosophic Sets and Systems, 42(1).
Chaira, T. (2019). Fuzzy set and its extension: The intuitionistic fuzzy set. Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set, March, 1-288.
Cường, Bùi Công, Tống Hòang Anh, & Bùi Dương Hải (2012). Some operations on type-2 intuitionistic fuzzy sets. Journal of Computer Science and Cybernetics, 28(3), 274-283.
Hariri, R. H., Fredericks, E. M. & Bowers, K. M. (2019). Uncertainty in big data analytics: Survey, opportunities, and challenges. Journal of Big Data, 6(1), 1-16.
Mendel, Jerry M. (2007). Type-2 fuzzy sets and systems: An overview. IEEE Computational Intelligence Magazine, 2(1), 20-29.
Roy, S. K., & Bhaumik, A. (2017). Intelligent water management: A Triangular type-2 intuitionistic fuzzy matrix games approach. Water Resources Management 2017, 32(3), 949-68.
Singh, S., & Garg, H. (2016). Distance measures between type-2 intuitionistic fuzzy sets and their application to multicriteria decision-making process. Applied Intelligence 2016, 46(4), 788-799.
Szmidt, E. (2007). Uncertainty and information: foundations of generalized information theory (Klir, G.J.; 2006). IEEE Transactions on Neural Networks, 18(5), 1551.
Tas, Ferhat, and Selcuk Topal. (2017). Bezier curve modeling for neutrosophic data problem. Neutrosophic Sets and Systems, 15, 3-5.
Tolga, A. C. (2020). Real options valuation of an iot based healthcare device with interval type-2 fuzzy numbers. Socio-Economic Planning Sciences, 69, 100693.
Wahab, A. F., Ali, J. M. & Majid, A. A. (2009). Fuzzy Geometric Modeling. Proceedings of the 2009 6th International Conference on Computer Graphics, Imaging and Visualization: New Advances and Trends, CGIV2009, 276-280.
Wahab, A. F., & Zulkifly, M. I. E. (2015). Intuitionistic fuzzy in spline curve/surface. Malaysian Journal of Fundamental and Applied Sciences, 11(1), 21-23.
Wahab, A. F., & Zulkifly, M. I. E. (2017). A new fuzzy bezier curve modeling by using fuzzy control point relation. Applied Mathematical Sciences, 11, 39-57.
Wahab, A. F., Zulkifly, M. I. E., & Husain, M. S. (2016). Bezier curve modeling for intuitionistic fuzzy data problem. AIP Conference Proceedings, 1750.
Wahab, A. F., Zulkifly, M. I. E., & Ismail, N. B. (2019). Fuzzy bézier curve interpolation modeling by using fuzzy control point relation. Advances and Applications in Discrete Mathematics, 21(1), 1-23.
Yazdinejad, A., Dehghantanha, A., Parizi, R. M., & Epiphaniou, G. (2023). An optimized fuzzy deep learning model for data classification based on NSGA-II. Neurocomputing, 522, 116-128.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353.
Zadeh, L. A. (1975). Fuzzy logic and approximate reasoning. Synthese, 30, 407-428.
Zakaria, R., Wahab, A. F., Ismail, I., & Zulkifly, M. I. E. (2021). Complex uncertainty of surface data modeling via the type-2 fuzzy b-spline Model. Mathematics 2021, 9, 1054.
Zakaria, R., Wahab, A. F., and Gobithaasan, R. U. (2013). Normal type-2 fuzzy rational b-spline curve. ArXiv 7(13-16), 789-806.
Zakaria, R., Wahab, A. F., and Gobithaasan, R. U. (2013). Type-2 fuzzy bezier curve modeling. AIP Conference Proceedings, 1522, 945-952.
Zakaria, R., Wahab, A. F., and Gobithaasan, R. U. (2014). Fuzzy B-spline surface modeling. Journal of Applied Mathematics, 2014.
Zakaria, R., Wahab, A. F., and Gobithaasan, R. U. (2015). Normal type-2 fuzzy interpolating B-spline curve. AIP Conference Proceedings, 1605(1), 476.
Zakaria, R., Wahab, A. F., and Gobithaasan, R. U (2016). The series of fuzzified fuzzy bezier curve. Jurnal Teknologi, 78(2-2), 103-107.
Zeinali, S., Dehghani, M., & Talebbeydokhti, N. (2021). Artificial neural network for the prediction of shoreline changes in Narrabeen, Australia. Applied Ocean Research, 107, 102362.
Zakaria, R., Jifrin, A. N., Jaman, S. N., & Roslee, R. (2022). Fuzzy interpolation curve modelling of earthquake magnitude data. IOP Conference Series, 1103(1), 012029.
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