Biquartic Hesitant Fuzzy Bézier Surface Approximation Model with Its Visualization

Jin Pa Wei — 2024-09-20

Geometric modeling has evolved significantly since its inception, with pioneers like Pierre Bézier laying the foundation for curve modeling. Concurrently, fuzzy set theory, introduced by Lotfi A. Zadeh in 1965, addressed uncertainty in decision-making processes. Integrating fuzzy set theory with geometric modeling has led to advancements in handling imprecise data and uncertainty. This paper proposes a novel approach, the hesitant fuzzy Bézier surface (HFBS) approximation model, which combines geometric modeling with hesitant fuzzy sets to address uncertainty in surface approximation. The model utilizes hesitant fuzzy control net relations to construct HFBSs, enabling visualization of surfaces under varying degrees of uncertainty. A biquartic HFBS example is presented, demonstrating the model’s ability to handle hesitancy among experts’ opinions. The paper discusses the properties of HFBS and suggests its extension to interpolation models for broader applicability. Ultimately, the HFBS model offers an approach to geometric modeling in situation where uncertainty is inherent, which aim to handle complex data in real-world applications.

Spectral Bipartition via Gap Cut on DNA Sequences

Hung Lik Goh — 2024-09-20

Deoxyribonucleic Acid (DNA) and graph partitioning are two distinct fields of study which can be linked in the structure of biological networks. Graph partitioning has been extensively studied but not its application in the biological field. This research explored on the application of spectral graph partitioning in DNA splicing, aiming to simulate the cleavage of DNA by performing spectral bipartition on DNA sequences in a DNA splicing system. This research incorporates Fiedler theory and algebraic graph theory, which are commonly utilized in network analysis and the analysis of graph connectivity. Some DNA sequences of even length are selected and expressed in graphical representations. The adjacency matrix, Laplacian matrix, and degree matrix are computed from the graphs, as well as the Fiedler value and Fiedler vector associated with the graphs. Gap cut is used as a method of spectral bipartition which produces two partitions of DNA sequence of unequal lengths. The generalizations of gap cut on DNA sequences of even length are provided as lemmas and theorem.

Semarak International Journal of Fundamental and Applied Mathematics

Biquartic Hesitant Fuzzy Bézier Surface Approximation Model with Its Visualization

Spectral Bipartition via Gap Cut on DNA Sequences