Convex rough sets on finite domains

Alcantud, José Carlos R.; Zhan, Jianming

doi:10.1016/j.ins.2022.08.013

Cited by 9 publications

(3 citation statements)

References 43 publications

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“…Whether connectedness of fuzzifying matroids could be applied to some fuzzy combinatorial problems, we shall consider this problem in the future. Of course, applications in decision-making problems as in [31][32][33][34] should also be considered; (4) We are also extending our work to m-polar fuzzifying matroids by imitating reference [15].…”

Section: Discussionmentioning

confidence: 99%

Connected Degree of Fuzzifying Matroids

Xin

Garg

et al. 2022

Journal of Mathematics

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Polya’s plausible reasoning methods are crucial not only in discovery of mathematics results, modeling methods, and data processing methods but also in many practical problems’ solving. This paper exemplifies how to use Polya’s plausible reasoning methods to generalize the popularized notion of 2-connectedness of graphs to a more universal notion of the connected degree of fuzzifying matroids. We introduce the connectedness of fuzzifying matroids, which is generalized from 2-connectedness of graphs, connectedness of matroids, and 2-connectedness of fuzzy graphs. Moreover, the connected degree of fuzzifying matroids is presented by considering the fuzziness degree of connectedness. It is proved that a fuzzifying matroid M is connected, which is equivalent to its connectedness degree Con M is the biggest (i.e., Con M = 1 ). This, together with other properties of the connected degree of fuzzifying matroids, demonstrates the rationality of the proposed notion. Finally, we describe the concepts of this paper through some examples.

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Section: Discussionmentioning

confidence: 99%

Connected Degree of Fuzzifying Matroids

Xin

Garg

et al. 2022

Journal of Mathematics

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“…If the chord length is larger than the threshold, keep P 2 as the starting point and calculate the chord length l 23 , if the chord length is smaller than the threshold, delete the point and calculate the chord length l 13 until the chord length is larger than the threshold. The threshold value of l ε is given in equation (1).…”

Section: Establishment Of Hs Model Based On Real-time Data Streamliningmentioning

confidence: 99%

“…(3.15), F 1 and F 2 denote the generated model file size before and after streamlining, respectively, V ol 1 and V ol 2 denote the generated model volume before and after point cloud streamlining, respectively, and T R is the generated model time. For the needs of 3D modeling, the study constructs a combined HS and LS ITL modeling system based on traditional geometric modeling, see Figure 3.5 [1]. Figure 3.5 modeling process is as follows, first of all, Different modeling methods are selected according to the modeling objects, the regular geometric shape selected traditional 3D modeling, irregular shape selected HS modeling, need to reverse the existing physical creation of data models selected LS modeling.…”

Section: Integration and Improvement Of Hs And Lals-ls Itl Modelmentioning

confidence: 99%

Virtual Reality Scenario Analysis of Art Design Taking into Account Interactive Digital Media Pattern Generation Technology

Liu

2024

SCPE

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In art design, 3D printing technology is crucial, and more and more creators conceive scenes using 3D modeling software to get a three-dimensional and beautiful work. Due to the large amount of noise and redundant points in the raw data collected during the modeling process, the generation speed and rendering effect of 3D models are reduced. Given the above problems, the study designed an interactive 3D lightweight modeling system based on the combination of hand-drawn sketching and laser 3D scanning based on the streamlined algorithm. The experimental results showed that when the hand-drawn speed was 300, the number of triangular slices, model size, and time required to generate the model of the hand-drawn sketching model based on the streamlined algorithm were reduced by 67.39%, 65.48%, and 63.79%, respectively. In the real-time point cloud data streamlining process of the laser 3D scanning model, the point cloud data reduction ratio and the streamlining goodness index of the point cloud streamlining algorithm are 71.99% and 3.06%, respectively. The system performance is robust, and the data processing speed and rendering effect are good.

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