Optimal Scale Combination Selection Integrating Three-Way Decision With Hasse Diagram

Zhang, Qinghua; Cheng, Yunlong; Zhao, Fan; Wang, Guoyin; Xia, Shuyin

doi:10.1109/tnnls.2021.3054063

Cited by 38 publications

(10 citation statements)

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“…Point 1 is the point 1 of point set {1}, and the vertical distribution diagram of Q(A (0) ) = {{1}} is obtained. Therefore, the vertical distribution diagram of P(A (0) ) and Q(A (0) ) constitutes the vertical distribution diagram of P(A (1) ) = P(A (0) ) + Q(A (0) ). Finally, point 0 and 1 are connected to obtain line segment 0..1; This is shown in figure 4.…”

Section: The Distribution Of Finite Power Setsmentioning

confidence: 99%

“…(ii) ( ii) Connect points 0 and 2 to obtain line segment 0 .. 2, crossing point 2 as the parallel line of segment 0..1 intersects 2 ordinal line π 2 at 12, namely the point of subset {1,2}. The vertical distribution graph of Q(A (1) ) = {{2}, {1,2}} is obtained. In this way, the vertical distribution of P(A (1) ) and Q(A (1) ) is yielded, which makes up the vertical distribution of P(A ( 2) ) = P(A (1) ) + Q(A (1) ).…”

Section: Amds-2022mentioning

confidence: 99%

“…The vertical distribution graph of Q(A (1) ) = {{2}, {1,2}} is obtained. In this way, the vertical distribution of P(A (1) ) and Q(A (1) ) is yielded, which makes up the vertical distribution of P(A ( 2) ) = P(A (1) ) + Q(A (1) ). Finally, connect points 2 and 12 to obtain line segment 2..12, as shown in figure 5.…”

Section: Amds-2022mentioning

confidence: 99%

“…Venn Diagram graphically describes the relations and operations between sets. It is well known that a power set is a poset, a Hass diagram of a diagram describing a poset relationship, which has a wide range of applications in many fields [1][2][3][4][5][6][7][8]. For example, the authors combine the three-way decision with the Hasse graph to establish a sequential three-way decision model in scale space, which can reduce the search space [1].…”

Section: Introductionmentioning

confidence: 99%

“…It is well known that a power set is a poset, a Hass diagram of a diagram describing a poset relationship, which has a wide range of applications in many fields [1][2][3][4][5][6][7][8]. For example, the authors combine the three-way decision with the Hasse graph to establish a sequential three-way decision model in scale space, which can reduce the search space [1]. In order to improve the groundwater quality assessment model based on the Hasse diagram technique, a new assessment model based on game theory and the Hasse diagram technique is established [2].…”

Section: Introductionmentioning

confidence: 99%

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Fractals and Finite Distributions of Power Sets

Zheng¹,

Li²

2023

J. Phys.: Conf. Ser.

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In this paper, we are committed to investigating the fractal decomposition of power sets. Our main result is that every power set can be decomposed into a sum of a power set and an isomorphic set that does not intersect with it. For the finite power set, this property can be drawn on the ordinal line by constructing the fractal number axis of the ordinal line, and the fractal distribution and fractal graph of the finite power set can be obtained by using the parallel translation drawing method. Moreover, the distributions do not overlap or cross. The results in this paper provide a new perspective for further investigation of the fractal distribution of power sets.

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Section: The Distribution Of Finite Power Setsmentioning

confidence: 99%