# Discretization Algorithm for Incomplete Economic Information in Rough Set Based on Big Data

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Discrete Algorithm Design of Rough Set Incomplete Economic Information

#### 2.1. The Algorithm for Filling of Incomplete Economic Information Based on Deep Learning

#### 2.2. The Discretization Algorithm Based on Breakpoint Discrimination in Rough Set

#### 2.2.1. Calculation Method for $P\left(j,{c}_{m}^{a}\right)$

- Step 1 ${P}_{L}\left(j,{c}_{m}^{a}\right)$ is calculated;
- Step 2 ${P}_{R}\left(j~{c}_{m}^{a}\right)$ is calculated;
- Step 3 $P\left(j,{c}_{m}^{a}\right)$ is calculated.

#### 2.2.2. Calculation Method for $ced\left({c}_{m}^{a}\right)$

#### 2.2.3. Discrete Algorithm Design Based on Big Data

- Step 1
- $P=\varphi $; $L=\left\{U\right\}$.
- Step 2
- For $c\in \mathrm{C}$, $ced\left({c}_{m}^{a}\right)$ should be calculated;
- Step 3
- Select maximum breakpoint ${c}_{\mathrm{max}}$ of $ced\left({c}_{m}^{a}\right)$ and add it to P;
- Step 4
- For all $X\in L$, if ${c}_{\mathrm{max}}$ divides the equivalence class X into ${X}_{1}$ and ${X}_{2}$, then remove X from L and add equivalence classes ${X}_{1}$ and ${X}_{2}$ to L;
- Step 5
- If the instances have the same decision in each of the equivalence classes of L, then stop; otherwise go to Step 2.

## 3. Experimental Process and Analysis

- Discrete the incomplete economic information data set with the selected three methods;
- Select the information entropy algorithm for attribute reduction, use the inductive value reduction algorithm to perform value reduction and get the rules. Finally, test the knowledge gained.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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Combination | d_{2} | RMSE | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Single | Multiple | Single | Multiple | |||||||||

Deletion Rate /% | Algorithm in This Paper | FIMUS | DMI | Algorithm in This Paper | FIMUS | DMI | Algorithm in This Paper | FIMUS | DMI | Algorithm in This Paper | FIMUS | DMI |

1 | 0.843 | 0.742 | 0.733 | 0.818 | 0.728 | 0.722 | 0.152 | 0.262 | 0.288 | 0.175 | 0.268 | 0.294 |

3 | 0.892 | 0.728 | 0.713 | 0.848 | 0.709 | 0.698 | 0.119 | 0.273 | 0.303 | 0.144 | 0.296 | 0.318 |

5 | 0.856 | 0.693 | 0.685 | 0.841 | 0.682 | 0.673 | 0.137 | 0.294 | 0.307 | 0.157 | 0.318 | 0.329 |

10 | 0.866 | 0.658 | 0.644 | 0.843 | 0.636 | 0.617 | 0.162 | 0.317 | 0.337 | 0.177 | 0.329 | 0.363 |

Sample Size/Individual | Number of Condition Properties/Individual | Decision Number/Individual | Extreme Outliers/Individual | Noise /Intensity |
---|---|---|---|---|

151 | 5 | 4 | 2 | 1 |

215 | 10 | 7 | 5 | 5 |

271 | 14 | 3 | 7 | 9 |

337 | 8 | 8 | 9 | 10 |

691 | 15 | 3 | 11 | 12 |

769 | 9 | 3 | 17 | 15 |

847 | 19 | 5 | 21 | 17 |

5001 | 8 | 11 | 25 | 19 |

20,001 | 17 | 27 | 27 | 22 |

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**MDPI and ACS Style**

Li, X.; Shen, Y.
Discretization Algorithm for Incomplete Economic Information in Rough Set Based on Big Data. *Symmetry* **2020**, *12*, 1245.
https://doi.org/10.3390/sym12081245

**AMA Style**

Li X, Shen Y.
Discretization Algorithm for Incomplete Economic Information in Rough Set Based on Big Data. *Symmetry*. 2020; 12(8):1245.
https://doi.org/10.3390/sym12081245

**Chicago/Turabian Style**

Li, Xiangyang, and Yangyang Shen.
2020. "Discretization Algorithm for Incomplete Economic Information in Rough Set Based on Big Data" *Symmetry* 12, no. 8: 1245.
https://doi.org/10.3390/sym12081245