# A New Multi-Sensor Fusion Target Recognition Method Based on Complementarity Analysis and Neutrosophic Set

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## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

#### 2.1. Neutrosophic Set

**Definition**

**1.**

**Definition**

**2.**

#### 2.2. Commonly Used Evaluation Indicators for Multi-Classification Problems

- True Positive(TP): The true category is a positive example, and the predicted category is a positive example.
- False Positive (FP): The true category is negative, and the predicted category is positive.
- False Negative (FN): The true category is positive, and the predicted category is negative.
- True Negative (TN): The true category is negative, and the predicted category is negative.

- Precision or precision rate, also known as precision (P):$$P=\frac{TP}{TP+FP}$$
- Recall rate, also known as recall rate (R):$$R=\frac{TP}{TP+FN}$$
- F1 score is an index used to measure the accuracy of the classification model. It also takes into account the accuracy and recall of the classification model. The score can be regarded as a harmonic average of model accuracy and recall. Its maximum value is 1 and its minimum value is 0:$${F}_{1}=\frac{2\times P\times R}{P+R}$$

#### 2.3. AdaBoost Algorithm

- Train weak classifiers with sample sets.
- Calculate the error rate of the weak classifier, and obtain the correct and incorrect sample sets.
- Adjust the sample set weight according to the classification result to obtain a redistributed sample set.

#### 2.4. HOG Feature

#### 2.5. Gabor Feature

#### 2.6. D-AHP Theory

## 3. The Proposed Method

#### 3.1. Complementarity

- According to the data test result, the sensor recognition matrix can be obtained.
- The sensor preference matrix for different target types is obtained from multiple sensor recognition matrices.
- The sensor complementarity vector is gotten from the sensor preference relationship matrix.

#### 3.1.1. Sensor Recognition Matrix

#### 3.1.2. Sensor Preference Matrix

#### 3.1.3. Sensor Complementarity Vector

- Express the importance of the index relative to the evaluation target through the preference relationship, and construct the D number preference matrix ${R}_{D}$.
- According to the integrated representation of the D number, transform the D number preference matrix into a certain number matrix ${R}_{I}$.
- Construct a probability matrix ${R}_{I}$ based on the deterministic number matrix ${R}_{P}$, and calculate the preference probability between the indicators compared in pairs.
- Convert the probability matrix ${R}_{P}$ into a triangularized probability matrix ${{R}^{T}}_{P}$, and sort the indicators according to their importance.
- According to the index sorting result, the deterministic number matrix ${R}_{I}$ is expressed as a matrix ${{R}^{T}}_{I}$, finally ${C}^{j}$ is obtained.

#### 3.2. Data Fusion

## 4. Simulation

#### 4.1. Data Set

#### 4.2. Sensor

#### 4.3. Base Sensor Recognition Confusion Matrix

#### 4.4. Preference Matrix

#### 4.5. Complementarity Vector

#### 4.6. Data Fusion

#### 4.7. Recognition Result

## 5. Results

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Complementary vector generation process [62].

**Table 1.**${R}_{j}^{i}$: The recognition situation of a certain sensor to the target of category ${Y}_{j}$.

Real-Recognition | ${\mathit{Y}}_{\mathit{j}}$ | Non-${\mathit{Y}}_{\mathit{j}}$ |
---|---|---|

${Y}_{j}$ | ${{r}^{i}}_{jj}$ | ${\displaystyle \sum}_{k\ne j}}{{r}^{i}}_{jk$ |

non-${Y}_{j}$ | ${\displaystyle \sum}_{k\ne j}}{{r}^{i}}_{kj$ | ${\displaystyle \sum}_{l\ne j}}{\displaystyle {\displaystyle \sum}_{k\ne j}}{{r}^{i}}_{kl$ |

Infrared Light Data | Train Set | Validation Set | Test Set |
---|---|---|---|

Sailboat | 65 | 28 | 28 |

Cargo ship | 68 | 35 | 35 |

Speed boat | 63 | 25 | 25 |

Fishing boat | 79 | 35 | 35 |

Visible Light Data | Train Set | Validation Set | Test Set |
---|---|---|---|

Sailboat | 65 | 28 | 28 |

Cargo ship | 79 | 35 | 35 |

Speed boat | 70 | 25 | 25 |

Fishing boat | 78 | 35 | 35 |

Sensor 1 | Sensor 2 |

Visible light + HOG + AdaBoost | Infrared light + HOG + AdaBoost |

Sensor 3 | Sensor 4 |

Visible light + GABOR + AdaBoost | Infrared light + GABOR + AdaBoost |

Real Category/Identify Category | Sailboat | Cargo Ship | Speedboat | Fishing Boat |
---|---|---|---|---|

Sailboat | 23 | 0 | 2 | 0 |

Cargo ship | 0 | 29 | 3 | 0 |

Speed boat | 1 | 1 | 20 | 0 |

Fishing boat | 0 | 0 | 0 | 31 |

Real Category/Identify Category | Sailboat | Cargo Ship | Speedboat | Fishing Boat |
---|---|---|---|---|

Sailboat | 16 | 3 | 6 | 0 |

Cargo ship | 1 | 13 | 17 | 1 |

Speed boat | 0 | 0 | 18 | 4 |

Fishing boat | 0 | 1 | 9 | 21 |

Real Category/Identify Category | Sailboat | Cargo Ship | Speedboat | Fishing Boat |
---|---|---|---|---|

Sailboat | 16 | 1 | 8 | 0 |

Cargo ship | 5 | 17 | 10 | 0 |

Speed boat | 0 | 0 | 22 | 0 |

Fishing boat | 0 | 0 | 0 | 31 |

Real Category/Identify Category | Sailboat | Cargo Ship | Speedboat | Fishing Boat |
---|---|---|---|---|

Sailboat | 25 | 0 | 0 | 0 |

Cargo ship | 5 | 25 | 0 | 2 |

Speed boat | 0 | 10 | 1 | 11 |

Fishing boat | 0 | 0 | 6 | 25 |

$\mathit{P}(1,1)$ | Sensor 1 | Sensor 2 | Sensor 3 | Sensor 4 |
---|---|---|---|---|

Sensor 1 | 0.500 | 0.801 | 0.821 | 0.690 |

Sensor 2 | 0.198 | 0.500 | 0.532 | 0.355 |

Sensor 3 | 0.178 | 0.467 | 0.500 | 0.326 |

Sensor 4 | 0.309 | 0.644 | 0.673 | 0.500 |

$\mathit{P}(1,2)$ | Sensor 1 | Sensor 2 | Sensor 3 | Sensor 4 |
---|---|---|---|---|

Sensor 1 | 0.500 | 0.859 | 0.826 | 0.794 |

Sensor 2 | 0.140 | 0.500 | 0.436 | 0.386 |

Sensor 3 | 0.173 | 0.563 | 0.500 | 0.448 |

Sensor 4 | 0.205 | 0.614 | 0.551 | 0.500 |

$\mathit{P}(1,3)$ | Sensor 1 | Sensor 2 | Sensor 3 | Sensor 4 |
---|---|---|---|---|

Sensor 1 | 0.500 | 0.856 | 0.769 | 0.802 |

Sensor 2 | 0.143 | 0.500 | 0.358 | 0.403 |

Sensor 3 | 0.230 | 0.641 | 0.500 | 0.548 |

Sensor 4 | 0.197 | 0.596 | 0.451 | 0.500 |

$\mathit{P}(1,4)$ | Sensor 1 | Sensor 2 | Sensor 3 | Sensor 4 |
---|---|---|---|---|

Sensor 1 | 0.500 | 1.000 | 0.500 | 1.000 |

Sensor 2 | 0 | 0.500 | 0 | 0.561 |

Sensor 3 | 0.500 | 1.000 | 0.500 | 1.000 |

Sensor 4 | 0 | 0.438 | 0 | 0.500 |

Sensor 1 | Sensor 2 | Sensor 3 | Sensor 4 | |
---|---|---|---|---|

$C(1,1)$ | 0.473 | 0.138 | 0.106 | 0.283 |

$C(1,2)$ | 0.513 | 0.102 | 0.166 | 0.219 |

$C(1,3)$ | 0.500 | 0.086 | 0.231 | 0.183 |

$C(1,4)$ | 0.382 | 0.132 | 0.382 | 0.104 |

Type | Sailboat | Cargo Ship | Speedboat | Fishing Boat |
---|---|---|---|---|

Sensor 1 | 0.256 | 0.122 | 0.180 | 0.442 |

Sensor 2 | 0.136 | 0.237 | 0.315 | 0.312 |

Sensor 3 | 0.078 | 0.107 | 0.352 | 0.463 |

Sensor 4 | 0.099 | 0.162 | 0.286 | 0.453 |

Sensor 1 | Sensor 2 | Sensor 3 | Sensor 4 | |
---|---|---|---|---|

$W(1,1)$ | 0.817 | 0.238 | 0.183 | 0.487 |

$W(1,2)$ | 0.833 | 0.167 | 0.262 | 0.355 |

$W(1,3)$ | 0.853 | 0.147 | 0.393 | 0.311 |

$W(1,4)$ | 0.789 | 0.274 | 0.789 | 0.210 |

Real Category/Identify Category | Sailboat | Cargo Ship | Speedboat | Fishing Boat |
---|---|---|---|---|

Sailboat | 27 | 0 | 1 | 0 |

Cargo ship | 1 | 31 | 3 | 0 |

Speed boat | 0 | 0 | 25 | 0 |

Fishing boat | 0 | 0 | 0 | 35 |

Real Category/Identify Category | Sailboat | Cargo Ship | Speedboat | Fishing Boat |
---|---|---|---|---|

Sailboat | 27 | 0 | 1 | 0 |

Cargo ship | 1 | 33 | 1 | 0 |

Speed boat | 1 | 1 | 21 | 2 |

Fishing boat | 0 | 0 | 0 | 35 |

Real Category/Identify Category | Sailboat | Cargo Ship | Speedboat | Fishing Boat |
---|---|---|---|---|

Sailboat | 26 | 1 | 1 | 0 |

Cargo ship | 2 | 28 | 5 | 0 |

Speed boat | 0 | 0 | 25 | 0 |

Fishing boat | 0 | 0 | 2 | 33 |

Real Category/Identify Category | Sailboat | Cargo Ship | Speedboat | Fishing Boat |
---|---|---|---|---|

Sailboat | 25 | 0 | 3 | 0 |

Cargo ship | 0 | 31 | 4 | 0 |

Speed boat | 1 | 1 | 23 | 0 |

Fishing boat | 0 | 0 | 0 | 35 |

Real Category/Identify Category | Sailboat | Cargo Ship | Speedboat | Fishing Boat |
---|---|---|---|---|

Sailboat | 17 | 3 | 8 | 0 |

Cargo ship | 1 | 14 | 18 | 2 |

Speed boat | 0 | 1 | 19 | 5 |

Fishing boat | 0 | 1 | 10 | 24 |

Real Category/Identify Category | Sailboat | Cargo Ship | Speedboat | Fishing Boat |
---|---|---|---|---|

Sailboat | 17 | 1 | 10 | 0 |

Cargo ship | 6 | 18 | 11 | 0 |

Speed boat | 0 | 0 | 25 | 0 |

Fishing boat | 0 | 0 | 0 | 35 |

Real Category/Identify Category | Sailboat | Cargo Ship | Speedboat | Fishing Boat |
---|---|---|---|---|

Sailboat | 28 | 0 | 0 | 0 |

Cargo ship | 6 | 27 | 0 | 2 |

Speed boat | 0 | 12 | 1 | 12 |

Fishing boat | 0 | 0 | 6 | 29 |

Category | Accuracy Rate | Recall Rate | F1 Score | Count Time | Correct Rate | |
---|---|---|---|---|---|---|

Sensor 1 | Sailboat | 0.962 | 0.893 | 0.926 | 54S | 92.68% |

Cargo ship | 0.969 | 0.886 | 0.925 | |||

Speedboat | 0.767 | 0.920 | 0.836 | |||

Fishing boat | 1.000 | 1.000 | 1.000 | |||

Sensor 2 | Sailboat | 0.944 | 0.607 | 0.739 | 52S | 60.16% |

Cargo ship | 0.737 | 0.400 | 0.519 | |||

Speedboat | 0.345 | 0.760 | 0.475 | |||

Fishing boat | 0.774 | 0.686 | 0.727 | |||

Sensor 3 | Sailboat | 0.739 | 0.607 | 0.667 | 162S | 77.24% |

Cargo ship | 0.947 | 0.514 | 0.667 | |||

Speedboat | 0.543 | 1.000 | 0.704 | |||

Fishing boat | 1.000 | 1.000 | 1.000 | |||

Sensor 4 | Sailboat | 0.824 | 1.000 | 0.903 | 158S | 69.11% |

Cargo ship | 0.692 | 0.771 | 0.730 | |||

Speedboat | 0.143 | 0.040 | 0.063 | |||

Fishing boat | 0.674 | 0.829 | 0.744 | |||

D-S fusion | Sailboat | 0.929 | 0.929 | 0.929 | 434S | 91.56% |

Cargo ship | 0.966 | 0.800 | 0.875 | |||

Speedboat | 0.758 | 1.000 | 0.862 | |||

Fishing boat | 1.000 | 0.943 | 0.971 | |||

Simple fusion | Sailboat | 0.931 | 0.964 | 0.947 | 413S | 94.30% |

Cargo ship | 0.971 | 0.943 | 0.957 | |||

Speedboat | 0.913 | 0.840 | 0.875 | |||

Fishing boat | 1.000 | 0.946 | 0.972 | |||

Proposed method | Sailboat | 0.964 | 0.964 | 0.964 | 398S | 95.93% |

Cargo ship | 1.000 | 0.886 | 0.940 | |||

Speedboat | 0.862 | 1.000 | 0.926 | |||

Fishing boat | 1.000 | 1.000 | 1.000 |

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**MDPI and ACS Style**

Gong, Y.; Ma, Z.; Wang, M.; Deng, X.; Jiang, W.
A New Multi-Sensor Fusion Target Recognition Method Based on Complementarity Analysis and Neutrosophic Set. *Symmetry* **2020**, *12*, 1435.
https://doi.org/10.3390/sym12091435

**AMA Style**

Gong Y, Ma Z, Wang M, Deng X, Jiang W.
A New Multi-Sensor Fusion Target Recognition Method Based on Complementarity Analysis and Neutrosophic Set. *Symmetry*. 2020; 12(9):1435.
https://doi.org/10.3390/sym12091435

**Chicago/Turabian Style**

Gong, Yuming, Zeyu Ma, Meijuan Wang, Xinyang Deng, and Wen Jiang.
2020. "A New Multi-Sensor Fusion Target Recognition Method Based on Complementarity Analysis and Neutrosophic Set" *Symmetry* 12, no. 9: 1435.
https://doi.org/10.3390/sym12091435