# Pruning Fuzzy Neural Network Applied to the Construction of Expert Systems to Aid in the Diagnosis of the Treatment of Cryotherapy and Immunotherapy

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## Abstract

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## 1. Introduction

## 2. Literature Review

#### 2.1. Human Papillomavirus Concepts

#### 2.2. Artificial Intelligence, Artificial Neural Networks and Fuzzy Systems

#### 2.3. Related Works

#### 2.4. Fuzzy Neural Network

## 3. Pruning Fuzzy Neural Network Applied to Problems of Cryotherapy and Immunotherapy

#### 3.1. First Layer

#### 3.2. Second Layer

- each pair (${a}_{i}$, ${w}_{i}$) is transformed into a single value ${b}_{i}$ =
**h**(${a}_{i}$, ${w}_{i}$) - calculate the unified aggregation of the transformed values
**U**(${b}_{1},{b}_{2}\dots {b}_{n}$), where n is the number of inputs.

#### 3.3. Third Layer

**y**as

**Z * v**, where

**v**is the vector of weights of the output layer,

**y**is the vector of outputs.

**Z**is determined to be [21]:

**a**$={[{a}_{1},{a}_{2},\dots ,{a}_{N}]}_{m\times N}^{T}$.

**z**-vector representing unineurons) with the number of positive instances ${n}_{+}$, negative instances ${n}_{+}$ and the number of all the instances N, the F-score value of the i-th feature is defined by [83]:

**z**have their calculated f-score and the new group of neurons is composed of all those that have the calculated value more significant than the average of the f-scores.

- the number of membership functions, M
- the type of fuzzy logic neuron, unineuron

Algorithm 1: Fuzzy neural network for detection of immunotherapy and cryotherapy treatments—fuzzy neural network (FNN) training. |

(1) Define the number os membership functions, M. (2) Calculate M neurons for each characteristic in the first layer using ANFIS. (3) Construct L fuzzy neurons with Gaussian membership functions constructed with center and $\sigma $ values derived from ANFIS. (4) Define the weights and bias of the fuzzy neurons randomly. (5) Construct L fuzzy logical neurons with random weights and bias on the second layer of the network by welding the L fuzzy neurons of the first layer. (6) Use f-scores to define the most significant neurons to the problem (${L}_{p}$). (7) For all K input do (7.1) Calculate the mapping ${z}_{k}\left({x}_{k}\right)$ using logical neurons (8) Estimate the weights of the output layer using Equation (7). (9) Calculate output y using Equation (5). |

## 4. Results

#### 4.1. Database Used in the Test

- Sex (41 male (1), and 49 female (2));
- Age (minimum of 15 years and a maximum of 56 years with mean in 31.04 years and standard deviation of 12.23);
- Time (minimum of one and maximum of 12-time units with a mean of 7.23 and a standard deviation of 3.09);
- Number of warts (minimum one and maximum of 19 warts with a mean of 6.14 and a standard deviation of 4.21);
- Type (type (1) in 47 people, type (2) in 22 people and type (3) in 21 people);
- Area (minimum of 6 and maximum of 900 measurements with the mean of 95.7 and standard deviation of 136.61);
- Induration diameter (only in immunotherapy database) (minimum of two and maximum of 70 measurements with a mean of 14.3 and a standard deviation of 17.21);
- The outcome of the treatment (19 people who did not give (0) and 71 people that the treatment was effective (1) for immunotherapy and 48 has effective (1), and 42 have not been successful in the treatment of warts in cryotherapy treatment).

#### 4.2. Test Settings

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

HPV | Human papillomavirus |

WHO | World Health Organization |

FNN | Fuzzy neural network |

ELM | Extreme learning machine |

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**Figure 1.**Source of contamination by human papillomavirus (HPV). Available in https://image.shutterstock.com/image-vector/human-papillomavirus-infection-hpv-symptoms-450w-534910597.jpg.

**Figure 2.**Cryotherapy treatment. Available in: https://www.shutterstock.com/pt/image-photo/ cosmetology-woman-facial-oxygen-cryotherapy-beauty-1182525277?src=66-BtCbz-IOjSWnYhzOvMw-2-80.

**Figure 3.**Elements used in the treatment of immunotherapy. Available in: https://www.shutterstock.com/pt/image-illustration/allergy-diagnosis-stamp-stethoscope-syringe-blood\-475153798?src=J2NUVnneJIcuOBlYx85EMQ-8-25.

**Figure 4.**Pruning fuzzy neural network model [3].

**Figure 7.**ANFIS- Adaptative Network based Fuzzy Inference Systems model obtained by the fuzzy neural network (FNN) through the immunotherapy database.

Models | Accuracy | AUC | Sens. | Spec. | Time |
---|---|---|---|---|---|

This paper | 84.32 (5.21) | 0.69 (0.01) | 0.41 (0.12) | 0.97 (0.03) | 1.11 (0.06) |

FNN | 81.91 (7.64) | 0.65 (0.01) | 0.36 (0.24) | 0.94 (0.02) | 17.39 (1.03) |

MLP | 78.02 (7.44) | 0.74 (0.12) | 0.60 (0.21) | 0.88 (0.10) | 1.18 (0.08) |

J48 | 83.92 (4.69) | 0.71 (0.03) | 0.52 (0.20) | 0.91 (0.03) | 0.01 (0.00) |

NB | 76.67 (6.55) | 0.69 (0.13) | 0.51 (0.18) | 0.87 (0.13) | 0.01 (0.00) |

ZR | 79.13 (1.42) | 0.50 (0.00) | 0.50 (0.00) | 0.50 (0.00) | 0.01 (0.00) |

RT | 81.24 (7.56) | 0.74 (0.10) | 0.54 (0.07) | 0.94 (0.06) | 0.21 (0.01) |

Models | Accuracy | AUC | Sens. | Spec. | Time |
---|---|---|---|---|---|

This paper | 88.64 (5.83) | 0.89 (0.05) | 0.93 (0.08) | 0.86 (0.08) | 1.04 (0.08) |

FNN | 85.75 (8.08) | 0.85 (0.05) | 0.90 (0.16) | 0.80 (0.11) | 22.78 (2.11) |

MLP | 86.17 (7.91) | 0.91 (0.05) | 0.92 (0.06) | 0.90 (0.05) | 1.05 (0.02) |

J48 | 85.91 (6.42) | 0.89 (0.05) | 0.90 (0.09) | 0.88 (0.02) | 0.02 (0.01) |

NB | 85.67 (6.18) | 0.95 (0.05) | 0.90 (0.08) | 1.00 (0.00) | 0.52 (0.06) |

ZR | 53.64 (1.33) | 0.50 (0.00) | 0.50 (0.00) | 0.50 (0.00) | 0.05 (0.00) |

RT | 87.27 (7.98) | 0.87 (0.01) | 0.84 (0.02) | 0.90 (0.01) | 0.21 (0.01) |

1. If (SEX is lndifferent) and (AGE is New) and (TIME is Righ) and (NumberWarts is Medium) and |

(TYPE is Two) and (AREA is Big) and (DIAMETER is Hard) then (TREATMENT is effective)(1) |

2. If (SEX is Male) and (AGE is Medium) and (TIME is Medium) and (NumberWarts is Elevated) and |

(TYPE is Two) and (AREA is Medium) and (DIAMETER is Hard) then (TREATMENT is non-effective) (1) |

3. If (SEX is Male) and (AGE is New) and (TIME is Little) and (NumberWarts is Elevated) and |

(TYPE is Two) and (AREA is Medium) and (DIAMETER is Medium) then (TREATMENT is non-effective) (1) |

4. If (SEX is Female) and (AGE is Old) and (TIME is Medium) and (NumberWarts is Few) and |

(TYPE is Two) and (AREA is Big) and (DIAMETER is Small) then (TREATMENT is effective)(1) |

5. If (SEX is Male) and (AGE is Old) and (TIME is Medium) and (NumberWarts is Medium) and |

(TYPE is Two) and (AREA is Medium) and (DIAMETER is Small) then (TREATMENT is effective)(1)) |

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## Share and Cite

**MDPI and ACS Style**

Junio Guimarães, A.; Vitor de Campos Souza, P.; Jonathan Silva Araújo, V.; Silva Rezende, T.; Souza Araújo, V.
Pruning Fuzzy Neural Network Applied to the Construction of Expert Systems to Aid in the Diagnosis of the Treatment of Cryotherapy and Immunotherapy. *Big Data Cogn. Comput.* **2019**, *3*, 22.
https://doi.org/10.3390/bdcc3020022

**AMA Style**

Junio Guimarães A, Vitor de Campos Souza P, Jonathan Silva Araújo V, Silva Rezende T, Souza Araújo V.
Pruning Fuzzy Neural Network Applied to the Construction of Expert Systems to Aid in the Diagnosis of the Treatment of Cryotherapy and Immunotherapy. *Big Data and Cognitive Computing*. 2019; 3(2):22.
https://doi.org/10.3390/bdcc3020022

**Chicago/Turabian Style**

Junio Guimarães, Augusto, Paulo Vitor de Campos Souza, Vinícius Jonathan Silva Araújo, Thiago Silva Rezende, and Vanessa Souza Araújo.
2019. "Pruning Fuzzy Neural Network Applied to the Construction of Expert Systems to Aid in the Diagnosis of the Treatment of Cryotherapy and Immunotherapy" *Big Data and Cognitive Computing* 3, no. 2: 22.
https://doi.org/10.3390/bdcc3020022