# Using Resistin, Glucose, Age and BMI and Pruning Fuzzy Neural Network for the Construction of Expert Systems in the Prediction of Breast Cancer

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Reference

#### 2.1. Breast Cancer

#### 2.2. Artificial Neural Networks

#### 2.3. Fuzzy Systems

#### 2.4. Fuzzy Logic Neurons

**X**x

**W**– [0,1] [34].

- Transform each pair (${a}_{i},{w}_{i}$) 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 input.

#### 2.5. Related Work

## 3. Fuzzy Neural Network for Detection of Breast Cancer

#### Neural Network Neural Network Architecture and Training for Binary Classification Problems

**y**is 1, just as if v1 and v2 were large, the class of

**y**is 2. Within this fuzzy rule model, v1 and v2 by elements of a cancer research base and responses 1 and two by people with cancer and people without cancer. In this context one can apply, for example, the value of v1 a dimension as age and v2 as the BMI of women. However, as described in [7], the database groupings were made from rules of statistical membership, and the final results of the classifier tests did not calculate the test accuracy and the interpretability of the results, highlighting only the value AUC, specificity and sensibility.

**z**. To determine which elements will be selected within this approach, the criterion will be adopted in [62] and replicated in the where the ${s}_{j}$ variables are smaller than theaverage of all the f-scores found. This approach willallow a choice of the most significant neurons (candidate neurons) (${L}_{s}$) participating in the fuzzy neural network response [20].

**v**= [${v}_{0},{v}_{1},{v}_{2},\dots ,{v}_{Ls}$] is the weight vector of the output layer and

**z**(${x}_{i}$) = [${z}_{0},{z}_{1}\left({x}_{i}\right),{z}_{2}\left({x}_{i}\right)\dots {z}_{Ls}({x}_{i}$)] the output vector of the second layer, for ${z}_{0}$ = 1 and sign is a step function that transforms values greater than zero into 1 and values smaller than zero into −1. In this context,

**z**(${x}_{i}$) is considered as the non-linear mapping of the input space for a space of fuzzy characteristics of dimension ${L}_{s}$ [20]. The learning algorithm has only to estimate the output layer vector

**v**= [${v}_{0},{v}_{1},{v}_{2}\dots {v}_{L}{]}^{T}$ which best adjustment the wanted output. In this paper these parameters are computed using the Moore-Penrose pseudo-inverse [64]:

**z**, which is the minimum norm of the least squares solution for the output weights.

- the number of membership functions, M;
- the type of fuzzy logic neuron, unineuron, andneuron or orneuron;

Algorithm 1: 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 or Triangular membership functions constructed with center and $\sigma $ values derived from ANFIS (Using genfis1 approach). (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 (${L}_{s}$). (7) For all K input do(7.1) Calculate the mapping ${z}_{k}\left({x}_{k}\right)$ using logical neurons end for(8) Estimate the weights of the output layer using Equation (6). (9) Calculate output y using Equation (5). |

## 4. Patient Classification Tests Using Fuzzy Neural Network

#### 4.1. Dabase on Breast Cancer Prediction Research

- V1 = Glucose
- V2 = Resistin
- V3 = Age
- V4 = BMI − body mass
- V5 = HOMA − evaluation of the homeostasis model for insulin resistance
- V6 = Leptin
- V7 = Insulin
- V8 = Adiponectin
- V9 = MCP-1 − monocyte-1 chemotactic protein.

#### 4.2. Test Configuration

#### 4.3. Patient Classification Tests

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

FNN | Fuzzy Neural Network |

AUC | Area Under Curve |

UNI | unineuron |

AND | andneuron |

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**Figure 1.**Breast cancer [29].

**Figure 2.**Artificial neural network of multiple layers and outputs [31].

**Figure 3.**Concepts present in fuzzy logic [33].

**Figure 5.**Structure of the fuzzy neural network used in the paper [78].

Models | Accuracy | AUC | Sensitivity | Specificity | Time |
---|---|---|---|---|---|

AndNet | 80.01 (6.98) | 0.8052 (0.1011) | 0.7841 (0.1124) | 0.7905 (0.1003) | 1.94 (0.03) |

OrNet | 81.04 (4.85) | 0.8019 (0.0918) | 0.8193 (0.1024) | 0.8118 (0.1203) | 1.89 (0.02) |

UniNet | 78.49 (4.97) | 0.7624 (0.1207) | 0.8248 (0.1412) | 0.7105 (0.0311) | 2.19 (0.06) |

MLP | 73.80 (11.38) | 0.7409 (0.1206) | 0.4187 (0.2102) | 0.7803 (0.1018) | 15.62 (6.04) |

J48 | 71.83 (14.27) | 0.7114 (0.1243) | 0.5276 (0.1206) | 0.7895 (0.1032) | 0.78 (0.01) |

NB | 69.71 (12.61) | 0.6925 (0.1213) | 0.3687 (0.1786) | 0.7112 (0.2142) | 15.22 (0.76) |

ZR | 55.15 (3.10) | 0.5004 (0.0012) | 0.5500 (0.0021) | 0.5500 (0.0016) | 7.12 (0.43) |

RT | 79.67 (11.67) | 0.7421 (0.1120) | 0.5301 (0.1703) | 0.8718 (0.0613) | 8.21 (0.01) |

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## Share and Cite

**MDPI and ACS Style**

Silva Araújo, V.J.; Guimarães, A.J.; de Campos Souza, P.V.; Rezende, T.S.; Araújo, V.S. Using Resistin, Glucose, Age and BMI and Pruning Fuzzy Neural Network for the Construction of Expert Systems in the Prediction of Breast Cancer. *Mach. Learn. Knowl. Extr.* **2019**, *1*, 466-482.
https://doi.org/10.3390/make1010028

**AMA Style**

Silva Araújo VJ, Guimarães AJ, de Campos Souza PV, Rezende TS, Araújo VS. Using Resistin, Glucose, Age and BMI and Pruning Fuzzy Neural Network for the Construction of Expert Systems in the Prediction of Breast Cancer. *Machine Learning and Knowledge Extraction*. 2019; 1(1):466-482.
https://doi.org/10.3390/make1010028

**Chicago/Turabian Style**

Silva Araújo, Vinícius Jonathan, Augusto Junio Guimarães, Paulo Vitor de Campos Souza, Thiago Silva Rezende, and Vanessa Souza Araújo. 2019. "Using Resistin, Glucose, Age and BMI and Pruning Fuzzy Neural Network for the Construction of Expert Systems in the Prediction of Breast Cancer" *Machine Learning and Knowledge Extraction* 1, no. 1: 466-482.
https://doi.org/10.3390/make1010028