# Review of Recent Type-2 Fuzzy Image Processing Applications

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## Abstract

**:**

## 1. Introduction

## 2. Type-2 Fuzzy Sets

## 3. Type-2 Fuzzy Logic Applied on Image Processing

#### 3.1. T2 FS in Image Segmentation

#### Summary

#### 3.2. T2 FS in Image Filtering

#### Summary

#### 3.3. T2 FS in Edge Detection

#### Summary

#### 3.4. T2 FS in Image Classification

#### Summary

## 4. General Overview and Future Trend

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**Pie chart showing the distribution of existing publications in the areas of focus for this paper.

**Figure 4.**Pie chart showing the distribution of received combined citations in the areas of focus for this review paper.

Fuzzy Set Type | Representation |
---|---|

IT2 FS | $A=\left\{\left(\left(x,u\right),{\mu}_{A}\left(x,u\right)=1\right)|\forall x\in X,\forall u\in \left[0,1\right]\right\}$ |

GT2 FS | $\tilde{A}=\left\{\left(\left(x,u\right),{\mu}_{\tilde{A}}\left(x,u\right)\right)|\forall x\in X,\forall u\in \left[0,1\right]\right\}$ where $X$ is the universe for the primary variable of $\tilde{A}$, $x$. The 3D membership function is usually denoted by ${\mu}_{\tilde{A}}\left(x,u\right)$, where $x\text{}\u03f5\text{}X$ and $\mathrm{u}\text{}\u03f5\text{}U\subseteq \left[0,1\right]$ and $0\le {\mu}_{\tilde{A}}\left(x,u\right)\le 1$. |

Fuzzy Set Type | FOU Representation | Description |
---|---|---|

IT2 FS | $FOU\left(A\right)={{\displaystyle \cup}}_{\forall x\in X}[{\underset{\_}{\mu}}_{A}\left(x\right),{\overline{\mu}}_{A}\left(x\right)]$ | Upper membership function (UMF) is associated with the upper bound of the FOU$\left(A\right)$ and is denoted by ${\overline{\mu}}_{A}\left(x\right),\forall x\in X$. The lower membership function (LMF) is associated with the lower bound of the FOU$\left(A\right)$ and is denoted by ${\underset{\_}{\mu}}_{A}\left(x\right)$. |

GT2 FS | $FOU(\tilde{A})=\left\{\left(x,u\right)\in X\times \left[0,1\right]{\mu}_{\tilde{A}}\left(x,u\right)>0\right\}$ | The FOU of $(\tilde{A})$ is the 2D support of ${\mu}_{\tilde{\tilde{A}}}\left(\mathrm{x},\mathrm{u}\right)$ and represents uncertainty in the primary membership function of a GT2 FS. |

**Table 3.**Relation between number of combined citations and number of publications per research area.

Area | Number of Combined Citations | Number of Publications |
---|---|---|

Classification | 73 | 3 |

Filter | 306 | 5 |

Edge detection | 157 | 7 |

Segmentation | 88 | 20 |

Edge Detection | Number of Recurring Publications |
---|---|

Melin P. | 5 |

Mendoza O. | 5 |

Castillo O. | 4 |

Castro J.R. | 3 |

Gonzalez C.I. | 3 |

Segmentation | Number of Recurring Publications |
---|---|

Fnaiech F. | 2 |

Han L. | 2 |

Manimegalai D. | 2 |

Murugeswari P. | 2 |

Qiu C. | 2 |

Sayadi M. | 2 |

Shi J. | 2 |

Tlig L. | 2 |

Turksen I.B. | 2 |

Xiao J. | 2 |

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**MDPI and ACS Style**

Castillo, O.; Sanchez, M.A.; Gonzalez, C.I.; Martinez, G.E.
Review of Recent Type-2 Fuzzy Image Processing Applications. *Information* **2017**, *8*, 97.
https://doi.org/10.3390/info8030097

**AMA Style**

Castillo O, Sanchez MA, Gonzalez CI, Martinez GE.
Review of Recent Type-2 Fuzzy Image Processing Applications. *Information*. 2017; 8(3):97.
https://doi.org/10.3390/info8030097

**Chicago/Turabian Style**

Castillo, Oscar, Mauricio A. Sanchez, Claudia I. Gonzalez, and Gabriela E. Martinez.
2017. "Review of Recent Type-2 Fuzzy Image Processing Applications" *Information* 8, no. 3: 97.
https://doi.org/10.3390/info8030097