# Modeling the Vagueness of Areal Geographic Objects: A Categorization System

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## Abstract

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## 1. Introduction

## 2. Modeling Vague Regions from an Ontological Perspective

## 3. A Categorization System for Vague Regions

#### 3.1. Five Categories of Vague Regions

#### 3.1.1. Direct Field-Cutting Objects

#### 3.1.2. Focal Operation-Based Field-Cutting Objects

#### 3.1.3. Element-Clustering Objects

#### 3.1.4. Object-Referenced Objects

#### 3.1.5. Dynamic Boundary Objects

#### 3.2. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MF | Membership function |

DFCO | Direct field-cutting object |

FoFCO | Focal operation based field-cutting object |

ECO | Element-clustering object |

ORO | Object-referenced object |

DBO | Dynamic boundary object |

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**Figure 2.**The dilemma in conceptualizing a woodland. (

**a**) A single tree is clearly not a piece of woodland. (

**b**) A woodland consists of a number of trees with a certain density. (

**c**) Whether a tree belongs to a woodland depends on the distance between this particular tree and other trees.

**Figure 6.**An example of ORO: northern and southern California. (

**a**) Vague regions purely based on spatial relations; (

**b**) Vague cognitive regions using social media data.

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**MDPI and ACS Style**

Liu, Y.; Yuan, Y.; Gao, S.
Modeling the Vagueness of Areal Geographic Objects: A Categorization System. *ISPRS Int. J. Geo-Inf.* **2019**, *8*, 306.
https://doi.org/10.3390/ijgi8070306

**AMA Style**

Liu Y, Yuan Y, Gao S.
Modeling the Vagueness of Areal Geographic Objects: A Categorization System. *ISPRS International Journal of Geo-Information*. 2019; 8(7):306.
https://doi.org/10.3390/ijgi8070306

**Chicago/Turabian Style**

Liu, Yu, Yihong Yuan, and Song Gao.
2019. "Modeling the Vagueness of Areal Geographic Objects: A Categorization System" *ISPRS International Journal of Geo-Information* 8, no. 7: 306.
https://doi.org/10.3390/ijgi8070306