# Using Fuzzy Logic to Analyze the Spatial Distribution of Pottery in Unstratified Archaeological Sites: The Case of the Pobedim Hillfort (Slovakia)

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Site Description—Pobedim Hillfort

#### 2.2. Fieldwork Methodology

#### 2.3. Fuzzy Sets

#### 2.4. Analytical Workflow

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- Field data collection during the archaeological research.
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- 3D modeling of the depths of all archeological finds using the ArcScene 10.2.2 software (Figure 5). This particular visualization represents the maximum depth in each individual excavation pit. In this study, 3D models were used for visualization purposes only in order for the reader to have a better idea of the depths of the individual excavation pits.
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- Vectorization of data collected in the field using ArcGIS 10.2.2 software.
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- Classification of the occurrence of pottery finds and their quantity in specific depth layers, using five intervals (Table 1). Due to the number of excavation pits in individual squares, the interval sorting was not performed since the maximum number of excavation pits in one square was three. Since clusters of archaeological finds (pottery) were created on the basis of two observed criteria (existence of pottery finds and their quantity in specific depth layers), there will be 25 possible combinations (clusters) when using classical statistical methods. If we limit the number of clusters, i.e., they will be determined in advance, those features that will not meet the required criteria will not be classified at all. However, the use of fuzzy set methods allowed us, based on the use of a membership function, to include also those features in the cluster that met the given attribute only to the required level. In this case, the value of 0.9 was used, as mentioned also later.
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- Conversion of the vector layers to raster layers using the Feature to Raster tool for further raster analysis in ArcGIS. The reason for converting vector to raster layers is that fuzzy tools, which are mentioned in the next step, work only with raster data.
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- Use of fuzzy set theory methods in ArcGIS, specifically the Fuzzy Membership tool (Linear function) and the Fuzzy Overlay tool (gamma operator) to obtain fuzzy clusters.

#### 2.5. Fuzzy Membership (Linear Function)

#### 2.6. Fuzzy Overlay (Gamma Operator)

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Reconstruction of the watchtower according to Bialeková [1].

**Figure 3.**LiDAR visualization of the former Pobedim hillfort using CloudCompare 2.12 software (Source of products LLS: Geodesy, Cartography and Cadastre Authority of the Slovak Republic). The study site is currently covered by the arable land.

**Figure 7.**Comparison of results using the fuzzy overlay method (gamma operator equals 0.9) and spatial autocorrelation method (as presented by Vojteková et al. [22]).

Depth Intervals | Number of Pottery Fragments in Interval |
---|---|

<30 cm | <70 |

31–60 cm | 71–140 |

61–90 cm | 141–210 |

91–120 cm | 211–280 |

>121 cm | >281 |

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**MDPI and ACS Style**

Tirpáková, A.; Vojteková, J.; Vojtek, M.; Vlkolinská, I. Using Fuzzy Logic to Analyze the Spatial Distribution of Pottery in Unstratified Archaeological Sites: The Case of the Pobedim Hillfort (Slovakia). *Land* **2021**, *10*, 103.
https://doi.org/10.3390/land10020103

**AMA Style**

Tirpáková A, Vojteková J, Vojtek M, Vlkolinská I. Using Fuzzy Logic to Analyze the Spatial Distribution of Pottery in Unstratified Archaeological Sites: The Case of the Pobedim Hillfort (Slovakia). *Land*. 2021; 10(2):103.
https://doi.org/10.3390/land10020103

**Chicago/Turabian Style**

Tirpáková, Anna, Jana Vojteková, Matej Vojtek, and Ivona Vlkolinská. 2021. "Using Fuzzy Logic to Analyze the Spatial Distribution of Pottery in Unstratified Archaeological Sites: The Case of the Pobedim Hillfort (Slovakia)" *Land* 10, no. 2: 103.
https://doi.org/10.3390/land10020103