# The Selection of Anchoring System for Floating Houses by Means of AHP Method

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## Abstract

**:**

## 1. Introduction

## 2. Materials

#### 2.1. Mooring Piles

- a sea-bedded pile,
- a clamp surrounding a pile,
- a buffer,

#### 2.2. Booms

- a boom (e.g., a steel pipe),
- a steel cable (a pull cable),
- a loop or a mooring hinge.

#### 2.3. MooringLines

#### 2.4. Deadweight Anchors Using Elastic Connectors

- deadweight anchors,
- rope (the pull cable),
- additional pulling element (e.g., elastic connector).

- homogenous pull cables-chains or lines,
- mixed pull cables—a line joined with a chain or a chain with a thin tape,
- pull cables with weights—e.g., a line with hanging weights,
- pull cables with flotation elements [7].

## 3. Methods

#### 3.1. Methodology

- Prioritizing a problem—the aim of this stage is the detailed description of the problem, identification of the participants, defining the main objective and expectations. Thereafter, a decomposition of the problem is undertaken in the form of the primary objective, the main and partial factors and variants considered, which generate some fulfillment of aims function on particular levels of the hierarchical model. The general structure of the hierarchy is presented in Figure 1.

- The next stage is to enter data received from the judges in the matrix of comparison with pairs A. The general record of matrix A is as follows:

- As a result of the undertaken calculations, weights describing the meaning of a specific element are obtained. The scope of the values of weighting factors is defined by the formula below:

- The last factor is CR (consistency ratio). If the ratio of CI is significantly small, the estimate of w can be accepted. CR is determined by the formula [23]:

- The analysis of the selected results—choosing the best variant, which would address the main objective [23].

#### 3.2. Group Decision Making

- Aggregating individual judgements (AIJ),
- Aggregating individual priorities (AIP).

- identifying a problem,
- the appropriate selection of the participants
- 5 to 10 is recommended,
- designation of a place and length of a session,
- setting a place to carry out a brainstorming session,
- presentation of the rules of the session to the participants—guidance of the session—recommended time—45 min,
- formulation of the results [35].

## 4. Results

#### 4.1. Input Data

#### 4.2. Hierarchy Structure Tree

- Goal: the selection of anchoring system for floating houses;
- Groups of criteria: time (T), cost (C), external risk factors (R), geospatial factors (E);
- Criteria: the construction/completion expenditure C1 (T), the cost of ownership C2 (T), the repair cost C3 (T), the time of designing C4 (C), the time of the constructing/builing C5 (C), the exploitation time C6 (C), the damage C7 (R), the flood C8 (R), the drought C9 (R), the intentional human activity C10 (R), ), the proximity of the water way C11 (G), the depth of the water area C12 (G), the size of the water area C13 (G), the shores’ types C14 (G), the speed of the current C15 (G), the natural waving C16 (G), a type of the ground C17 (G), icing of the water area C18 (G);
- Alternatives: mooring piles, booms, mooring lines, deadweight using elastic connectors [37].

#### 4.3. Comparison Matrices

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Hierarchy structure tree of anchoring Floating Houses applying AHP [37].

**Figure 4.**Indication of the most advantageous mooring system for an Investor using AHP-OS software [38].

Definition | Intensity of Importance |
---|---|

Equal Importance | 1 |

Weak or slight | 2 |

Moderate importance | 3 |

Moderate plus | 4 |

Strong importance | 5 |

Strong plus | 6 |

Very strong or demonstrated importance | 7 |

Very, very strong | 8 |

Extreme importance | 9 |

n | RI | n | RI |
---|---|---|---|

2 3 4 5 6 | 0 0.52 0.89 1.11 1.25 | 7 8 9 10 12 | 1.35 1.40 1.45 1.52 1.54 |

Cost | Time | External Risk f. | Geospatial f. | Priority Vector | |
---|---|---|---|---|---|

Cost | 1 | 4 | 7 | 5 | 0.61434 |

Time | $\frac{1}{4}$ | 1 | 3 | 2 | 0.19717 |

External risk f. | $\frac{1}{7}$ | $\frac{1}{3}$ | 1 | $\frac{1}{2}$ | 0.06988 |

Geospatial f. | $\frac{1}{5}$ | $\frac{1}{2}$ | 2 | 1 | 0.11861 |

CR = 0.01696 |

C—Group | C1 | C2 | C3 | Priority Vector |
---|---|---|---|---|

C1 | 1 | $\frac{1}{3}$ | 3 | 0.24264 |

C2 | 3 | 1 | 7 | 0.66942 |

C3 | $\frac{1}{3}$ | $\frac{1}{7}$ | 1 | 0.08795 |

CR = 0.00675 |

T—Group | C4 | C5 | C6 | Priority Vector |
---|---|---|---|---|

C4 | 1 | $\frac{1}{4}$ | $\frac{1}{8}$ | 0.07325 |

C5 | 4 | 1 | 3 | 0.25596 |

C6 | 8 | $\frac{1}{3}$ | 1 | 0.67079 |

CR = 0.01759 |

R—Group | C7 | C8 | C9 | C10 | Priority Vector |
---|---|---|---|---|---|

C7 | 1 | 6 | 7 | 3 | 0.57255 |

C8 | $\frac{1}{6}$ | 1 | 4 | $\frac{1}{3}$ | 0.11776 |

C9 | $\frac{1}{7}$ | $\frac{1}{4}$ | 1 | $\frac{1}{6}$ | 0.04844 |

C10 | $\frac{1}{3}$ | 3 | 6 | 1 | 0.26126 |

CR = 0.07311 |

G—Group | C11 | C12 | C13 | C14 | C15 | C16 | C17 | C18 | Priority Vector |
---|---|---|---|---|---|---|---|---|---|

C11 | 1 | $\frac{1}{5}$ | $\frac{1}{6}$ | 2 | $\frac{1}{2}$ | $\frac{1}{4}$ | 4 | 3 | 0.06376 |

C12 | 5 | 1 | $\frac{1}{2}$ | 4 | 3 | 2 | 7 | 6 | 0.22049 |

C13 | 6 | 2 | 1 | 7 | 5 | 4 | 9 | 8 | 0.36584 |

C14 | $\frac{1}{2}$ | $\frac{1}{4}$ | $\frac{1}{7}$ | 1 | $\frac{1}{2}$ | $\frac{1}{3}$ | 3 | 2 | 0.04954 |

C15 | 2 | $\frac{1}{3}$ | $\frac{1}{5}$ | 2 | 1 | $\frac{1}{3}$ | 5 | 4 | 0.08962 |

C16 | 4 | $\frac{1}{2}$ | $\frac{1}{4}$ | 3 | 3 | 1 | 6 | 5 | 0.15767 |

C17 | $\frac{1}{4}$ | $\frac{1}{7}$ | $\frac{1}{9}$ | $\frac{1}{3}$ | $\frac{1}{5}$ | $\frac{1}{6}$ | 1 | $\frac{1}{2}$ | 0.02228 |

C18 | $\frac{1}{3}$ | $\frac{1}{6}$ | $\frac{1}{8}$ | $\frac{1}{2}$ | $\frac{1}{4}$ | $\frac{1}{5}$ | 2 | 1 | 0.03080 |

CR = 0.03771 |

C—Group | Mooring Piles | Booms | Mooring Lines | Deadweight Anchors | Priority Vector | Mooring Piles | Booms | Mooring Lines | Deadweight Anchors | Priority Vector |
---|---|---|---|---|---|---|---|---|---|---|

C1—The Construction/Completion Expenditure | C2—The Cost Of Ownership | |||||||||

Mooring Piles | 1 | $\frac{1}{4}$ | $\frac{1}{7}$ | $\frac{1}{2}$ | 0.06288 | 1 | 2 | $\frac{1}{5}$ | 3 | 0.17827 |

Booms | 4 | 1 | $\frac{1}{4}$ | 3 | 0.22956 | $\frac{1}{2}$ | 1 | $\frac{1}{6}$ | 3 | 0.12254 |

Mooring Lines | 7 | 4 | 1 | 5 | 0.60370 | 5 | 6 | 1 | 6 | 0.63435 |

Deadweight Anchors | 2 | $\frac{1}{3}$ | $\frac{1}{5}$ | 1 | 0.10386 | $\frac{1}{3}$ | $\frac{1}{3}$ | $\frac{1}{6}$ | 1 | 0.06483 |

CR = 0.04129 | CR = 0.06644 | |||||||||

C3—The Repair Cost | ||||||||||

Mooring Piles | 1 | $\frac{1}{5}$ | $\frac{1}{6}$ | 3 | 0.09058 | |||||

Booms | 5 | 1 | $\frac{1}{3}$ | 7 | 0.29963 | |||||

Mooring Lines | 6 | 3 | 1 | 8 | 0.56480 | |||||

Deadweight Anchors | $\frac{1}{3}$ | $\frac{1}{7}$ | $\frac{1}{8}$ | 1 | 0.04500 | |||||

CR = 0.07159 |

T—Group | Mooring Piles | Booms | Mooring Lines | Deadweight Anchors | Priority Vector | Mooring Piles | Booms | Mooring Lines | Deadweight Anchors | Priority Vector |
---|---|---|---|---|---|---|---|---|---|---|

C4—The Time of Designing | C5—The Time of The Constructing/Building | |||||||||

Mooring Piles | 1 | $\frac{1}{6}$ | $\frac{1}{7}$ | $\frac{1}{3}$ | 0.04965 | 1 | $\frac{1}{4}$ | $\frac{1}{6}$ | 3 | 0.09461 |

Booms | 6 | 1 | $\frac{1}{4}$ | 4 | 0.26215 | 4 | 1 | $\frac{1}{4}$ | 6 | 0.25207 |

Mooring Lines | 7 | 4 | 1 | 5 | 0.58619 | 6 | 4 | 1 | 8 | 0.60679 |

Deadweight Anchors | 3 | $\frac{1}{4}$ | $\frac{1}{5}$ | 1 | 0.10201 | $\frac{1}{3}$ | $\frac{1}{6}$ | $\frac{1}{8}$ | 1 | 0.04653 |

CR = 0.09430 | CR = 0.07889 | |||||||||

C6—The Exploitation Time | ||||||||||

Mooring Piles | 1 | 8 | 7 | 4 | 0.61074 | |||||

Booms | $\frac{1}{8}$ | 1 | $\frac{1}{3}$ | $\frac{1}{6}$ | 0.04531 | |||||

Mooring Lines | $\frac{1}{7}$ | 3 | 1 | $\frac{1}{5}$ | 0.08437 | |||||

Deadweight Anchors | $\frac{1}{4}$ | 6 | 5 | 1 | 0.25958 | |||||

CR = 0.09759 |

R—Group | Mooring Piles | Booms | Mooring Lines | Deadweight Anchors | Priority Vector | Mooring Piles | Booms | Mooring Lines | Deadweight Anchors | Priority Vector |
---|---|---|---|---|---|---|---|---|---|---|

C7—The Damage | C8—The Flood | |||||||||

Mooring Piles | 1 | 7 | 7 | 4 | 0.61469 | 1 | 7 | 8 | 4 | 0.62046 |

Booms | $\frac{1}{7}$ | 1 | 1 | $\frac{1}{5}$ | 0.06489 | $\frac{1}{7}$ | 1 | 3 | $\frac{1}{4}$ | 0.09186 |

Mooring Lines | $\frac{1}{7}$ | 1 | 1 | $\frac{1}{5}$ | 0.06489 | $\frac{1}{8}$ | $\frac{1}{3}$ | 1 | $\frac{1}{5}$ | 0.04867 |

Deadweight Anchors | $\frac{1}{4}$ | 5 | 5 | 1 | 0.25553 | $\frac{1}{4}$ | 4 | 5 | 1 | 0.23900 |

CR = 0.05274 | CR = 0.07668 | |||||||||

C9—The Drought | C10—The Intentional Human Activity | |||||||||

Mooring Piles | 1 | 6 | 6 | 4 | 0.60434 | 1 | 7 | 8 | 3 | 0.57445 |

Booms | $\frac{1}{6}$ | 1 | 1 | $\frac{1}{4}$ | 0.07612 | $\frac{1}{7}$ | 1 | 4 | $\frac{1}{5}$ | 0.09609 |

Mooring Lines | $\frac{1}{6}$ | 1 | 1 | $\frac{1}{4}$ | 0.07612 | $\frac{1}{8}$ | $\frac{1}{4}$ | 1 | $\frac{1}{6}$ | 0.04382 |

Deadweight Anchors | $\frac{1}{4}$ | 4 | 4 | 1 | 0.24341 | $\frac{1}{3}$ | 5 | 6 | 1 | 0.28564 |

CR = 0.04591 | CR = 0.10222 |

G—Group | Mooring Piles | Booms | Mooring Lines | Deadweight Anchors | Priority Vector | Mooring Piles | Booms | Mooring Lines | Deadweight Anchors | Priority Vector |
---|---|---|---|---|---|---|---|---|---|---|

C11—The Proximity of the Water Area | C12—The Depth of the Water Area | |||||||||

Mooring Piles | 1 | 3 | $\frac{1}{4}$ | 4 | 0.23608 | 1 | $\frac{1}{4}$ | $\frac{1}{4}$ | 1 | 0.1 |

Booms | $\frac{1}{3}$ | 1 | $\frac{1}{4}$ | 4 | 0.13521 | 4 | 1 | 1 | 4 | 0.4 |

Mooring Lines | 4 | 4 | 1 | 7 | 0.57475 | 4 | 1 | 1 | 4 | 0.4 |

Deadweight Anchors | $\frac{1}{4}$ | $\frac{1}{4}$ | $\frac{1}{7}$ | 1 | 0.05397 | 1 | $\frac{1}{4}$ | $\frac{1}{4}$ | 1 | 0.1 |

CR = 0.09037 | CR = 0.00000 | |||||||||

C13—The Size of the Water Area | C14—The Shores’ Type | |||||||||

Mooring Piles | 1 | 3 | 1 | 5 | 0.38986 | 1 | 6 | 8 | 4 | 0.60006 |

Booms | $\frac{1}{3}$ | 1 | $\frac{1}{3}$ | 3 | 0.15235 | $\frac{1}{6}$ | 1 | 3 | $\frac{1}{5}$ | 0.08876 |

Mooring Lines | 1 | 3 | 1 | 5 | 0.38986 | $\frac{1}{8}$ | $\frac{1}{3}$ | 1 | $\frac{1}{6}$ | 0.04558 |

Deadweight Anchors | $\frac{1}{5}$ | $\frac{1}{3}$ | $\frac{1}{5}$ | 1 | 0.06792 | $\frac{1}{4}$ | 5 | 6 | 1 | 0.26559 |

CR = 0.01629 | CR = 0.09951 | |||||||||

C15—The Speed of the Current | C16—The Natural Waving | |||||||||

Mooring Piles | 1 | 4 | 2 | 6 | 0.48521 | 1 | 5 | 6 | 4 | 0.59122 |

Booms | $\frac{1}{4}$ | 1 | $\frac{1}{4}$ | 3 | 0.12311 | $\frac{1}{5}$ | 1 | $\frac{1}{2}$ | $\frac{1}{3}$ | 0.07614 |

Mooring Lines | $\frac{1}{2}$ | 4 | 1 | 5 | 0.33147 | $\frac{1}{6}$ | 2 | 1 | $\frac{1}{4}$ | 0.09625 |

Deadweight Anchors | $\frac{1}{6}$ | $\frac{1}{3}$ | $\frac{1}{5}$ | 1 | 0.06021 | $\frac{1}{4}$ | $3$ | 4 | 1 | 0.23640 |

CR = 0.04708 | CR = 0.08240 | |||||||||

C17—The Type of the Ground | C18—Icing of the Water Area | |||||||||

Mooring Piles | 1 | $\frac{1}{7}$ | $\frac{1}{7}$ | $\frac{1}{4}$ | 0.04721 | 1 | 3 | $\frac{1}{6}$ | $\frac{1}{4}$ | 0.09675 |

Booms | 7 | 1 | 1 | 5 | 0.41961 | $\frac{1}{3}$ | 1 | $\frac{1}{8}$ | $\frac{1}{5}$ | 0.04910 |

Mooring Lines | 7 | 1 | 1 | 5 | 0.41961 | 6 | 8 | 1 | 4 | 0.60928 |

Deadweight Anchors | 4 | $\frac{1}{5}$ | $\frac{1}{5}$ | 1 | 0.11357 | 4 | 5 | $\frac{1}{4}$ | 1 | 0.24487 |

CR = 0.05274 | CR = 0.07681 |

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**MDPI and ACS Style**

Miszewska, E.; Niedostatkiewicz, M.; Wiśniewski, R.
The Selection of Anchoring System for Floating Houses by Means of AHP Method. *Buildings* **2020**, *10*, 75.
https://doi.org/10.3390/buildings10040075

**AMA Style**

Miszewska E, Niedostatkiewicz M, Wiśniewski R.
The Selection of Anchoring System for Floating Houses by Means of AHP Method. *Buildings*. 2020; 10(4):75.
https://doi.org/10.3390/buildings10040075

**Chicago/Turabian Style**

Miszewska, Emilia, Maciej Niedostatkiewicz, and Radosław Wiśniewski.
2020. "The Selection of Anchoring System for Floating Houses by Means of AHP Method" *Buildings* 10, no. 4: 75.
https://doi.org/10.3390/buildings10040075