# A Spatial Multi-Criteria Model for the Evaluation of Land Redistribution Plans

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

**Figure 1.**General model of multi-attribute decision-making method (MADM) (adapted from Sharifi et al. [31]).

#### 2.1. Evaluation Criteria

#### 2.1.1. Parcel Concentration Coefficient (PCC)

_{hmc}and y

_{hmc}are the co-ordinates of the mean center of the holding; x

_{i}and y

_{i}are the co-ordinates of the centroid of parcel i; and n is the number of parcels belonging to a holding. The weighted mean center of a holding can be calculated in a similar way as:

_{whmc}and y

_{whmc}are the co-ordinates of the weighted mean center of the holding and w

_{i}is the weight of each parcel i. From these quantities, the dispersion of parcels (DoP) and the weighted version of DoP can be calculated as:

_{b}) and after (DoP

_{a}) land consolidation and then combined to calculate the PCC for three situations:

- If DoP
_{b}= DoP_{a}then PCC = 0 and the dispersion of parcels has not changed.In this situation, land consolidation has not achieved any concentration of parcels for the holding concerned independently of the number of new parcels allocated to a landowner (n') or the number of original parcels owned by the landowner (n). - If DoP
_{b}> DoP_{a}the PCC can be expressed as:In this situation, an improvement in the dispersion of parcels has occurred. The maximum value of 1 means that parcels have been concentrated after land consolidation into a single parcel, i.e., n' = 1 and perfect concentration has been achieved. This happens when the DoP_{a}equals 0 and consequently n' = 1. The numerator in Equation (5) represents the proportional change of dispersion before and after land consolidation of a holding. The denominator, i.e., n', adjusts the proportional change in dispersion (the level of concentration) since the PCC increases as n' decreases. In other words, the higher n', the less the concentration of new parcels and hence PCC reduces towards a value of zero. - If DoP
_{b}< DoP_{a}, then the PCC is expressed as:

_{b}equals 0 and consequently n = 1. The denominator n adjusts the proportional change in dispersion, i.e., the level of concentration, since the PCC increases as n increases. In other words, the greater the value of n, the less extreme the difference (before and after a project) in parcel concentration and hence PCC reduces towards zero because the dispersion was already poor.

#### 2.1.2. Landowner Satisfaction Rate (LSR)

_{i}is a variable that takes into account the number of parcels originally owned by a landowner (n) and the rank order of the preference of each original parcel i (RO

_{i}), and P is a linear function that expresses decreasing satisfaction for each landowner. The two variables, m

_{i}and P are computed as follows:

_{mi}is the m

_{i}value assigned to those new parcels that fall in the first part of original parcels as explained earlier. In this case, the parameter RO

_{i}in Equation (8) is replaced by the number of new parcels (n') as follows:

Number of New Parcels (n') Allocated to the Landowner | |||
---|---|---|---|

n | 1 | 2 | 3 |

1 | maxM × P = 5× 20 = 100% | maxM × P = 4× 25 = 100% | maxM × P = 3× 33.33 = 100% |

2 | M2 × P =(5 – 2 + 1)× 20 = 80% | maxM × P = 4× 25 = 100% | maxM × P = 3× 33.33 = 100% |

3 | M3 × P = (5 – 3 + 1)× 20 = 60% | M3 × P = (5 – 3 +1 )× 25 = 75% | maxM × P = 3× 33.33 = 100% |

4 | M4 × P = (5 – 4 + 1)× 20 = 40% | M4 × P = (5 – 4 + 1)× 25 = 50% | M4 × P = (5 – 4 + 1)× 33.33 = 66.66% |

5 | M5 × P = (5 – 5 + 1)× 20 = 20% | M5 × P = (5 − 5 + 1)× 25 = 25% | M5 × P = (5 – 5 + 1)× 33.33 = 33.33% |

#### 2.2. Weighting the Criteria

Rank Order | Scale of Importance | Score | Classes |
---|---|---|---|

1 | Extremely high | 100 | Upper |

2 | Very high | 80 | |

3 | High | 60 | |

4 | Intermediate | 40 | Middle |

5 | Moderate | 30 | Lower |

6 | Low | 20 | |

7 | Very low | 10 |

#### 2.3. Standardization Process

- Identify the minimum and maximum values of the criterion which correspond to values of 0 (worst) and 1 (best), respectively. In the context of this research, the minimum and maximum values for criteria C1, C3 and C4 were identified from 40 year statistical records provided by the Land Consolidation Department (LCD) of Cyprus for 74 land consolidation projects. For criteria C2 and C5, the minimum values are zero and the maximum values are 1 and 100%, respectively.
- Define characteristics of the value function, i.e., monotonicity, shape, etc.
- Assign values to selected criterion scores at equal intervals between the minimum and maximum.
- Fit a mathematical equation through these points using appropriate software.
- Validate the functions as representations of preference.

#### 2.4. Ranking the Alternatives

_{j}is the overall value (or performance score) of the jth alternative (j = 1 to M), v

_{ij}is the standardized value of the score α

_{ij}of the jth alternative with respect to the ith criterion/attribute (i = 1 to N) measured by utilizing an appropriate value function, and w

_{i}is the normalized weight for criterion/attribute i such that:

_{j}is the best alternative compared with the other competitive alternative solutions.

#### 2.5. Sensitivity Analysis

## 3. Case Study

^{2}) for the land consolidation area as set by legislation (F1); the minimum size limit (in m

^{2}) of the holding for a landowner to receive a parcel in the new plan as set by the Committee (F2); the minimum land value limit (in monetary values) of the holding for a landowner to receive a parcel in the new plan as set by the Committee (F3); the lower limit (in m

^{2}) of a small holding size (F4); the upper limit (in m

^{2}) of a small holding size (F5); the lower limit (in m

^{2}) of a medium holding size (F6); the upper limit (in m

^{2}) of a medium holding size (F7); the lower limit (in m

^{2}) of a large holding size (F8); the weight attached to the parcel area for the calculation of the parcel priority index(PPI ) (F9); the weight attached to the parcel land value for the calculation of the PPI (F10); and the minimum residual area limit (in m

^{2}) for the creation of a new parcel for those landowners who receive more than one parcel (F11). Each alternative is described briefly in Table 3 by comparing the facts with those of alternative 1, i.e., the solution given by the experts.

Alternative | Description |
---|---|

A1 | Experts solution (Irrigated project) |

A2 | Medium area and land value minimum limits |

A3 | High area and land value minimum limits |

A4 | Unequal PPI weights for area and land value |

A5 | Low small-medium-large holdings sizes |

A6 | High minimum area of new parcels with high area and land value minimum limits |

A7 | Low minimum area of new parcels with high area and land value minimum limits |

A8 | Low area and land value minimum limits with low small-medium-large holdings sizes |

A9 | Inverse unequal PPI weights for area and land value (comparing to alt-4) |

A10 | Arid project |

#### 3.1. Evaluating Alternatives: Scenario I

#### 3.1.1. Ranking Alternatives

**Table 4.**The performance score and the ranking order of each alternative for four weighting scenarios.

Case 1 | Case 2 | Case 3 | Case 4 | |||||
---|---|---|---|---|---|---|---|---|

Ranking | Alternative | Score | Alternative | Score | Alternative | Score | Alternative | Score |

1 | A3 | 0.823 | A10 | 0.791 | A3 | 0.875 | A10 | 0.797 |

2 | A2 | 0.820 | A3 | 0.765 | A2 | 0.873 | A3 | 0.789 |

3 | A4 | 0.809 | A2 | 0.761 | A9 | 0.863 | A2 | 0.784 |

4 | A9 | 0.809 | A4 | 0.751 | A4 | 0.863 | A4 | 0.775 |

5 | A1 | 0.808 | A9 | 0.749 | A1 | 0.862 | A9 | 0.774 |

6 | A10 | 0.804 | A1 | 0.749 | A5 | 0.839 | A1 | 0.773 |

7 | A5 | 0.787 | A5 | 0.729 | A7 | 0.818 | A5 | 0.750 |

8 | A6 | 0.737 | A6 | 0.652 | A6 | 0.816 | A6 | 0.695 |

9 | A7 | 0.735 | A7 | 0.646 | A10 | 0.815 | A7 | 0.690 |

10 | A8 | 0.647 | A8 | 0.555 | A8 | 0.734 | A8 | 0.612 |

#### 3.1.2. Sensitivity Analysis

Criteria | Case 1 | Case 2 | Case 3 | Case 4 | ||||
---|---|---|---|---|---|---|---|---|

SensC | Weight | SensC | Weight | SensC | Weight | SensC | Weight | |

C1 | 0.081 | 0.200 | 0.025 | 0.323 | 0.382 | 0.097 | 0.068 | 0.294 |

C2 | 0.028 | 0.200 | 0.006 | 0.258 | 0.241 | 0.129 | 0.016 | 0.176 |

C3 | 0.077 | 0.200 | 0.018 | 0.194 | 0.096 | 0.194 | 0.024 | 0.176 |

C4 | 0.068 | 0.200 | 0.010 | 0.129 | 0.196 | 0.258 | 0.024 | 0.118 |

C5 | 0.032 | 0.200 | 0.035 | 0.097 | 0.341 | 0.323 | 0.026 | 0.235 |

Case 1 | Case 2 | Case 3 | Case 4 | |
---|---|---|---|---|

Percent top critical criterion | C1 | C1 | C4 | C1 |

Percent any critical criterion | C1 | C5 | C1 | C1 |

Most critical alternative | A9 | A9 | A4 | A1 |

#### 3.2. Evaluating Alternatives: Scenario II

Scenario 1 | Scenario 2 | |||
---|---|---|---|---|

Ranking | Alternative | Score | Alternative | Score |

1 | A10 | 0.750 | A3 | 0.951 |

2 | A3 | 0.631 | A2 | 0.950 |

3 | A2 | 0.625 | A9 | 0.934 |

4 | A4 | 0.624 | A1 | 0.933 |

5 | A1 | 0.621 | A4 | 0.933 |

6 | A9 | 0.620 | A5 | 0.916 |

7 | A5 | 0.593 | A6 | 0.913 |

8 | A6 | 0.472 | A7 | 0.912 |

9 | A7 | 0.471 | A8 | 0.843 |

10 | A8 | 0.352 | A10 | 0.839 |

## 4. Conclusions

## References

- King, R.; Burton, S. Land fragmentation: Notes on a fundamental rural spatial problem. Prog. Hum. Geogr.
**1982**, 6, 475–494. [Google Scholar] [CrossRef] - FAO, The Design of Land Consolidation Pilot Projects in Central and Eastern Europe; FAO-Land Tenure Studies: Rome, Italy, 2003.
- FAO, Opportunities to Mainstream Land Consolidation in Rural Development Programmes of the European Union; FAO-Land Tenure Policy Series: Rome, Italy, 2008.
- Vitikainen, A. An overview of land consolidation in Europe. Nordic J. Surv. Real Estate Res.
**2004**, 1, 25–43. [Google Scholar] - Demetriou, D.; Stillwell, J.; See, L. Land consolidation in Cyprus: Why is an integrated planning and decision support system required? Land Use Policy
**2012**, 29, 131–142. [Google Scholar] [CrossRef] - Demetriou, D.; Stillwell, J.; See, L. An integrated planning and decision support system (IPDSS) for land consolidation: Theoretical framework and application of the land redistribution modules. Environ. Plan. B-Plan. Design
**2012**, 39, 609–628. [Google Scholar] - Demetriou, D.; Stillwell, J.; See, L. A new methodology for measuring land fragmentation. Comput. Environ. Urban Syst.
**2012**. [Google Scholar] - Demetriou, D.; Stillwell, J.; See, L. LandSpaCES: A Spatial Expert System for Land Consolidation. In Advancing Geoinformation Science for a Changing World; Geertman, S., Reinhardt, W., Toppen, F., Eds.; Springer-Verlag: Berlin/Heidelberg, Germany, 2011; pp. 249–274. [Google Scholar]
- Demetriou, D.; Stillwell, J.; See, L. LandParcelS: A Module for Automated Land Partitioning. Available online: http://www.geog.leeds.ac.uk/fileadmin/downloads/school/research/wpapers/12-02.pdf (accessed on 25 April 2012).
- Miranda, D.; Crecente, R. Suitability Model for Land Consolidation Projects: A Case Study in Galicia, Spain. In Proceedings of the Symposium on Modern Land Consolidation, Clermont-Ferrand, France, 10-11 September 2004.
- Zou, X.; Luo, M.; Su, W.; Li, D.; Jiang, Y.; Ju, Z.; Wang, J. Spatial decision support system for the potential evaluation of land consolidation projects. WSEAS Trans. Comput.
**2008**, 7, 887–898. [Google Scholar] - Thapa, G.; Niroula, G. Alternative options of land consolidation in the mountains of Nepal: An analysis based on stakeholders’ opinions. Land Use Policy
**2008**, 25, 338–350. [Google Scholar] [CrossRef] - Janssen, R.; Rietveld, P. Multicriteria evaluation of land reallotment plans: A case study. Environ. Plan. A
**1985**, 17, 1653–1668. [Google Scholar] - Huylenbroeck, G.; Coelho, J.; Pinto, P. Evaluation of land consolidation projects (LCPs): A multidisciplinary approach. J. Rural Stud.
**1996**, 12, 297–310. [Google Scholar] [CrossRef] - Coelho, C.; Pinto, PA.; Silva, M. A systems approach for the estimation of the effects of land consolidation projects (LCPs): A module and its application. Agr. Syst.
**2001**, 68, 179–195. [Google Scholar] [CrossRef] - Crecente, R.; Alvarez, C.; Fra, U. Economic, social and environmental impact of land consolidation in Galicia. Land Use Policy
**2002**, 19, 135–147. [Google Scholar] [CrossRef] - Miranda, D.; Crecente, R.; Alvarez, M.F. Land consolidation in inland rural Galicia, N.W. Spain, since 1950: An example of the formulation and the use of questions, criteria and indicators for the evaluation of rural development policies. Land Use Policy
**2006**, 23, 511–520. [Google Scholar] [CrossRef] - Sklenicka, P. Applying evaluation criteria for the land consolidation effect to three contrasting study areas in the Czech Republic. Land Use Policy
**2006**, 23, 502–510. [Google Scholar] [CrossRef] - Tourino, J.; Boullon, M.; Gonzalez, X. A GIS-embedded system to support land consolidation plans in Galicia. Int. J. Geogr. Inf. Sci.
**2003**, 17, 377–396. [Google Scholar] [CrossRef] - Gonzalez, X.P.; Alvarez, C.J.; Crecente, R. Evaluation of land distributions with joint regard to plot size and shape. Agr. Syst.
**2004**, 82, 31–43. [Google Scholar] [CrossRef] - Gonzalez, X.P.; Marey, M.F.; Alvarez, C.J. Evaluation of productive rural land patterns with joint regard to the size, shape and dispersion of plots. Agr. Syst.
**2007**, 92, 52–62. [Google Scholar] [CrossRef] - Aslan, T.; Gundogdu, K.; Arici, I. Some metric indices for the assessment of land consolidation projects. Pakistan J. Bio. Sci.
**2007**, 10, 1390–1397. [Google Scholar] [CrossRef] - Malczewski, J. GIS and Multicriteria Decision Analysis; John Wiley & Sons, Inc.: New York, NY, USA, 1999. [Google Scholar]
- Malczewski, J. GIS-based multicriteria decision analysis: a survey of the literature. Int. J. Geogr. Inf. Sci.
**2006**, 20, 703–726. [Google Scholar] [CrossRef] - Zeiler, M. Exploring ArcObjects. Vol. I-Applications and Cartography; ESRI Press: Redlands, CA, USA, 2001. [Google Scholar]
- Zeiler, M. Exploring ArcObjects. Vol. II-Geographic Data Management; ESRI Press: Redlands, CA, USA, 2001. [Google Scholar]
- Al-Shalabi, M.; Mansor, S.; Ahmed, N; Shiriff, R. GIS Based Multicriteria Approaches to Housing Site Suitability Assessment. In Proceedings of the XXIII FIG (International Federation of Surveyors) Congress, Munich, Germany, 8-13 October 2006.
- Carver, J. Integrating multicriteria evaluation with geographical information systems. Int.J. Geogr. Inf. Syst.
**1991**, 5, 321–339. [Google Scholar] [CrossRef] - Giupponi, C.; Mysiak, J.; Fassio, A. Mulino DSS. User’s Guide; Fondazione Eni Enrico Mattei : Venice, Italy, 2004. [Google Scholar]
- Jankowski, P. Integrating geographical information systems and multiple criteria decision making methods. Int. J. Geogr. Inf. Syst.
**1995**, 9, 251–273. [Google Scholar] [CrossRef] - Sharifi, A.; Herwijnen, M.; Toorn, W. Spatial Decision Support Systems, Lecture Notes; ITC,International Institute for Geo-Information Science and Earth Observation: Enschede, The Netherlands, 2004. [Google Scholar]
- Demetriou, D.; Stillwell, J.; See, L. A Multi-Attribute Decision-Making Module for the Evaluation of Alternative Land Consolidation Plans. Available online: http://www.geog.leeds.ac.uk/fileadmin/downloads/school/research/wpapers/11-02.pdf (accessed on 25 April 2012).
- Ebdon, D. Statistics in Geography; Replika Press: Kundli, India, 1985. [Google Scholar]
- Wong, D.; Lee, J. Statistical analysis of Geographic Information: With ArcView and ArcGIS; Wiley: Hopoken, NJ, USA, 2005. [Google Scholar]
- Beinat, E. Value Functions for Environmental Management; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1997. [Google Scholar]
- Steele, K.; Carmel, Y.; Cross, J.; Wilcox, C. Uses and misuses of multicriteria decision analysis (MCDA) in environmental decision making. Risk Anal.
**2009**, 29, 26–33. [Google Scholar] [CrossRef] - Malczewski, J. Local weighted linear combination. Trans. GIS
**2011**, 15, 439–455. [Google Scholar] [CrossRef] - Chakhar, S.; Mousseau, V. GIS-based multicriteria spatial modeling generic framework. Int. J. Geogr. Inf. Sci.
**2008**, 22, 1159–1196. [Google Scholar] [CrossRef] - Triantaphyllou, E. A sensitivity analysis approach for some deterministic multi-criteria decision making methods. Decision Sci.
**1997**, 28, 151–194. [Google Scholar] [CrossRef] - Delgado, M.G.; Sendra, J.B. Sensitivity analysis in multicriteria spatial decision making: A review. Hum. Ecol. Risk Assessment
**2004**, 10, 1173–1187. [Google Scholar] [CrossRef] - Triantaphyllou, E. Multi-Criteria Decision Making Methods: A Comparative Study; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2000. [Google Scholar]
- Jankowski, P.; Ligmann-Zielinska, A.; Swobodzinski, M. Choice modeler: A web-based spatial multiple criteria evaluation tool. Trans. GIS
**2008**, 12, 541–561. [Google Scholar] [CrossRef]

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**MDPI and ACS Style**

Demetriou, D.; See, L.; Stillwell, J.
A Spatial Multi-Criteria Model for the Evaluation of Land Redistribution Plans. *ISPRS Int. J. Geo-Inf.* **2012**, *1*, 272-293.
https://doi.org/10.3390/ijgi1030272

**AMA Style**

Demetriou D, See L, Stillwell J.
A Spatial Multi-Criteria Model for the Evaluation of Land Redistribution Plans. *ISPRS International Journal of Geo-Information*. 2012; 1(3):272-293.
https://doi.org/10.3390/ijgi1030272

**Chicago/Turabian Style**

Demetriou, Demetris, Linda See, and John Stillwell.
2012. "A Spatial Multi-Criteria Model for the Evaluation of Land Redistribution Plans" *ISPRS International Journal of Geo-Information* 1, no. 3: 272-293.
https://doi.org/10.3390/ijgi1030272