# Identifying Value-Increasing Actions for Cultural Heritage Assets through Sensitivity Analysis of Multicriteria Evaluation Results

## Abstract

**:**

## 1. Introduction

## 2. Methods

## 3. An Explanatory Example

## 4. Discussion

## Funding

## Conflicts of Interest

## Abbreviations

AHP | Analysis of the Hierarchical Process |

BWM | Best Worst Method |

EVAMIX | Evaluation of Mixed Data |

FUCOM | Full Consistency Method |

HBU | Highest and Best Use |

HDM | Hierarchical Decision Model |

MCDM | Multicriteria Decision Making |

SWARA | Step-Wise Weight Assessment Ratio Analysis |

VIKOR | Multicriteria Optimization and Compromise Solution |

(Serbian, Visekriterijumska Optimizacija I Kompromisno Resenje) | |

WPM | Weighted Product Model |

WSM | Weighted Sum Model |

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**Figure 1.**A generic hierarchy for a problem structured by a hierarchical decision model (HDM). There are five hierarchical layers: the top layer (pink) includes the target decision; immediately below, there is the criterion layer (light blue), then the sub-criterion layer (purple) and the indicator layer (light green). At the bottom of the hierarchy, there are the alternative decisions, marked with different colors, which must be assigned relative scores with respect to all the elements of the lowest hierarchical layers.

Criteria | Criterion 1 | Criterion 2 | Criterion 3 | … | Criterion M |

Weights | ${w}_{1}$ | ${w}_{2}$ | ${w}_{3}$ | ... | ${w}_{M}$ |

Alternatives | Local priorities | ||||

Alternative 1 | ${a}_{11}$ | ${a}_{21}$ | ${a}_{31}$ | ... | ${a}_{M1}$ |

Alternative 2 | ${a}_{12}$ | ${a}_{22}$ | ${a}_{32}$ | ... | ${a}_{M2}$ |

. | . | . | . | ... | . |

. | . | . | . | ... | . |

. | . | . | . | ... | . |

Alternative N | ${a}_{1N}$ | ${a}_{2N}$ | ${a}_{3N}$ | ... | ${a}_{MN}$ |

Criteria (Weights) | Indicators | Weight |
---|---|---|

Urban Sustainability (${w}_{1}=0.30$) | Presence of historical-cultural places within 1 km | ${w}_{11}=0.25$ |

Quality of the urban landscape | ${w}_{12}=0.30$ | |

Accessibility by private car | ${w}_{13}=0.15$ | |

Presence of commercial activities nearby | ${w}_{14}=h0.10$ | |

Presence of accommodation and hospitality services | ${w}_{15}=0.20$ | |

Project Sustainability (${w}_{2}=0.40$) | Total property availability | ${w}_{21}=0.20$ |

Flexibility of spaces to new functions | ${w}_{22}=0.40$ | |

Degradation level | ${w}_{23}=0.40$ | |

Economic Sustainability (${w}_{3}=0.30$) | Investment costs | ${w}_{31}=0.25$ |

Payback period | ${w}_{32}=0.25$ | |

Financial appeal for private investors | ${w}_{33}=0.50$ |

**Table 3.**Decision matrix and global priorities for the example in Section 3.

Value | Global Priorities | ||
---|---|---|---|

1 Very high | ${l}_{1}=0.131$ | ||

2 High | ${l}_{2}=0.252$ | ||

3 Medium | ${l}_{3}=0.236$ | ||

4 Poor | ${l}_{4}=0.210$ | ||

5 Very poor | ${l}_{5}=0.172$ | ||

Criteria | 1 Urban Sust. | 2 Project Sust. | 3 Economic Sust. |

Weights | ${w}_{1}=0.30$ | ${w}_{2}=0.40$ | ${w}_{3}=0.30$ |

Value | Local Priorities | ||

1 Very high | ${a}_{11}=0.046$ | ${a}_{21}=0.168$ | ${a}_{31}=0.165$ |

2 High | ${a}_{12}=0.111$ | ${a}_{22}=0.402$ | ${a}_{32}=0.193$ |

3 Medium | ${a}_{13}=0.207$ | ${a}_{23}=0.243$ | ${a}_{33}=0.254$ |

4 Poor | ${a}_{14}=0.317$ | ${a}_{24}=0.115$ | ${a}_{34}=0.229$ |

5 Very poor | ${a}_{15}=0.318$ | ${a}_{25}=0.071$ | ${a}_{35}=0.160$ |

**Table 4.**Minimum absolute variations ${\delta}_{k,i,j}$ in criteria weights to reverse the rankings of the alternative pairs.

Criteria | |||
---|---|---|---|

1 Urban Sust. | 2 Project Sust. | 3 Economic Sust. | |

Pairs of alternatives | |||

1-2: Very high–High | ${\delta}_{1,1,2}=N/F$ | ${\delta}_{2,1,2}=N/F$ | ${\delta}_{3,1,2}=N/F$ |

1-3: Very high–Medium | ${\delta}_{1,1,3}=N/F$ | ${\delta}_{2,1,3}=N/F$ | ${\delta}_{3,1,3}=N/F$ |

**Table 5.**Minimum percent variations (${\chi}_{i,j,k}\times 100$) in local priorities to reverse the rankings of the alternative pairs.

Criteria | |||
---|---|---|---|

1 Urban Sust. | 2 Project Sust. | 3 Economic Sust. | |

Pairs of alternatives | |||

1-2: Very high–High | ${\chi}_{1,1,2}=-1325.1$ | ${\chi}_{1,2,2}=-194.30$ | ${\chi}_{1,3,2}=-395.14$ |

1-3: Very high–Medium | ${\chi}_{1,1,3}=-930.82$ | ${\chi}_{1,2,3}=-192.33$ | ${\chi}_{1,3,3}=-287.92$ |

2-1: High–Very high | ${\chi}_{2,1,1}=N/F$ | ${\chi}_{2,2,1}=70.603$ | ${\chi}_{2,3,1}=N/F$ |

3-1: Medium–Very high | ${\chi}_{3,1,1}=N/F$ | ${\chi}_{3,2,1}=90.986$ | ${\chi}_{3,3,1}=N/F$ |

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**MDPI and ACS Style**

Salerno, E.
Identifying Value-Increasing Actions for Cultural Heritage Assets through Sensitivity Analysis of Multicriteria Evaluation Results. *Sustainability* **2020**, *12*, 9238.
https://doi.org/10.3390/su12219238

**AMA Style**

Salerno E.
Identifying Value-Increasing Actions for Cultural Heritage Assets through Sensitivity Analysis of Multicriteria Evaluation Results. *Sustainability*. 2020; 12(21):9238.
https://doi.org/10.3390/su12219238

**Chicago/Turabian Style**

Salerno, Emanuele.
2020. "Identifying Value-Increasing Actions for Cultural Heritage Assets through Sensitivity Analysis of Multicriteria Evaluation Results" *Sustainability* 12, no. 21: 9238.
https://doi.org/10.3390/su12219238