Ranking Urban Residential Areas Against Earthquake Hazards Using Shannon Entropy AND Topsis Techniques (Cace Study: Amol City)

Vulnerability is the social and economic tolerance of a society against environmental hazards. Accordingly, vulnerability is the extent to which a community can respond to and deal with environmental hazards [19].
The need to reduce the earthquake’s vulnerability of the city is one of the main goals of urban planning and design. In order to reduce the vulnerability of urban buildings to earthquakes beside the possible occurrence of earthquakes, it is necessary to assess the vulnerabilities of urban areas [4, 5, 11, 15, 25].  In this regard, different conditions are simulated before the occurrence of possible earthquakes in different intensities and based on that, zoning maps of vulnerabilities of urban buildings are prepared and evaluated [5, 11]. Accordingly, entropy is an approach used to deal with disorder, instability, confusion, and doubts in a system [2].
Shannon entropy is a measure of the degree of uncertainty in the information content of a parameter that calculates the effect of each parameter on the system results [8, 10, 20, 21, 22, 24].
The TOPSIS method is used to rank and select the best option and to determine the distances between the options and their grouping [1, 6, 7, 9, 13, 16, 17]. One of the advantages of this method is that the criteria or indicators used for comparison can have different units of measurement [3, 12, 14, 18, 23, 26].
Proposed Method
Shannon Entropy
Shannon entropy is a function of the probability distribution and a criterion for measuring the degree of uncertainty in the information content of a parameter. By considering the frequency of subgroups’ occurrence of that parameter, it indicates the level of heterogeneity and consequently calculates the effect of each parameter on the system results. [10, 24].
TOPSIS
TOPSIS method or technique for order performance by similarity to ideal solution is a multi-criteria decision making (MCDM) method. This method can be used to rank and compare different alternatives and select the best one and to determine the distances between alternatives, as well as to group them. [1, 6, 7, 9, 13, 16, 17].  One of the advantages of this method is that the criteria or indicators used for comparison can have different units of measurement and have a negative and positive nature. In other words, combination of negative and positive criteria can be used in this method [3, 12, 14, 18, 23, 26].
Results
In this study, at first, the spatial layers of the study area were prepared from different sources, including the Institute of Geophysics (University of Tehran), Statistics Center of Iran, Geological Survey, Housing and Urban Development of the Mazandaran province, Amol Municipality and Regional Water Organization. This information was then implemented in the GMT software environment.
These spatial layers were the energy released by the earthquakes (last 20 years in terms of tone TNT per area), the quality of buildings and structures, residential density, building density, population density, permeabilityand permeability of the road network, urban open space and groundwater depth. After implementing these layers in the city map, a decision matrix was created using the TOPSIS method. This matrix was then normalized and scaled. The MatNorm decision matrix is ​​parametric and must be quantified. For this purpose, the weights for each index were determined. In this regard,
 Shannon entropy method was used for weighting.   Using the relationships presented in Shannon's entropy theory, entropy values ​​were calculated for the effective parameters in the study area.
After weighting the normalized matrix, the positive ideal and negative ideal solutions were determined and the distance from the positive and negative ideals was determined and finally, we were ranked the areas by calculating the scores.
According to the TOPSIS method ranking, District 24 with coefficient of proximity (0.903), District 13 with coefficient of proximity (0.727) and then District 18 with coefficient of proximity (0.694) are the most vulnerable areas of Amol city against earthquakes. .
After the area rankings were implemented on the city map in GMT software, the areas were labeled based on proximity to the ideal (Figure 1).
 
Fig. 1. Earthquake vulnerability ranking of 27 areas of Amol city
Conclusion
According to the zoning of the areas using Shannon entropy, the ranking of the areas, and the distance to the ideal, obtained by the TOPSIS model, and finally, the mapping of the zoning map in GMT environment, the vulnerable areas of Amol city were determined. The results showed that the central areas, i.e. 24, 13, 18, 10, and 12, are very vulnerable. Moreover, areas 19, 17, 14, and 16 are highly vulnerable, areas 15, 21, 2, 6, 22, 25, 11, 20, 27, and 4 have moderate vulnerability, areas 26, 9, 23, 3, 1, and 5 have low vulnerability, and finally, areas 8 and 7 have very vulnerable to earthquakes, respectively. Therefore, it is expected that the vulnerability of urban areas will be considered in future constructions.