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JOSS_paper/paper.md

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 `ProMCDA` receives all the necessary input information via a configuration file in JSON format (for more details see the [README](https://github.com/wetransform-os/ProMCDA/blob/main/README.md)). The alternatives are represented in an input matrix (in CSV file format) as rows and described by the different values of the criteria in the columns. The sensitivity analysis is performed by comparing the different scores associated with the alternatives, which are obtained by using different combinations of normalization and aggregation functions. `ProMCDA` implements 4 different normalization and 4 different aggregation functions, as described in [Table 1](#Table 1) and [Table 2](#Table 2) respectively. However, the user can decide to run `ProMCDA` with a specific pair of normalization and aggregation functions, and thus switching off the sensitivity analysis. <br />
 
 <a name="Table 1"></a>*Table 1: Normalization functions used in `ProMCDA`.*
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 <br />
 
 <a name="Table 2"></a>*Table 2: Aggregation functions used in `ProMCDA`.The sum of the weights is normalized to 1 as in @langhans_method_2014.*
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+![](Table2.pdf)
 
 The user can also decide to run `ProMCDA` with or without a robustness analysis. The robustness analysis is triggered by adding randomness to either the weights or the criteria. This means that either the weights or the criteria values are randomly sampled using a Monte Carlo method. In `ProMCDA` randomness is not allowed for both weights and criteria in order to make the results as transparent as possible. In fact, mixing uncertainty from both weights and criteria would lead to a lack of distinction between the effect of one or the other. Randomness in the weights can be applied to one weight at a time or to all weights at the same time. In the first case, the aim is to be able to analyse the effect of each individual criteria on the scores; in the second case, it is to have an overview of the uncertainty associated with all the weights. In both cases, by default, the weights are sampled from a uniform distribution [0-1]. On the other hand, if the user decides to analyse the robustness of the criteria, he/she has to provide the parameters defining the marginal distribution (i.e. a probability density function, pdf) that best describes the criteria, rather than the criteria values. This means that if a criterion is characterized by a pdf described by 2 parameters, two columns should be allocated in the input CSV file for it. In `ProMCDA` 4 different pdfs describing the criteria uncertainty are considered:
 
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 Finally, in all possible cases (i.e. a simple MCDA; MCDA with sensitivity analysis for the different normalization/aggregation functions used; MCDA with robustness investigation related either to randomness on the weights or on the indicators), `ProMCDA` will output a CSV file with the scores/average scores and their plots. For a quick overview of the functionality of `ProMCDA`, refer to  [Table 3](#Table 3). For more details, refer to the [README](https://github.com/wetransform-os/ProMCDA/blob/main/README.md).
 
 <a name="Table 3"></a>*Table 3: Overview on the functionalities of ProMCDA.*
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 # Acknowledgements