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# Welcome to VectorMCDA’s documentation!

## Description of VectorMCDA

VectorMCDA implements some multicriteria decision aid (MCDA) algorithms using vector data in QGS GFOSS software. VectorMCDA assumes that each geographical object, described with a records in the attribute table, is a single alternative (geo-alternative) and the algorithms implemented in the plugin analyzes the attributes, elaborates these ones like criteria and return the output in one or more columns, added in the attribute table. The output are shows as geographic maps in QGIS canvas and in a graphical html page. The algorithms available in the current VectorMCDA version are the follow:

geoWeightedSum: [1] implements the classic weighted sum algorithm and return a maps shows the preference granted to the various geo-alternatives. The user may provide directly the weight values, or he can calculate them with AHP [2] approach implemented in the module.

geoTOPSIS: implements the ideal point algorithms base on TOPSYS model [3] and returns a maps shows the ranking alternative in a colour and numerical scale and in a graph in html page. Even in this case, the user may provide directly the weight values, or he can calculate them with AHP [2] approach implemented in the module

geoFuzzy: implements the fuzzy MCDA model proposed by Yager [4] and returns the fuzzy intersection and fuzzy union MCDA index. The linguistic modifier may be provided in the same way of weights, seen in the previous algorithms.

geoConcordance: calculates the concordance and discordance index for each geo-alternative, as a base for assessment with Electre [5] models family. The module returns two maps, one for concordance index and one for discordance index. The weighing step is the same seen in the previous algorithms.

geoPromethee: implements the Promethee [6] method in a geographic way. The weighing step is the same seen in the previous algorithms, the outputs are the negative flux, the positive flux, the net flux, stored in the attribute table, the relative maps and graphs in html separate page.

geoRSDB: the module implements the DOMLEM algorithm for rough set dominance based theory (RSDB)**[7]. The output is in a set of **decisional rules extracted from a pre-definited ranking stored in the attribute table. The module doesn’t make a classification of geo-alternatives, but pick up the rules from attribute table, with a column with ranking value. The current implementation of the module is “discovery knowledge oriented”, instead a proper MCDA algorithm. In the next implementation, the rules extracted will be used for perform a real MCDA classification.

geoXMCDA: is the first implementation of xMCDA standard (http://www.decision-deck.org/xmcda/) for grant the MCDA data interoperability. The module isn’t yet mature and it isn’t usable in production environment, anyway it is under active develop and test.

### Installation

The plugin works under QGIS 2.0 environment, but the first time we use it we need to follow the installation procedure:

1. from the menu Plugins choose Manage and Install plugin, the Plugin manager window will open;
2. if VectoMCDA is already installed, we will find it under the installed plugins in Plugin manager. Otherwise, the plugin will be listed under Get more and we can install it by clicking on Install plugin;
3. after the end of installation procedure, VectoMCDA will be accessible from the menu Plugins;

Figure 1: Plugin manager in QGIS

VectorMCDA implements several MCDA algorithms and the user can access from the menu shows in figure 1.

The user can download example data from the site http://maplab.alwaysdata.net/geomcda.html.

### Running geoWeightedSum

The user has to load a vector geographic data in qgis and select it clicking with the mouse over the name. The attribute table of that file has to contain the indicators we intend to use in the assessment and a label for identify the geo-alternatives. From the menu Plugins/VectorMCDA we can select geoWeightedSum and the window shown in figure 2 will open.

In the Criteria page the label Layer shows the active layer’s name, while the combo-box field hold the list of numerical fields in the attribute table. The Add field button insert the selected field in the combo-box as a new column in the table, as a new criteria used in MCDA analysis. The columns in the table in the card Standard holds all the numerical fields from the attribute table of the selected layer, used for the MCDA analysis, meaning as criteria. The first row of the table contain the weight for each criteria (column), the second row shows the preference function as cost/gain value. The user has to decide which criteria he want to use for the analysis, the ones he doesn’t want to use, have to be selected on the table (clicking with the mouse on the header) and removed with the menu activated with the right button of the mouse. We can add a field in the analysis using the Add field button on the card. The input of the weight in the first row can be done simply digit the values for each criteria shows on the header of the table; otherwise, and alternatively, is available the AHP approach with pairwise comparation matrix, in the Advance card. In the last case, the user has to digit the preference of column criteria respect the rows criteria, in a range [1/9....9/1]. The weight are calculated with the Calculate weight button and the values are inserted in the weighted row in the table of Standard card. In the next step the user has to define the preference function for each criteria; if a criterion is preferable if it’s value increase, the value to be selected is gain, otherwise the value has to be cost.

Figure 2.a: geoWeightedSum algorithm in VectorMCDA plugin. Criteria Tab.

Pressing the button Apply the user performs the analysis, on the table will add a new field named geoWSM that holds the values of each alternative (each row in the table of attribute, and each relative geographic object)

With the Analysis we can shows the graphical and geographical outputs. The Maps button load the map in QGIS, with the colour graduated with geoWSM field. The Graph button open an html page with bar-graph labeled with Label filed in the combo-box

Figure 2.b: geoWeightedSum algorithm in VectorMCDA plugin. Analysis Tab.

### Running geoTOPSIS

The geoTOPSIS module can be lunched from Plugins/VectorMCDA/geoTOPSIS. It shows the windows for perform geoTOPSIS MCDA analysis. The general input are the same seen in the geoWeightedSum. The table in the Standard page has the same field and meaning of the previous module, except for last two rows: ideal point and worst point. The Ideal point is the target and optimum value, the default value is the best in the attribute table for each single criterion, but the user can change it with different value. The worst point is the opposite of the ideal point and the default value is the worse in the attribute table. The Load maps and Graph buttons are described in geoWeightedSum and have the same meaning and behavior.

Figure 3: geoTOPSIS algorithm in VectorMCDA plugin.

### Running geoFuzzy

Figure 4: geoFuzzy algorithm in VectorMCDA plugin. Criteria tab.

Figure 5: geoFuzzy algorithm in VectorMCDA plugin. Fuzzify tab.

### Running geoConcordance

Figure 6: geoConcordance algorithm in VectorMCDA plugin.

### Running geoPromethee

Figure 7: geoPromethee algorithm in VectorMCDA plugin.

### Running geoRULES

Figure 8: geoRULES algorithm in VectorMCDA plugin.

### Running geoXMCDA

Figure 9: geoXMCDA algorithm in VectorMCDA plugin.

### Outputs

The page Analysis [figure 4] allows the user to get the outputs provided from the plugin. We can have three types of output:

1. cartographic: pressing the Load maps button, geoUmbriaSUIT loads four thematic maps, showing the environment (EnvIdeal), economic (EcoIdeal), social (SocIdeal) and the comprehensive sustainability performance of each research unit, based on the related indexes. The user can change the class numbers changing the value in Classes map control, but the label will be only numeric, from the lowest to the highest value.
2. graphic: the user has to select the field used for labeling the research units from the combo-box Label field. For example, if our assessment concerns the Italian regions, we have to select the field that holds the name of the regions. The same for Provinces, municipality or other administrative or phisical units. Pressing the Graph button, geoUmbriaSUIT will load an html page in a web browser with four graphs. The first shows a stack – histogram whose the overall height is proportional to the sustainability value, as the sum (linear combination) of the three indexes (environmental, economic and social values) calculated using TOPSIS algorithm. The second graph is a bubble-graph: the position, dimension and color of bubbles provide information about sustainability and its three dimensions. In particular, the x-axis is ordered with the environmental index, the y-axis is ordered with the economic index, while the color (from red to green) is ordered with the social index; the dimension of the bubble is proportional to the sustainability value. The first two graphs use Google chart API’s and require an active internet connection. The third and the fourth graphs are quite similar to the the first two, but they are static and they do not require an internet active connection.
3. alphanumeric: geoUmbriaSUIT implements the Dominance Based Rough Set theory [5] for discovering and explaining the data outputs. In the page Rules there is a button named Extract rules, for the extraction of decisional rules on the basis of a classification given from TOPSIS algorithm. If a rule has a syntax like IF A>= X THEN AT LEAST i-th, we can read it as: ** if criterion A has a value greater than or equal to x, then the class of membership will be at least the i-th . On the other hand, if the extracted rule has the syntax like **IF A>= X THEN AT MOST i-th, it can be read as: If the criterion A has a value greater than or equal to x, then the class of membership will be at most the i-th **. If the user selects a single rule, the **research units covered from that rule will be selected. In other words, selecting a single rule from the text box, we can see the examples which support that rule.

## Bibliography

[1] Triantaphyllou, E. (2000). Multi-Criteria Decision Making: A Comparative Study. Dordrecht, The Netherlands: Kluwer Academic Publishers (now Springer). p. 320. ISBN 0-7923-6607-7.

[2] Thomas L. Saaty, Decision Making for Leaders – The Analytic Hierarchy Process for Decisions in a Complex World, RWS Publishing, Pittsburgh, 1990.

[3] Hwang, C.L.; Yoon, K. (1981). Multiple Attribute Decision Making: Methods and Applications. New York: Springer-Verlag.

[4] Yager, R.R., 1978, Fuzzy decision making including unequal objectives, Fuzzy Sets and Systems, 1: 87–95.

[5] Roy B., (1991), “The outranking approach and the foundation of ELECTRE methods”, Theory an Decision, vol. 31, 49-73.

[6] J.P. Brans and P. Vincke (1985). “A preference ranking organisation method: The PROMETHEE method for MCDM”. Management Science.

[7] Greco, S., Matarazzo, B., Słowiński, R.: Rough sets theory for multi-criteria decision analysis. European Journal of Operational Research, 129, 1 (2001) 1–47

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