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Methods and Technologies

Information for the professional analysts ...

So, we have number of multicrireia alternatives to compare.

The task can be solved in two steps:
 Step 1. We create Plan of analysis
 Step 2. We run the Analysis

Let's take a close look at these steps.

1. We create Plan of analysis. This Plan includes the hierarhical structure of parameters: up to seven "artificial" General parameters describing the general features of alternatives (for example Safety, Effeciency etc.) and unlimited number of the parameters influencing every General Parameter.

So, we have three levels of hierarchy: the purpose of analysis on the top, General parameters at the second level and parameters of the alternatives at the third level.

This structure allows us not just estimate alternative 'in general', but analize as well the most important general features of every alternative, and even we can see the influence of every parameter at the final result.

We have to assign the weigt coefficient to every parameter and every General parameter. It is a numeric coefficient showing power of influence of this element at the element of the higher level of the hierarchy. You can assign the weight coefficient directly in numeric form, or they can be calcullated automatically as the result of pairwise comparison procedure (Analysis of Hierarchies technology by T. Saaty, the weight coefficient calcullated as eigenvector of the matrix of parwise comparisons). During this procedure user just has to answer number of questions like "Which of these two parameters is more important?"

We also have to assign an Utility Function to every parameter in the Plan. Utility function maps the values of parameter to the scale between 0 and 1. Utility Function allows prioritize different values of the Parameter.

2. So, we have created Plan of analysis - the structure which reflects our understanding of the problem, our preferences and requirements. Now we can run the analysis for selected alternatives.

2.1 At the first phase the system calculates ratings of the alternatives separately for every General parameter. We use for this purpose the most popular 'simple weighing' method:
    R_ij = S_k W_kj * U_kj    , where R is rating of the alternative "i" on General parameter "j",
W is the weight coefficient of the parameter "k" of the alternative "i" in General parameter "j",
U is the value of the Utility function of the parameter "k" of the alternative "i" in General parameter "j".

In other words, we just sum up the values of the Utility function for every parameter multiplied by corresponding weight.

2.2 At the second phase of the analysis the system calculates final ratings of the alternatives using the same 'simple weighing' method. And now we use weight coefficients of the General pareameters and calculated ratings of the alternatives as values of the Utility function for every General parameter. E.a. the final rating of the alternative is a sum of its rating on every General parameter multiplied by corresponding weight of the General parameter.

Well, our task of comparison of multicriteria alternatives has been solved. We calculated the final ratings for every alternative and individual ratings for every General parameter. This approach allows us not only estimate alternatives "in general", but understand their weak and strong aspects.

You should remember that 'simple weighing' method belongs to "compensatory" methods. It means that, for example, some alternative with rather weak main parameters may get a very high rating due to its good values on the minor parameters.

To eliminate this compensatory effect system provides Pareto analysis of the alternatives on all parameters and on a subset of the most important parameters. So in previous example the results of the Pareto analysis will show you that in spite of high rating this alternative is dominated by some other alternatives on a subset of the most important parameters. This allows you to get rid of serious mistakes in decision making.

And at last you can run a Benefit / Cost analysis of alternatives based on the results of the multicriteria analysis. This procedure provides you with ratings of alternatives, calculated from their pairwise comparisons on the Benefit /Cost chart.

Estimation and Choice system allows you to process even incomplete data - if no more than 50% of values for some parameter are missed, they will be restored as average from the existing values.