# Example: Employee Selection

This is an example of a simple didactic DEX model aimed at the assessment of applicants for a Project Manager position in a small company. In contrast with the Car Evaluation example, this particular model contains two continuous attributes and two discretization functions, and can be thus utilized in full only in DEXi Suite. All figures and charts on this page have been generated using DEXiWin.

## Tree of Attributes

The Employee Selection model has the following tree structure of attributes:

The same structure, displayed with descriptions of attributes:

Notice that attributes *ExperYears* and *AgeYears* are continuous.
In the model, they are discretized and mapped to their respective parents,
*Experience* and *Age*.

## Scales

The scales of attributes are defined as follows:

Apart from the two continous scales, *ExperYears* and *AgeYears*, all the remaining scales are
qualitative. Among these, *Age* is unordered, and all the others are
preferentially ordered in the ascending order.

Most of the qualitative values are represented by words: ‘unacc’, ‘high’, etc. Even though some values, for instance ‘1–5’ and ‘21–25’, are formulated as numeric intervals, they still represent single qualitative symbols.

The symbol ‘<>’ denotes an unordered continuous scale of *AgeYears*. The continuous scale of *ExperYears*,
denoted ‘<0; 10>’, is preferentially ordered and has two bounds: 0 and 10.
All values below and including 0 are considered preferentially ‘bad’,
and all values above and including 10 are considered ‘good’.

## Aggregation Functions

The Employee Selection model contains seven qualitative attributes: *Employ*, *Educat*, *Years*,
*Personal*, *Abilit*, *Experience*, and *Age*. The former five of them are associated with
aggregation functions. For brevity, only two of those are shown below
in the form of complex decision rules.

## Discretization Functions

Discretization functions map numeric values of continuous input
attributes to the qualitative values of the corresponding parent attributes. The two discretization
function in the Employee Selection model are associated with *Experience* and *Age*, and are
defined as follows:

Notice the symbols ‘[’, ‘]’, ‘(’ and ‘)’, associated with intervals:

‘[’ and ‘]’ denote the closed interval, so that the corresponding value belongs to the interval

‘(’ and ‘)’ denote the open interval, so that the associated value does not belong to that interval, but to the neighboring one

## Description of Employees

Alternatives - employee candidates - are defined by values of input (basic) attributes as follows:

There are five candidates, named A, B, C, D, and E. The former four are represented by single values, assigned to the five qualitative and two continuous input attributes.

The candidate E is an exception, aimed at illustrating
the use of other types of DEX values. The asterisk ‘*’ denotes
the whole set of values of the corresponding attribute *Comm*, indicating that
nothing is known about E’s communicative abilities. The value of *Leader* is
also somewhat uncertain, described by the value distribution ‘approp/0.50; more/0.50’.
This distribution is interpreted later in the evaluation
either as a probability or fuzzy distribution, but the basic interpretation is that
E’s leadership abilities are assessed as ‘appropriate’ or ‘more’ (with equal strength),
but not ‘less’.

## Evaluation of Employees

The above five employee candidates are evaluated, using the *probabilistic* value
interpretation and evaluation method, as follows:

The final evaluations are: candidate A is ‘good’, candidates B and C are ‘unacc’, candidate D is ‘exc’, and the evaluation of candidate E is a probability distribution of ‘unacc’ (with probability 0.25) and ‘exc’ (0.75).

In order to explain why the evaluations are such, one can look at the respective columns and inspect lower-level values that affected the evaluation.

## Analysis of Employees

### Selective explanation

Selective explanation highlights particular advantages and disadvantages of an alternative. The method finds and displays only those connected sub-trees of attributes for which the alternative has been evaluated as particularly good or bad.

This example shows that candidate C has both weak and strong points. Her particular
weakness is *Leader*, which is ‘less’ and largely affects the ‘unacc’ evaluation
of *Employ*. On the other hand, the candidate is very strong regarding her *Educat*
(both *Formal* and *For. lang*) and *Years* (age and experience).

### Plus-minus analysis

This is an example of “Plus-minus analysis” of candidate A:

Overall, candidate A has been evaluated as ‘good’, as shown in the first row.
Column **+1** shows that evaluation can be improved by one step (i.e., to ‘exc’)
only by changing the value of *For. lang* by one step (from ‘pas’ to ‘act’);
in this case, the overall evaluation would become ‘exc’. In a similar way, the columns
**-1** and **-2** show the overall evaluation results when the corresponding attributes
(only one at a time) change by one or two steps, respectively.

The brackets ‘[’ and ‘]’ indicate that the values of the corresponding
attributes (*For. lang* and *Leader*) cannot be changed by the requested number of steps.

### Target Analysis

Target analysis tries to find the smallest changes of input values that improve or degrade the value of some selected aggregate attribute. In contrast with Plus-Minus analysis, possible changes of more than one attribute at a time are observed. The following example shows the results of Target Analysis for candidate C:

There are two possible ways of improving his evaluation:

improving

*Leader*from ‘less’ to ‘approp’ and*Test*from C to Bimproving

*Comm*from ‘good’ to ‘exc’ and*Leader*from ‘less’ to ‘approp’

In both cases, an improvement of two basic attributes at the same time is required. In any case, improving candidate’s leadership abilities from ‘less’ to ‘approp’ is mandatory.

## Charts

This example shows some charts that can be obtained in DEXiWin. The charts differ in the number of evaluation dimensions and chart settings.

### Bar Chart

This chart displays evaluation results according to one evaluation
dimension. In this case, this is the root attribute *Employ*, so the chart
shows the overall evaluation of the five candidates.

The evaluation of candidate E is distributed between ‘unacc’ and ‘exc’. Point diameters indicate the relative difference of the corresponding probabilities, 0.25 and 0.75.

### Scatter Chart

A scatter chart displays evaluation results according to two selected
evaluation dimensions. In this case, the selected dimensions are *Personal*
and *Years*. The candidate E is excluded from this chart.

The following is the scatter chart of E, illustrating the display of value distributions:

### Charts Displaying Three or More Attributes

There are three types of charts that display evaluation results using three or
more selected attributes: linear, radar and radar grid. Examples below show all of them. The
second-level attributes *Educat*, *Years* and *Personal* have been selected as main chart dimensions.
Candidate E has been excluded for clarity.

**Linear Chart**

**Radar Grid Chart**

**Radar Chart**