Author details

Andrzej Łodziński

member 1 has improved, while the solution for member 2 and member 3 has deteriorated. The group now wishes to correct the solution for member 3 and increases the aspiration level for member 3, but does not change the aspiration levels for members 1 and 2. As a result (Iteration 3), the solution for member 2 and member 3 has improved, while the solution for member 1 has deteriorated. The group still wishes to correct the solution for member 3 and provides a higher value of the aspiration level for member 3, but does not change the aspiration levels for members 1 and 2. As a result (Iteration 4), the solution for member 2 and member 3 has improved, but the solution for member 1 has deteriorated. The group now wishes to correct the solution for member 1 and member 3 and reduces the aspiration level for member 2, but does not reduce the aspiration levels for members 1 and 3. As a result (Iteration 5), the solution for member 1 has improved, while the solution for members 2 and 3 has deteriorated. A further change to the value of the aspiration levels causes either an improvement in the solution for member 1 and at the same time a deterioration in the solution for member 3 or vice versa, as well as slight changes in the solution for member 2. Such a solution results from the specific nature of the examined problem—the solution for member 2 lies between solutions for members 1 and 3. The group decision for Iteration 5 is as follows: <sup>x</sup><sup>5</sup> <sup>¼</sup> ð Þ <sup>14</sup>:81; <sup>10</sup>:<sup>12</sup> .

Iteration Member 1 Member 2 Member 3

Solution <sup>b</sup><sup>y</sup> <sup>750</sup> <sup>1200</sup> <sup>1100</sup> POF 0.166 0 0.153

Solution <sup>b</sup><sup>y</sup> <sup>800</sup> <sup>1192</sup> <sup>1007</sup> POF 0.111 0.006 0.224

Solution <sup>b</sup><sup>y</sup> <sup>775</sup> <sup>1196</sup> <sup>1053</sup> POF 0.138 0.003 0.189

Solution <sup>b</sup><sup>y</sup> <sup>750</sup> <sup>1200</sup> <sup>1100</sup> POF 0.166 0 0.153

Solution <sup>b</sup><sup>y</sup> <sup>755</sup> <sup>1199</sup> <sup>1090</sup> POF 0.161 0.0006 0.160

1. Aspiration levels y 900 1200 1320

2. Aspiration levels y 850 1000 1200

3. Aspiration levels y 850 1000 1250

4. Aspiration levels y 850 1000 1300

5. Aspiration levels y 850 990 1300

<sup>b</sup>y<sup>1</sup> <sup>b</sup>y<sup>2</sup> <sup>b</sup>y<sup>2</sup>

The final choice of a specific solution depends on the preferences of the members in the group. This example shows that the presented method allows the members to get to know their decision-making possibilities within interactive analysis and to search for a solution that

would be satisfactory for the group.

Table 2. Interactive analysis of seeking a solution.

54 Optimization Algorithms - Examples

Address all correspondence to: andrzej\_lodzinski@sggw.pl

Faculty of Applied Informatics and Mathematics, Warsaw University of Life Sciences, Warsaw, Poland
