# Algorithm for constructing a normalized vector - Environmental...

## Algorithm for constructing a normalized vector

Let the non-standardized vector and ', be given. its components do not meet the condition: . In order to normalize a vector, we find the sum of all its components , after which the components of the normalized vector can be defined as follows:

Example

The problem situation is reflected in Fig. 2.4. At the mouth of the river. Further, flowing into the sea bay, there is a settlement, to which the railway is suitable. On the shore of the bay it is planned to build an oil loading port. Three variants of port A, B, B are considered, the areas for which are indicated in the figure in dotted lines. It is necessary to choose the most suitable site for construction, taking into account the main ecological features of the territory and water area of ​​the bay. Obviously, from an environmental perspective, each option has its own advantages and disadvantages.

Variant A is good because it takes uncomfortable, and therefore cheap land, does not affect forest and arable land, is located close to the settlement, the length of new roads and pipelines that will have to be laid to a new port , is not large. At the same time, during the construction of the port in this place it will be necessary to carry out significant dredging to create a sea channel, the predicted level of water pollution is unfavorable because of the high background pollution of fresh waters carried by the river. The fairway is complex, and the probability of accidents on it is greatest.

Variant B differs in that it is located in the deep-water part of the bay and a large amount of dredging works that adversely affect hydrobionts will not be required. However, not far from the reserve is a small village. The future port will not affect the borders of the reserve, but it will have an additional impact on it. The laying of transport highways to the port will require the occupation of arable land, because along the shore in the water protection zone it is impossible to lay the main lines. In addition, the pipeline will have to cross the river.

Fig. 2.4. Ports layout options

Variant В requires dredging, but their volume is much less than for option A. The laying of the main lines will require the removal of forest and partially uncomfortable land. An unfavorable moment is the proximity to the future port of the recreation area.

Define the purpose of the study. It is required to choose the most acceptable option from the environmental position for the new port.

Next, you need to build a hierarchy, starting with the vertex (goal), through intermediate levels (criteria) to the lowest level, which is a list of options. In order to correctly choose the criteria and, even more so, meaningfully give them weighted scores in a paired comparison, the working group, and then the experts should thoroughly and thoroughly study the problem, master all available information. In this training example, it is not possible to describe in detail the problem situation, to give exhaustive characteristics of the environment, so we confine ourselves to the available modest information. The simplest hierarchical structure is constructed below, where there is only one level of criteria (only for environmental reasons) and a list of the alternatives A, B, and B under consideration (figure 2.5).

The selected criteria for the convenience of further calculations are numbered:

- withdrawal of farmland - No. 1;

- Forests removal - No. 2;

- the effect on the atmosphere - No. 3;

- noise impact - No. 4;

- impact on water, including the impact of dredging - No. 5;

- impact on the animal and plant world - № 6;

- environmentally hazardous accidents - No. 7.

Fig. 2.5. Port layout options

The matrices of paired comparisons for the level of criteria are given in the form of tables. 2.2, using a 9-point rating scale.

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