Mathematical methods for selecting areas, Weighted...

Mathematical methods for selecting areas

Problems of regionalization of territories are the subject of study of many scientific disciplines.

In geography, they are one of the main. To the concept of district researchers come up in different ways. There is an approach that determines the narrow, unambiguous meaning of an area allocated on the basis of any one characteristic; but much more often this concept is considered in a broader context.

Allocation of districts (zoning) can be considered as one of the stages of classification, where similar areas are united on the basis of a commonality of properties and connections. It is carried out in two ways: by combining or dividing. A union performed on the basis of a commonality of properties leads to the isolation of a homogeneous region, and a union based on a commonality of reciprocal links leads to the allocation of a nodal region.

When zoning, you must adhere to the following basic principles: 1) zoning should be based on the commonality of properties and relationships; 2) no region should be included in the zoning process twice; 3) the principles of division or association should be maintained at all levels of regionalization; 4) zoning criteria should be determined from geographical positions.

A lot of methods of territory partitioning have been developed. However, not all of them can be used with equal success to distinguish the areas under study. Consider the most appropriate of them.

Weighted scores method

This method allows you to evaluate natural conditions using any number of factors. It has been used quite successfully in geographic studies for various purposes of territorial division. First of all, the studied territory is divided into primary territorial units. They can be physical and geographical units: elementary pools, landscapes, squares or any other contours of the territory. Before choosing a territorial unit, one restriction must be adhered to: each zoning criterion should be approximately the same within the allocated territorial units so that they can be estimated unambiguously (as a point) from the position of the feature being studied.

The choice of indicators, which should form the basis of regionalization, is determined by the purpose of the work. The selected primary indicators of the factors are estimated using the scores (x 1 , x 2, ..., x n ). > For each such indicator or factor (F) within the territorial unit, the maximum (Fmax) and the minimum (Fmin) values ​​are determined. The difference Fmax - Fmin, commensurate with the number of points, represents the interval of division (i) for each gradation, which is estimated by the corresponding score. For example, for a five-point system, the primary indicators can be estimated according to the scheme presented in Table. 11.7

Table 11.7

Scale of primary indicators for a five-point system

Score, points

Grades of primary metrics






Using this technology, all primary indicators within each territorial unit are assessed in scores.

A simple sum of scores of primary indicators within a territorial unit can not be objectively assessed, as they do not reflect the significance of the relevant factors. In order for the sum of scores to express an objective evaluation, it is necessary to use additional values ​​- the weighting coefficients.

They are determined with the help of one more - common for all territorial units - indicator ( x total). After its evaluation, on the same scoring scale, a pairwise value of the correlation coefficient between the total indicator and each of the selected ( r total 1, r total 2, ... , r commonly n ). Two methods are used. One of them, more accurate, is to correlate the values ​​of r i and x in general in absolute values ​​of the indicators. Pair correlation coefficients are used for these purposes. The second method is associated with the expression x total in points and finding the rank coefficient between x i and x total. From the correlation coefficients obtained, the largest is selected and all the others are assigned to it. Let the maximum is the exponent x total 2. Then the weights (γi) are found using the ratio γi = r total 1/ r total 2 (= r total 1/ r total 2; γ2 = r total 2/ r total 2 = 1; ., γn = r total n /r total 2) • The resulting weighting factors (γi) are multiplied (or divide) by the score of the corresponding factor, resulting in weighted scores (Bi). Within each territorial unit, the weighted scores are added up, obtaining an estimated amount.

By analogy with the scale of assessments of primary indicators (see Table 11.7), gradations of the sums of weighted scores (ΣΒi) are established for assigning each territorial unit to one or another unification of areas (Table 11.8).

Table 11.8

Gradations of sums of weighted scores



Area #:






In the last column, enter the numbers of the districts having the required sum of weighted scores. The zoning is carried out by combining into one area all theoioooal units that have a sum of weighted points etc

VV Shkurkov used this technique in 1967 to draw up a map of the assessment of the living conditions of the population of Northern Kazakhstan.

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