The concept of fuzzy central place as the approach to compare distribution of central functions within urban agglomerations

The conception of fuzzy central places (FCP), proposed by P. Em, made possible the understanding of the central functions' (CF) heterogenic distribution inside the urban agglomerations. The FCP is a bounded region of a set of points with CF. The correlation analysis proved a strong relation between the density of service enterprises and the population density. It is assumed that CF value is in direct proportion to the average population density. The index of key centers equilibrium (IKCE) permits to estimate the equilibrium between positions of expected and real focuses of the CF localization. The CF quasi-relief (QR) is a graphic model of a non-uniform dispersal CF spatial distribution. The steadiest modifications of the system with the minimum deviation from the theoretically determined IKCE are found by means of the analysis of the CF QR different relative elevations. "Flooded" areas performed the service area. The range of CF values at a higher level in the FCP system is twice as great as that at the next lower level. With a rising to a higher level, not only the number of facilities increases, but also the quality of provided services grows. The urban agglomerations are the greatest CF focuses. They can be studied as FCP systems. A considerable differentiation of CF value has been found within the limits of the Capital agglomerations of two Korean countries. It has been revealed that average CF values in agglomerations do not necessarily tend to decrease from the center to periphery. The constructed profiles of CF QF show conspicuous variations in CF values between the system elements in agglomerations. An analysis of the CF QR profile averaged over the agglomerations under study reveals a similarity between the CF distribution curve and the curve in the Clark's model. The fractal theory is a useful tool to study FCP systems. The fractal dimension (D) allows defining the degree of the CF distribution's uniformity. The analysis showed that degree of the CF distribution's uniformity in elements of Capital agglomeration of the Republic of Korea in new-built areas is higher than in regions with traditional building. Also, it was found that CF value and D in elements of FCP system have a strong relation: the higher the CF volume in one FCP, the higher the degree of CF distribution's uniformity in neighbor elements is. Analyzing the indexes, a hypothesis about the presence of exponential relationship between the CF value and D was made.