Page 15 - Azerbaijan State University of Economics

Gorkhmaz Imanov, Asif Aliyev : Fuzzy Linguistic Forecasting of Social Mobility

In the graph (i = 1,...,5) denotes economic strata of population , (j = 1,...,3) –

years of analysis, (i = 1,...,5;j = 1,…,3) – number of people in the economic

∗
strata in the corresponding year, and - portion of people moving to other

strata and remaining in the same strata respectively.

It is obvious that, in all cases between social strata the number of ascending
movements equals the number of descending movements.

Since the phenomenon of social mobility is consistent with the Markov chain
process, this theory is used to forecast social mobility see Zadeh (1976), G. J.
Imanov and Akperov (2013), Cheong and Hui (2001).

Consequently, G. S. Fields and E. A. Ok mobility indices, estimated for each socio-
economic strata have to be fuzzified primarily see İmanov and et all (2003), Zadeh
(1975). Assuming the mobility index is a linguistic variable, the range of obtained
mobility data can be divided into three intervals: L(0-0.12), M(0.11-0.26),
H(0.24-0.38).

Where, L – low, M – medium, H – high are linguistic terms. In other words, the
mobility variables get their values within these intervals. We can assume the fuzzy
interpretation of these linguistic variables according to membership functions given
below:

= 1/0 + 0.7/0.03 + 0.5/0.04 + 0.2/0.07 + 0/0.10

= 0.1/0.11 + 0.4/0.14 + 1/0.19 + 0.6/0.22 + 0/0.25

= 0/0.26 + 0.2/0.28 + 0.4/0.30 + 0.7 /0.35 + 1/0.38

= 1/0 + 0.49/0.03 + 0.25/0.04 + 0.04/0.07 + 0/0.10

= 0.01/0.11 + 0.16/0.14 + 1/0.19 + 0.36/0.22 + 0/0.25
= 0/0.26 + 0.04/0.28 + 0.16/0.30 + 0.49 /0.35 + 1/0.38

Where, added VL – very low, VM – very medium, VH – very high are
concentrated forms of the above given terms.

The status vector 2017 = (0, 0.04, 0.38, 0.11, 0.03) of social mobility indices in
the economic strata for the last period (2017) is in line with the linguistic social
mobility vector (VL, L,VH, VM, L).

According to the analysis of Figure 1. the matrix of transition from one economic
stratum to another can be represented as follows:

15