Page 16 - Azerbaijan State University of Economics

THE JOURNAL OF ECONOMIC SCIENCES: THEORY AND PRACTICE, V.76, # 2, 2019, pp. 4-20

3
4
1
5
2
1 0 1 0 0 0

2 0 1 0 0 0
‖
2017 = 0 0.04 0.9 0.06 0 ‖
‖
‖
3
4 0 0 0 1 0
5 0 0 0 0.08 0.92

In order to forecast social mobility indices for 2018 for each social strata the fuzzy
linguistic Markov chain is applied:

2
2018 = 2017 ◦ 2018 = 2017 ◦ 2017 (18)

2
5
3
4
1
1 0 1 0 0 0
2 0 1 0 0 0
‖

2
2017 = 0 0.04 0.9 0.06 0 ‖
‖
3
‖
4 0 0 0 1 0
5 0 0 0 0.08 0.92

As it is known, by maxmin multiplication of transition matrices, the resulting

transition matrix is the limit matrix itself. And the stationary solution of the fuzzy
system does depend on the initial state, even though the system can freely move
from one state to another. This is a crucial distinction between fuzzy Markov chains
and probabilistic Markov chains. Markov chain is referred as the ergodic chain if it
is aperiodic, convergent and transition matrix has identical rows (Avrachenkov and
Sanchez, 2002).

But, in this case of interest the transition matrix is aperiodic and convergent, but not
ergodic.

Assuming again that the probability of transition between social strata is a linguistic
variable, the probability range [0,1] can be divided into three intervals: L(0-0.3),
M(0.3-0.7), H(0.7-1).

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