Discrete homogeneous Markov chain for fuzzy states

Abstract

As a result of the conducted research, a method for constructing a homogeneous Markov chain for a system with fuzzy states based on processing time series data of system outputs has been developed. Unlike the well-known fuzzy Markov chains, the transition matrix is not considered as a fuzzy relation, but remains an ordinary stochastic matrix. This approach makes it possible to obtain stationary states of the system, which characterize its status at a given time interval. This information can be used in the decision support system for purposeful status changes. A feature of the obtained Markov chain for fuzzy states of the system is the possibility of taking into account the dynamics of changes in the states of the system when calculating the average status values, in contrast to the widely used orientation to averaging based on the calculation of arithmetic averages. Numerical experiments have been carried out with the constructed Markov chain for fuzzy states, which confirm its adequacy and the possibility of taking into account dynamics. The experiments are implemented on the example of assessing the status of a student in the education system.