Complex multidimensional fuzzy models of monitoring and rehabilitation processes for patients with uneven observation interval

Abstract

Purpose. The work is devoted to the development of mathematical models and methods of fuzzy modeling of multidimensional time series (CDM) for the processes of monitoring and rehabilitation of patients with uneven intervals between observations. CDM takes into account the system properties and unity of the components of the studied processes by forming combined/complex multidimensional fuzzy models (CFTS). Methodology. The implementation of CFTS models takes into account the intrinsic features of these processes. The peculiarity of CFTS is that uneven intervals of observations, as well as other parameters, reflect the systemic unity of the controlled process, rather than the externally established form of observations, regulations. SFTS generalize models of multidimensional fuzzy time series of order n with m input parameters and one output parameter, i.e., different components may have different order of prehistory n, individual parameters may be measured by different types of data and forms of uncertainty. Findings. The article presents a comprehensive improved structure of CFTS models of order n with m input and one output parameter, which is adapted to the properties of monitoring and rehabilitation processes with uneven observation intervals. To form the SFTS, a step-by-step procedure is proposed that allows forming the composition of parameters. An example of modeling the process of rehabilitation of patients with diabetes based on the SFTS is presented, which demonstrates its differences and effectiveness. The comparative properties of SFTS and FTS models are presented. Originality. The development of CDM models and methods for monitoring and rehabilitation processes at uneven intervals is obtained, and complex SFTS models are formed. The difference between the SFTS is that the component of uneven intervals is represented as other multiparameters m, which can have different order of prehistory n, as well as different types of data and forms of uncertainty. A procedure for the step-by-step formation of the composition of the parameters of SFTS models is proposed. Practical value. SFTS models ensure the implementation of multiparameter monitoring and rehabilitation processes with uneven observation intervals, simplify the structure and reduce the number of relational relations, and eliminate the conflict of product rules in case of ensuring the required accuracy of results. The example of modeling the rehabilitation process for diabetics with such parameters as sugar level, interval between observations, and blood pressure has confirmed the reliability and practical significance of CFTS models.

Keywords

• analysis and forecasting
• complex fuzzy models
• uneven interval
• rehabilitation
• monitoring
• multiparametric processes