Type-1 and Interval Type-2 Fuzzy Sets along with 3D Cellular Automaton: Tools for Qualitative Study of a SIRD Model

• Autores: Rosana Sueli da Motta Jafelice, Jefferson Beethoven Martins, Ana Maria Amarillo Bertone
• Localización: Mathware & soft computing: The Magazine of the European Society for Fuzzy Logic and Technology, ISSN-e 1134-5632, Vol. 28, Nº. 1, 2023, págs. 134-154
• Idioma: inglés
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• Resumen

  • A dynamic of the evolution of an epidemic based on the classic SIRD model (Susceptible, Infected, Recovered, Dead) is developed using a three-dimensional cellular automaton in combination with fuzzy rule-based systems of type-1 and interval type-2 that interpret the infection and recovery rates. These systems interact with the automaton rules to determine the next generation behavior in terms of infection and, once infected, determining if the cell is recovered or dead. The aim of working with both types of fuzzy sets is to increase the uncertainty of the phenomenon studied through fuzzy systems, in particular those that originated by the interval type-2 fuzzy sets. The main contribution of this work is the interaction between fuzzy rules of two types with the rules of the cellular automaton itself. In fact, the novelty of this study is the development of its own computer program, with the possibility of implementing other dynamics of epidemiological or population origin. The modeling proposed has been validated through building, for each population of individuals, a range generated by the cellular automaton outputs related to the interval type-2 fuzzy rule-based system. This range contains the deterministic solution of the system of ordinary differential equations that govern the phenomenon and the cellular automaton output corresponding to the type-1 fuzzy rule-based system. As a result, equivalent qualitative aspects are observed.