Heliyon (Jul 2024)
An investigation on the recurrent function of the Pythagorean fuzzy cellular topological dynamical system
Abstract
This study is about Pythagorean fuzzy cellular topological dynamical system which is generated using Pythagorean fuzzy cellular space. A dynamical system receives input for a certain function and performs an iterative procedure for that same function. A continuous function can be employed in a topological dynamical system and the same function is iterated again and again. As it is an iterative process, there is a perspective that the views of every individual may be ambiguous or imprecise. To overcome this uncertainty, Pythagorean fuzzy sets are employed in dynamical system. Fixing a boundary on the Pythagorean fuzzy dynamical system culminates in a Pythagorean fuzzy cellular topological dynamical system. It is shown that the Pythagorean fuzzy cellular space is compact, normal and homeomorphic and it is called the Pythagorean fuzzy cellular topological dynamical system. The Pythagorean fuzzy sets in the Pythagorean fuzzy cellular topological dynamical system are iterated under the action of Pythagorean fuzzy cellular continuous map. Then, the Pythagorean fuzzy orbit* set is obtained. Additionally, it is discussed that the stipulated dynamical system is topologically transitive and different aspects of topological transitivity are investigated.
