Abstract
In this paper by considering a fuzzy continuous action of a fuzzy topological group on a fuzzy topological space we have fuzzifiifed the notion of topological dynamical system. Some properties of this fuzzy structure are investigated. Then we have constructed mixed fuzzy topological dynamical system from two given fuzzy topological dynamical systems.
Highlights
The theory of dynamical systems deals with the action of groups of continuous transformations of topological spaces
A classical dynamical system(Wieslaw Szlenk, 1984) is a structure ( π, G, X,) where G is a topological group, X is a topological space and π is a continuous function from G × X → X satisfying π(0, x) = x and π(s, (t, x)) = π(s + t, x), where 0 is the identity of G
We propose the following definition Definition 3.20 Let (π, K, X, ) be a fuzzy topological dynamical system
Summary
The theory of dynamical systems deals with the action of groups of continuous transformations of topological spaces. A classical dynamical system(Wieslaw Szlenk, 1984) is a structure ( π, G, X,) where G is a topological group, X is a topological space and π is a continuous function from G × X → X satisfying π(0, x) = x and π(s, (t, x)) = π(s + t, x), where 0 is the identity of G. In this paper we fuzzify the above concept as a natural transition from the corresponding crisp structure. For this fuzzification we will consider a fuzzy topological group(Wieslaw Szlenk, 1984), a fuzzy topological space and a fuzzy continuous map from G × X → X satisfying the above stated conditions. In this paper we will construct fuzzy mixed topological dynamical system.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
