Let X be a compact metric space and let f : X → X be continuous. It is well known that a given discrete dynamical system (X, f) induces a map Φ on the space F(X) of fuzzy sets. In this paper we study relations between sizes of topological entropies of a given crisp dynamical system (X, f) and its fuzzy counterpart (F(X),Φ). Among another things, we present a constructive proof of the fact that ...

We describe in this paper the application of soft computing techniques to controlling non-linear dynamical systems in real-world problems. Soft computing consists of fuzzy logic, neural networks , evolutionary computation, and chaos theory. Controlling real-world non-linear dynamical systems may require the use of several soft computing techniques to achieve the desired performance in practice....

The direct adaptive regulation of nonlinear dynamical systems in Brunovsky form with modeling error effects, is considered in this paper. The method is based on a new Neuro-Fuzzy Dynamical System definition, which uses the concept of Fuzzy Adaptive Systems (FAS) operating in conjunction with High Order Neural Network Functions (HONNFs). Since the plant is considered unknown, we first propose it...

This paper provides a review on major ergodic features of semi-independent hyper MV {algebra dynamical systems. Theorems are presentedto make contribution to calculate the entropy. Particularly, it is proved that thetotal entropy of those semi-independent hyper MV {algebra dynamical systemsthat have a generator can be calculated with respect to their generator ratherthan considering all the par...

In this work we propose a Dynamical Fuzzy Cognitive Map (DFCM) where its casual relationships are based on fuzzy rules, in a way that the structure of the map changes during the phase of execution (runtime). We propose the modification of the values of the relationships between the concepts through of fuzzy rules derived from the concept states that represent the system modeled by the map. Our ...

we study interior operators and interior structures in a fuzzy setting.we investigate systems of “almost open” fuzzy sets and the relationshipsto fuzzy interior operators and fuzzy interior systems.

We consider the problem of passivity control for a kind of T-S fuzzy system in the literature [1].We will extend it to the uncertain T-S fuzzy descriptor systems with time-delay in this paper. Generally speaking, a mathematical model cannot be used to exactly describe a dynamical system in practice because it is inevitable to include some degrees of uncertainties in the systems. Moreover, time-...

In this paper we study a large class of renormalization transformations of measures on lattices. An image of a Gibbs measure under such transformation is called a fuzzy Gibbs measure. Transformations of this type and fuzzy Gibbs measures appear naturally in many fields. Examples include the hidden Markov processes (HMP), memoryless channels in information theory, continuous block factors of sym...

Lattice control can unify nonlinear control systems where the basic vector and signal superpositions or transformations are based on the lattice supremum and infimum. In this paper we introduce a special case of lattice control that can model fuzzy dynamical systems in state space. Vector and signal transformations are represented as lattice dilations or erosions. The state and output responses...

In this paper we present different results and studies around the world about the Fuzzy Cognitive Maps. This technique is the fusion of the advances of the fuzzy logic and cognitive maps theories. At this moment, there are several applications in different domains (control, multiagent systems, etc.) and new works (dynamical characteristics, learning procedures, etc.) to improve the performance ...