In this work we study the asymptotic behavior of fuzzy solutions obtained by using Zadeh’s extension at the deterministic solutions of initial value problems. We obtain some result regarding the existence of fuzzy equilibrium points that generalize the already known results. As show earlier, the membership function of the fuzzy equilibrium points may be obtained in a relatively simple way. Also...

In this paper, we present two results concerning the fuzzy modeling and control of nonlinear systems. The first result is on the approximation of smooth nonlinear dynamical systems using linear Takagi-Sugeno fuzzy models. The second result is on the approximation of smooth nonlinear state-feedback controllers using the the so-called parallel distributed compensation (PDC) controller. Both resul...

In many application areas, there is a need for clustering, and there is a need to take fuzzy uncertainty into account when clustering. Most existing fuzzy clustering techniques are based on the idea that an object belongs to a certain cluster if this object is close to a typical object from this cluster. In some application areas, however, this idea does not work well. One example of such appli...

Dagmar Markechová 1,* and Beloslav Riečan 2,3 1 Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01 Nitra, Slovakia 2 Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica, Slovakia; [email protected] 3 Mathematical Institute, Slovak Academy of Scienc...

In this paper variation of constants formula for the inhomogeneous fuzzy matrix difference system X(n + 1) = A(n)X(n) + F (n) is constructed by considering corresponding matrix difference inclusion Xβ(n+ 1) ∈ AβXβ(n) +Fβ(n), xβ(0) ∈ X0 β after presenting a procedure for solving the fuzzy difference equation by an example. Mathematics Subject Classification: 26E50, 34A12, 34A30

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...

A fuzzy-modeling method for the emulation of expert decision behavior for static as well as dynamic systems is presented. The input – output dataset of the system – or expert behavior is changed using fuzzy-sets into examples in linguistic form. These resulting examples build the fundament of the machine learning process for rule production (ID3).

Fuzzy logic control systems are structured numerical estimators. They combine both the numerical process and human like reasoning. Neural networks are numerical trainable dynamical systems that are able to emulate human brain functions; their connectionist structure can be used to find the proper parameters and structures that resemble human thinking rules for fuzzy logic controllers. Generally...

In this paper, we provide a way to combine matrix Lyapunov systems with fuzzy sets to form a new system called fuzzy dynamical matrix Lyapunov system and obtain a sufficient condition for the controllability of this system. AMS Subject Classification (2010). 93B05, 93C42, 34A07

In this paper the notion of minimality is extended to relative semi-dynamical systems. We consider transitivity from the point of view of an observer which is a fuzzy set. Relative topological entropy of a relative semi-dynamical system as an invariant object of relative conjugate relations is studied. Finally illustrated example in polynomial functions is given to explain the idea of the paper.