scholarly journals Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems

Entropy ◽  
2016 ◽  
Vol 18 (1) ◽  
pp. 19 ◽  
Author(s):  
Dagmar Markechová ◽  
Beloslav Riečan
Keyword(s):  
Dynamical Systems ◽  
Fuzzy Partitions ◽  
Fuzzy Dynamical Systems

scholarly journals Tsallis Entropy of Fuzzy Dynamical Systems

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 264
Author(s):  
Dagmar Markechová
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Conditional Entropy ◽  
Tsallis Entropy ◽  
Positive Real ◽  
Fuzzy Dynamical System ◽  
Fuzzy Partitions ◽  
Definition Of ◽  
Mathematical Behavior ◽  
Fuzzy Dynamical Systems

This article deals with the mathematical modeling of Tsallis entropy in fuzzy dynamical systems. At first, the concepts of Tsallis entropy and Tsallis conditional entropy of order where is a positive real number not equal to 1, of fuzzy partitions are introduced and their mathematical behavior is described. As an important result, we showed that the Tsallis entropy of fuzzy partitions of order satisfies the property of sub-additivity. This property permits the definition of the Tsallis entropy of order of a fuzzy dynamical system. It was shown that Tsallis entropy is an invariant under isomorphisms of fuzzy dynamical systems; thus, we acquired a tool for distinguishing some non-isomorphic fuzzy dynamical systems. Finally, we formulated a version of the Kolmogorov–Sinai theorem on generators for the case of the Tsallis entropy of a fuzzy dynamical system. The obtained results extend the results provided by Markechová and Riečan in Entropy, 2016, 18, 157, which are particularized to the case of logical entropy.

Stability of fuzzy dynamical systems based on quasi-level-wise system

2017 ◽  
Vol 33 (6) ◽  
pp. 3515-3528 ◽  
Author(s):  
Debnarayan Khatua ◽  
Kalipada Maity
Keyword(s):  
Dynamical Systems ◽  
Fuzzy Dynamical Systems

An Efficient Numerical Simulation for Solving Dynamical Systems With Uncertainty

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Ali Ahmadian ◽  
Soheil Salahshour ◽  
Chee Seng Chan ◽  
Dumitur Baleanu
Keyword(s):  
Dynamical Systems ◽  
Stability And Convergence ◽  
Uncertain Parameters ◽  
Crucial Issue ◽  
Computational Costs ◽  
First Order ◽  
Wide Range ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Fuzzy Dynamical Systems

In a wide range of real-world physical and dynamical systems, precise defining of the uncertain parameters in their mathematical models is a crucial issue. It is well known that the usage of fuzzy differential equations (FDEs) is a way to exhibit these possibilistic uncertainties. In this research, a fast and accurate type of Runge–Kutta (RK) methods is generalized that are for solving first-order fuzzy dynamical systems. An interesting feature of the structure of this technique is that the data from previous steps are exploited that reduce substantially the computational costs. The major novelty of this research is that we provide the conditions of the stability and convergence of the method in the fuzzy area, which significantly completes the previous findings in the literature. The experimental results demonstrate the robustness of our technique by solving linear and nonlinear uncertain dynamical systems.

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