Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems
TLDR
An analogy of the Kolmogorov–Sinai Theorem on generators is proved for fuzzy dynamical systems because it is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamicals systems.Abstract:
In the paper we define three kinds of entropy of a fuzzy dynamical system using different entropies of fuzzy partitions. It is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamical systems. The relationships between these entropies are studied and connections with the classical case are mentioned as well. Finally, an analogy of the Kolmogorov–Sinai Theorem on generators is proved for fuzzy dynamical systems.read more
Citations
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Journal ArticleDOI
Logical Entropy of Fuzzy Dynamical Systems
TL;DR: The chain rules for logical entropy and for logical mutual information of fuzzy partitions are established and it is proved that the logical entropy of fuzzy dynamical systems is invariant under isomorphism of fuzzy dynamic systems.
Journal ArticleDOI
Weighted Regression-Based Extremum Response Surface Method for Structural Dynamic Fuzzy Reliability Analysis
TL;DR: In this paper, a weighted regression-based extremum response surface method (WR-ERSM) is proposed to improve structural dynamic fuzzy reliability analysis, by considering the randomness of design parameters and the fuzziness of the safety criterion.
Journal ArticleDOI
Logical Entropy of Dynamical Systems—A General Model
TL;DR: Using the suggested concept of entropy of partitions, the logical entropy of a dynamical system is defined and it is proved that it is the same for two dynamical systems that are isomorphic.
Journal ArticleDOI
Logical Entropy and Logical Mutual Information of Experiments in the Intuitionistic Fuzzy Case
TL;DR: The concepts of logical entropy and logical mutual information of experiments in the intuitionistic fuzzy case are introduced, and an analogy of the Kolmogorov-Sinai theorem on generators for IF-dynamical systems is proved.
Journal ArticleDOI
Logical entropy of dynamical systems
TL;DR: It is shown that by replacing the Shannon entropy function by the logical entropy function the authors obtain the results analogous to the case of classical Kolmogorov–Sinai entropy theory of dynamical systems.
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