Markechová Dagmar, Riečan Beloslav
Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01 Nitra, Slovakia.
Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica, Slovakia.
Entropy (Basel). 2017 Aug 21;19(8):429. doi: 10.3390/e19080429.
In this contribution, we introduce the concepts of logical entropy and logical mutual information of experiments in the intuitionistic fuzzy case, and study the basic properties of the suggested measures. Subsequently, by means of the suggested notion of logical entropy of an IF-partition, we define the logical entropy of an IF-dynamical system. It is shown that the logical entropy of IF-dynamical systems is invariant under isomorphism. Finally, an analogy of the Kolmogorov-Sinai theorem on generators for IF-dynamical systems is proved.
在本论文中，我们引入了直觉模糊情形下实验的逻辑熵和逻辑互信息的概念，并研究了所提出度量的基本性质。随后，借助所提出的直觉模糊划分的逻辑熵概念，我们定义了直觉模糊动力系统的逻辑熵。结果表明，直觉模糊动力系统的逻辑熵在同构下是不变的。最后，证明了直觉模糊动力系统关于生成元的柯尔莫哥洛夫 - 西奈定理的一个类似结论。
