Markechová Dagmar, Mosapour Batool, Ebrahimzadeh Abolfazl
Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01 Nitra, Slovakia.
Department of Mathematics, Farhangian University, 7616914111 Kerman, Iran.
Entropy (Basel). 2018 Feb 16;20(2):129. doi: 10.3390/e20020129.
In the paper we propose, using the logical entropy function, a new kind of entropy in product MV-algebras, namely the logical entropy and its conditional version. Fundamental characteristics of these quantities have been shown and subsequently, the results regarding the logical entropy have been used to define the logical mutual information of experiments in the studied case. In addition, we define the logical cross entropy and logical divergence for the examined situation and prove basic properties of the suggested quantities. To illustrate the results, we provide several numerical examples.
在我们提出的论文中，利用逻辑熵函数，给出了乘积MV - 代数中一种新的熵，即逻辑熵及其条件形式。已展示了这些量的基本特征，随后，关于逻辑熵的结果被用于定义所研究情形下实验的逻辑互信息。此外，我们为所考察的情形定义了逻辑交叉熵和逻辑散度，并证明了所提量的基本性质。为说明结果，我们给出了几个数值例子。
